<table><caption>Table 4.29 Best, average and worst IGD values on DTLZ(2,15) et DTLZ(3,5) for different population sizes</caption><tbody><tr><td rowspan="12">DTLZ2</td><td rowspan="3">5</td><td>250</td><td>1.302 E-3</td><td>1.239 E-3</td><td>4.364 E-3</td><td>4.236 E-4</td><td rowspan="3">90</td></tr><tr><td></td><td>1.603 E-3</td><td>1.698 E-3</td><td>4.992 E-3</td><td>4.512 E-4</td></tr><tr><td></td><td>1.964 E-3</td><td>1.804 E-3</td><td>5.238 E-3</td><td>4.704 E-4</td></tr><tr><td rowspan="3">350</td><td>1.103 E-3</td><td>1.448 E-3</td><td>4.337 E-3</td><td>3.705 E-4</td><td rowspan="3">130</td></tr><tr><td></td><td>1.548 E-3</td><td>1.675 E-3</td><td>4.994 E-3</td><td>4.544 E-4</td></tr><tr><td></td><td>1.635 E-3</td><td>1.906 E-3</td><td>5.208 E-3</td><td>5.509 E-4</td></tr><tr><td rowspan="3">750</td><td>1.303 E-3</td><td>1.307 E-3</td><td>4.108 E-3</td><td>3.307 E-4</td><td rowspan="3">255</td></tr><tr><td></td><td>1.504 E-3</td><td>1.489 E-3</td><td>4.987 E-3</td><td>4.734 E-4</td></tr><tr><td></td><td>1.607 E-3</td><td>1.603 E-3</td><td>5.230 E-3</td><td>6.228 E-4</td></tr><tr><td rowspan="3">1000</td><td>1.228 E-3</td><td>1.128 E-3</td><td>4.254 E-3</td><td>4.203 E-4</td><td rowspan="3">280</td></tr><tr><td></td><td>1.437 E-3</td><td>1.291 E-3</td><td>4.982 E-3</td><td>4.760 E-4</td></tr><tr><td></td><td>1.727 E-3</td><td>1.424 E-3</td><td>5.862 E-3</td><td>4.992 E-4</td></tr><tr><td rowspan="3">1200</td><td>1.130 E-3</td><td>1.195 E-3</td><td>4.109 E-3</td><td>3.438 E-4</td><td rowspan="3">290</td></tr><tr><td></td><td>1.413 E-3</td><td>1.224 E-3</td><td>4.982 E-3</td><td>4.768 E-4</td></tr><tr><td></td><td>1.603 E-3</td><td>1.363 E-3</td><td>5.307 E-3</td><td>7.126 E-4</td></tr><tr><td rowspan="12">10</td><td rowspan="3">250</td><td>2.423 E-3</td><td>3.367 E-3</td><td>1.408 E-2</td><td>1.206 E-2</td><td rowspan="3">270</td></tr><tr><td>2.681 E-3</td><td>3.862 E-3</td><td>1.679 E-2</td><td>1.624 E-2</td></tr><tr><td>3.967 E-3</td><td>4.063 E-3</td><td>1.838 E-2</td><td>2.368 E-2</td></tr><tr><td rowspan="3">350</td><td>2.490 E-3</td><td>3.404 E-3</td><td>1.408 E-2</td><td>1.326 E-3</td><td rowspan="3">290</td></tr><tr><td>2.692 E-3</td><td>3.833 E-3</td><td>1.633 E-2</td><td>1.597 E-2</td></tr><tr><td>3.309 E-3</td><td>4.068 E-3</td><td>1.904 E-2</td><td>2.085 E-2</td></tr><tr><td rowspan="3">750</td><td>2.235 E-3</td><td>3.368 E-3</td><td>1.209 E-2</td><td>1.206 E-3</td><td rowspan="3">320</td></tr><tr><td>2.724 E-3</td><td>3.794 E-3</td><td>1.578 E-2</td><td>1.534 E-2</td></tr><tr><td>3.058 E-3</td><td>4.234 E-3</td><td>1.802 E-2</td><td>2.668 E-2</td></tr><tr><td rowspan="3">1000</td><td>2.474 E-3</td><td>3.223 E-3</td><td>1.350 E-2</td><td>1.104 E-2</td><td rowspan="3">350</td></tr><tr><td>2.778 E-3</td><td>3.752 E-3</td><td>1.528 E-2</td><td>1.459 E-2</td></tr><tr><td>3.235 E-3</td><td>4.145 E-3</td><td>1.697 E-2</td><td>1.858 E-2</td></tr><tr><td rowspan="3">1200</td><td>2.308 E-3</td><td>3.367 E-3</td><td>1.403 E-2</td><td>1.236 E-3</td><td rowspan="3">350</td></tr><tr><td>2.703 E-3</td><td>3.604 E-3</td><td>1.504 E-2</td><td>1.423 E-2</td></tr><tr><td>3.024 E-3</td><td>4.089 E-3</td><td>1.868 E-2</td><td>2.634 E-2</td></tr></tbody></table>

<table><thead><tr><th>Test Ph</th><th>Population size</th><th>MOEA/D (PBI)</th><th>MOEA/DD</th><th>NSGA-III</th><th>Two_Arch2</th><th>Number of reference points (MOEA/D, NSGA-III)</th></tr></thead><tbody><tr><td rowspan="12">DTLZ5(2,15)</td><td rowspan="3">100</td><td>7.014 E-2</td><td>2.785 E-2</td><td>1.923 E-3</td><td>2.428 E-2</td><td rowspan="3">90</td></tr><tr><td>8.032 E-2</td><td>3.034 E-2</td><td>7.985 E-2</td><td>3.024 E-2</td></tr><tr><td>0.026 E-1</td><td>6.327 E-2</td><td>8.231 E-2</td><td>6.320 E-2</td></tr><tr><td rowspan="3">600</td><td>2.453 E-2</td><td>4.985 E-3</td><td>2.129 E-3</td><td>3.216 E-3</td><td rowspan="3">130</td></tr><tr><td>2.978 E-2</td><td>7.088 E-3</td><td>4.093 E-2</td><td>9.601 E-3</td></tr><tr><td>3.127 E-2</td><td>8.124 E-3</td><td>7.055 E-2</td><td>0.995 E-2</td></tr><tr><td rowspan="3">1000</td><td>1.134 E-2</td><td>1.641 E-3</td><td>2.034 E-3</td><td>1.344 E-3</td><td rowspan="3">255</td></tr><tr><td>1.326 E-2</td><td>3.195 E-3</td><td>4.985 E-3</td><td>2.786 E-3</td></tr><tr><td>1.667 E-2</td><td>4.034 E-3</td><td>9.031 E-3</td><td>4.239 E-3</td></tr><tr><td rowspan="3">1200</td><td>1.012 E-2</td><td>2.385 E-3</td><td>2.023 E-3</td><td>2.029 E-3</td><td rowspan="3">280</td></tr><tr><td>1.023 E-2</td><td>2.632 E-3</td><td>4.981 E-3</td><td>2.634 E-3</td></tr><tr><td>1.985 E-2</td><td>4.158 E-3</td><td>5.302 E-3</td><td>5.870 E-3</td></tr><tr><td rowspan="12">DTLZ5(3,5)</td><td rowspan="3">350</td><td>0.931 E-4</td><td>2.805 E-4</td><td>3.137 E-4</td><td>1.896 E-4</td><td rowspan="3">130</td></tr><tr><td>1.498 E-4</td><td>3.123 E-4</td><td>3.203 E-4</td><td>4.149 E-4</td></tr><tr><td>4.682 E-4</td><td>5.301 E-4</td><td>5.112 E-4</td><td>4.268 E-4</td></tr><tr><td rowspan="3">750</td><td>1.235 E-4</td><td>2.083 E-4</td><td>2.043 E-4</td><td>0.932 E-4</td><td rowspan="3">255</td></tr><tr><td>1.402 E-4</td><td>3.069 E-4</td><td>3.198 E-4</td><td>1.145 E-4</td></tr><tr><td>1.638 E-4</td><td>5.360 E-4</td><td>6.302 E-4</td><td>6.029 E-4</td></tr><tr><td rowspan="3">1000</td><td>1.194 E-4</td><td>0.634 E-4</td><td>1.985 E-4</td><td>0.736 E-4</td><td rowspan="3">280</td></tr><tr><td>1.265 E-4</td><td>3.056 E-4</td><td>3.192 E-4</td><td>0.925 E-4</td></tr><tr><td>1.703 E-4</td><td>6.238 E-4</td><td>8.054 E-4</td><td>2.362 E-4</td></tr><tr><td rowspan="3">1200</td><td>1.134 E-4</td><td>1.869 E-4</td><td>2.793 E-4</td><td>0.760 E-4</td><td rowspan="3">290</td></tr><tr><td>1.203 E-4</td><td>2.863 E-4</td><td>3.107 E-4</td><td>0.887 E-4</td></tr><tr><td>4.678 E-4</td><td>4.864 E-4</td><td>5.027 E-4</td><td>4.561 E-4</td></tr></tbody></table>

Results presented in Table 4.28 show that MOEA/DD has the best IGD median values in DTLZ1 test function for different population sizes and different objective numbers. However, in DTLZ2, MOEA/D and Two_Arch2 share the best IGD median values. Another interesting finding, in this set of experiments, is that the tested algorithms do not have the same behavior as the previously-tested real world problem. For example, MOEA/D variants are better than NSGA-III in DTLZ1. Moreover, it can be concluded from the experimental results that determining an appropriate population size according to the number of objectives is an important area of research.

### 4.3.3 Testing the effect of the choice of the scalarizing functions in MOEA/D

In this section we test the effect of the choice of the scalarizing functions in MOEA/D for different population sizes and objective numbers. In our experiments we use the following scalarizing functions: the weighted sum, the weighted Tchebycheff with $\alpha = 1, 1.01, 1.1$, and the PBI with $\theta = 0.01, 0.5, 1, 5$ for $\alpha = 1, 1.01, 1.1$. The median IGD values are calculated for each scalarizing function over 15 runs. The objective number varies from 3 to 15. The
population is set to 1000 and the number of generations varies from 400 to 1500 for DTLZ1 and from 250 to 1000 for DTLZ2. The mutation probability is 1/500 (Bit-flip mutation) and the recombination probability is 0.8 (SBX crossover). There is no neighbor mating in recombination. The results are shown in Table 4.30.

<table><caption>Table 4.30 IGD median values on DTLZ1 and DTLZ2 for different population sizes</caption><thead><tr><th colspan="2">Test problem</th><th colspan="4">DTLZ1</th><th colspan="4">DTLZ2</th></tr><tr><th colspan="2">Objective number</th><th>3</th><th>5</th><th>10</th><th>15</th><th>3</th><th>5</th><th>10</th><th>15</th></tr><tr><th colspan="2">Number of generations</th><th>400</th><th>600</th><th>1000</th><th>1500</th><th>250</th><th>350</th><th>750</th><th>1000</th></tr></thead><tbody><tr><td colspan="2">Weighted sum</td><td>1.361 E-4</td><td>5.642 E-4</td><td>6.208 E-3</td><td>2.763 E-2</td><td>1.210 E-4</td><td>1.897 E-3</td><td>2.236 E-3</td><td>3.864 E-3</td></tr><tr><td rowspan="2">Weighted Tchebycheff</td><td>α=1</td><td>6.641 E-3</td><td>3.618 E-4</td><td>0.905 E-3</td><td>3.087 E-2</td><td>2.431 E-4</td><td>4.426 E-4</td><td>8.631 E-4</td><td>2.632 E-3</td></tr><tr><td>α=1.01</td><td>2.103 E-3</td><td>3.172 E-4</td><td>0.686 E-3</td><td>3.005 E-2</td><td>2.273 E-4</td><td>1.267 E-4</td><td>7.087 E-4</td><td>1.639 E-3</td></tr><tr><td rowspan="2">PBI (θ=0.01)</td><td>α=1</td><td>1.132 E-4</td><td>6.450 E-4</td><td>4.874 E-3</td><td>4.032 E-3</td><td>8.464 E-4</td><td>2.234 E-3</td><td>3.461 E-3</td><td>6.821 E-3</td></tr><tr><td>α=1.01</td><td>2.532 E-3</td><td>7.896 E-4</td><td>6.890 E-3</td><td>5.281 E-2</td><td>8.791 E-4</td><td>2.467 E-3</td><td>5.032 E-3</td><td>8.058 E-3</td></tr><tr><td rowspan="2">PBI (θ=0.5)</td><td>α=1</td><td>1.986 E-4</td><td>5.783 E-4</td><td>4.462 E-3</td><td>4.230 E-3</td><td>8.469 E-4</td><td>2.391 E-3</td><td>3.467 E-3</td><td>7.364 E-3</td></tr><tr><td>α=1.01</td><td>1.925 E-4</td><td>6.652 E-4</td><td>4.687 E-3</td><td>3.975 E-3</td><td>8.269 E-4</td><td>1.618 E-3</td><td>3.102 E-3</td><td>5.983 E-3</td></tr><tr><td rowspan="2">PBI (θ=1)</td><td>α=1</td><td>2.452 E-3</td><td>7.139 E-4</td><td>6.302 E-3</td><td>4.659 E-2</td><td>8.135 E-4</td><td>2.109 E-3</td><td>4.689 E-3</td><td>7.364 E-3</td></tr><tr><td>α=1.1</td><td>2.238 E-4</td><td>6.754 E-4</td><td>4.892 E-3</td><td>3.624 E-3</td><td>7.149 E-4</td><td>2.462 E-3</td><td>3.236 E-3</td><td>6.203 E-3</td></tr><tr><td rowspan="2">PBI (θ=5)</td><td>α=1</td><td>0.923 E-4</td><td>5.036 E-4</td><td>2.367 E-3</td><td>2.231 E-3</td><td>8.146 E-4</td><td>1.539 E-3</td><td>2.892 E-3</td><td>5.682 E-3</td></tr><tr><td>α=1.01</td><td>2.102 E-3</td><td>6.568 E-4</td><td>5.236 E-3</td><td>3.364 E-2</td><td>8.058 E-4</td><td>1.632 E-3</td><td>4.324 E-3</td><td>7.036 E-3</td></tr><tr><td rowspan="2">PBI (θ=5)</td><td>α=1.1</td><td>1.807 E-4</td><td>5.068 E-4</td><td>4.651 E-3</td><td>2.789 E-3</td><td>7.085 E-4</td><td>1.457 E-3</td><td>3.097 E-3</td><td>5.891 E-3</td></tr><tr><td>α=1</td><td>0.963 E-4</td><td>3.352 E-4</td><td>3.931 E-3</td><td>1.267 E-2</td><td>4.368 E-4</td><td>1.249 E-3</td><td>2.362 E-3</td><td>5.326 E-3</td></tr><tr><td rowspan="2">PBI (θ=5)</td><td>α=1.01</td><td>1.495 E-3</td><td>6.372 E-4</td><td>5.073 E-3</td><td>1.431 E-2</td><td>6.406 E-4</td><td>1.437 E-3</td><td>2.778 E-3</td><td>6.005 E-3</td></tr><tr><td>α=1.1</td><td>1.237 E-4</td><td>2.047 E-4</td><td>4.685 E-3</td><td>1.143 E-2</td><td>5.023 E-4</td><td>1.401 E-3</td><td>2.234 E-3</td><td>5.568 E-3</td></tr></tbody></table>

It is interesting to investigate the behavior of the different scalarizing functions on DTLZ1 and DTLZ2, according to the number of objectives. According to the results provided in Table 4.30 which are in agreement with the results obtained by the real-world problem (see section 4.2), the performance of the weighted Tchebycheff scalarizing function is dependent on the value of α. In both test problems, DTLZ1 and DTLZ2, poor results were obtained when using the weighted Tchebycheff with α = 1, while good results were provided if this value is set to 1.01 and 1.1. Moreover, using the PBI function, the parameter α has a variable behavior. In DTLZ1, for example, better results were generally got with α = 1.0 and α = 1.1. However, unlike the results obtained by the real world problem, for both test functions (DTLZ1 and DTLZ2), good ones were provided by using both the PBI function with θ = 5 and the weighted sum. In fact, the PBI with θ = 0.01 is often the worst. To sum up, it is preferable to use either the weighted Tchebycheff with α = 1.1 or the PBI with θ = 5 for both DTLZ1 and DTLZ2. Obviously, the weighted sum is more suitable for DTLZ2.

### 4.3.4 Testing the effect of using neighborhood mating restrictions and adaptive recombination operators

In this section, we examined the effect of using neighborhood mating restrictions and adaptive operators (see section 3.3.2.1 for more details). The used scalarizing function (for MOEA/D and MOEA/DD) is PBI (5.0). The performance of each algorithm is evaluated using the average HV over 15 runs. The size of the population is set to 1000. The number of generations varies from 600 to 1000 for DTLZ1 and from 350 to 750 for DTLZ2. The mutation probability is 1/500 and the recombination probability is 0.8. The number of reference points is set to 250. The obtained results are shown in tables 4.31 and 4.32.

<table><caption>Table 4.31 IGD median values on DTLZ1 and DTLZ2 obtained using neighborhood mating restrictions and adaptive recombination</caption><thead><tr><th>Test Problem</th><th>Operators</th><th>Objective Number</th><th>Number of generations</th><th>MOEA/D(PBI)</th><th>MOEA/DD</th><th>NSGA-III</th><th>Two_Arch2</th></tr></thead><tbody><tr><td rowspan="4">DTLZ1</td><td rowspan="2">Bit-flip mutation / SBX crossover</td><td>5</td><td>600</td><td>3.179 E-4<br>6.372 E-4<br>1.635 E-3</td><td>2.635 E-4<br>2.916 E-4<br>3.109 E-4</td><td>5.116 E-4<br>5.980 E-4<br>5.979 E-3</td><td>6.034 E-4<br>6.372 E-4<br>6.967 E-4</td></tr><tr><td>10</td><td>1000</td><td>3.872 E-3<br>5.073 E-3<br>6.132 E-3</td><td>1.828 E-3<br>2.225 E-3<br>2.467 E-3</td><td>2.215 E-3<br>3.462 E-3<br>6.869 E-3</td><td>2.368 E-3<br>2.962 E-3<br>3.101 E-3</td></tr><tr><td rowspan="2">Using neighborhood mating restrictions and adaptive operators</td><td>5</td><td>600</td><td>3.129 E-4<br>6.324 E-4<br>2.654 E-3</td><td>1.436 E-4<br>2.883 E-4<br>6.317 E-4</td><td>6.302 E-4<br>0.931 E-3<br>3.364 E-3</td><td>1.309 E-4<br>6.344 E-4<br>7.038 E-4</td></tr><tr><td>10</td><td>1000</td><td>1.703 E-3<br>4.856 E-3<br>8.032 E-3</td><td>1.784 E-3<br>2.021 E-3<br>5.033 E-3</td><td>2.718 E-3<br>3.146 E-3<br>7.037 E-3</td><td>1.384 E-3<br>2.875 E-3<br>5.031 E-3</td></tr></tbody></table>
<table><tbody><tr><td rowspan="10">DTLZ2</td><td rowspan="3">Bit-flip mutation / SBX crossover</td><td>5</td><td>350</td><td>1.219 E-3</td><td>1.128 E-3</td><td>4.254 E-3</td><td>4.203 E-4</td></tr><tr><td rowspan="2">10</td><td rowspan="2">750</td><td>1.437 E-3</td><td>1.291 E-3</td><td>4.982 E-3</td><td>4.760 E-4</td></tr><tr><td>1.727 E-3</td><td>1.424 E-3</td><td>5.862 E-3</td><td>4.992 E-4</td></tr><tr><td rowspan="6">Using neighborhood mating restrictions and adaptive operators</td><td rowspan="3">5</td><td rowspan="3">350</td><td>2.474 E-3</td><td>3.223 E-3</td><td>1.350 E-2</td><td>1.104 E-2</td></tr><tr><td>2.778 E-3</td><td>3.752 E-3</td><td>1.528 E-2</td><td>1.459 E-2</td></tr><tr><td>3.235 E-3</td><td>4.145 E-3</td><td>1.697 E-2</td><td>1.858 E-2</td></tr><tr><td rowspan="3">10</td><td rowspan="3">750</td><td>2.097 E-4</td><td>1.783 E-4</td><td>0.341 E-4</td><td>1.961 E-4</td></tr><tr><td>5.346 E-4</td><td>3.245 E-4</td><td>2.996 E-4</td><td>4.643 E-4</td></tr><tr><td>4.963 E-3</td><td>3.978 E-3</td><td>4.032 E-3</td><td>7.784 E-4</td></tr></tbody></table>

From the results presented in Table 4.31 which are in accordance with those provided by the real world problem, we notice that the use of neighborhood mating and adaptive operators with different number of objectives improve considerably the search performance. For DTLZ1 (DTLZ2, respectively), best IGD median values were obtained using MOEA/DD (MOEA/D, respectively) especially with a high number of objectives. However, MOEA/D improved considerably the average IGD values, compared to other algorithms. Moreover, our results prove that the diversity was enhanced without deteriorating the convergence when mating similar parents.

<table><caption>Table 4.32 IGD median values on DTLZ(2,15) and DTLZ(3.15) provided by applying neighborhood mating restrictions and adaptive recombination operators</caption><thead><tr><th>Test Problem</th><th>Operators</th><th>MOEA/D(PBI)</th><th>MOEA/DD</th><th>NSGA-III</th><th>Two_Arch2</th></tr></thead><tbody><tr><td rowspan="3">DTLZ5(2,15)</td><td>Bit-flip mutation / SBX crossover</td><td>1.134 E-2<br>1.326 E-2<br>1.667 E-2</td><td>1.641 E-3<br>3.195 E-3<br>4.034 E-3</td><td>2.034 E-3<br>4.985 E-3<br>9.031 E-3</td><td>1.344 E-3<br>2.786 E-3<br>4.239 E-3</td></tr><tr><td>Using neighborhood mating restrictions and adaptive operators</td><td>1.068 E-2<br>1.261 E-2<br>1.661 E-2</td><td>1.327 E-3<br>2.857 E-3<br>4.906 E-3</td><td>2.031 E-3<br>3.934 E-3<br>9.017 E-3</td><td>2.323 E-3<br>2.407 E-3<br>7.301 E-3</td></tr><tr><td>DTLZ5(3,5)</td><td>Bit-flip mutation / SBX crossover</td><td>1.194 E-4<br>1.265 E-4<br>1.703 E-4</td><td>0.634 E-4<br>3.056 E-4<br>6.238 E-4</td><td>1.985 E-4<br>3.192 E-4<br>8.054 E-4</td><td>0.736 E-4<br>0.925 E-4<br>2.362 E-4</td></tr><tr><td></td><td>Using neighborhood mating restrictions and adaptive operators</td><td>0.806 E-4<br>1.103 E-4<br>1.698 E-4</td><td>1.038 E-4<br>3.042 E-4<br>6.179 E-4</td><td>1.964 E-4<br>3.036 E-4<br>8.031 E-4</td><td>0.852 E-4<br>0.863 E-4<br>5.296 E-4</td></tr></tbody></table>

According to the table 4.32, the improvement on the IGD values after including the reduction is clearer in DTLZ(2.15) than DTLZ(3.5). Surprisingly, in DTLZ5(3,5), the MOEA/D is more efficient than other algorithms when using neighborhood mating restrictions, adaptive operators and correlated objectives.

### 4.3.5 Testing the effect of hybridizing the EMOS with the dimensionality reduction approach

In this section, we test the effect of adding the proposed dimensionality reduction approach. The used scalarizing function (for MOEA/D and MOEA/DD) is PBI (5.0). The mutation probability is 1/400 with an index of 50 and the recombination probability is 0.9 with an index of 5. Neighbor mating and adaptive recombination is used. The size of the population is set to 1000. We employ 250 reference points for NSGA-III.

Overall, the detailed results of applying the proposed dimensionality reduction approach (The NL-MVU-PCA algorithm for non-linear objective reduction and L-PCA for linear objective reduction) to the DTLZ problems are not presented in this section. More details of its application on DTLZ and WFG problems can be found on (Saxena et al. 2013). Besides, the NL-MVU-PCA and L-PCA does not suggest a reduced set of objectives because the DTLZ2 is known by a PF that involves all the objectives (Sinha et al. 2013). Thus, our work only presents (Table 4.33), the smallest non-redundant objective set and the needed number of iterations of the different problems such as DTLZ5 (2, 15) and DTLZ5 (3, 5) to evaluate the proposed algorithm.

<table><caption>Table 4.33 The smallest non-redundant objectives and the needed iteration number for the proposed algorithms on DTLZ5(2,15) and DTLZ5(3,5)</caption><thead><tr><th></th><th colspan="2">DTLZ5(2,15)</th><th colspan="2">DTLZ5(3,5)</th></tr><tr><th></th><th>Smallest non-redundant</th><th>Needed iteration</th><th>Smallest non-redundant</th><th>Needed iteration</th></tr></thead></table>
<table><thead><tr><th></th><th>objectives (average)</th><th>number (average)</th><th>objectives (average)</th><th>number (average)</th></tr></thead><tbody><tr><td>MOEA/D(PBI)</td><td>2</td><td>3684</td><td>3</td><td>1875</td></tr><tr><td>MOEA/DD</td><td>2</td><td>3256</td><td>3</td><td>1822</td></tr><tr><td>NSGA-III</td><td>2</td><td>3894</td><td>3</td><td>1923</td></tr><tr><td>Two_Arch2</td><td>2</td><td>3866</td><td>3</td><td>1934</td></tr></tbody></table>

Although the obtained results in Table 4.33 shows that all tested algorithms are able to identify the smallest non-redundant objective set, the algorithms differ in the number of the needed iterations used to find the smallest set. For example, in the DTLZ5(2,15) problem, Two_Arch2 needs to perform 3866 iterations to find the smallest non-redundant objective set, while MOEA/DD requires only 3256 iterations.

Moreover, in order to investigate the quality of the obtained solution after adding the proposed dimensionality reduction approach, we present the median IGD values before and after applying the dimensionality reduction on the proposed algorithms.

<table><caption>Table 4.34 median IGD values before and after applying the dimensionality reduction</caption><thead><tr><th>Test Pb</th><th>Dimensionality Reduction</th><th>MOEA/D(PBI)</th><th>MOEA/DD</th><th>NSGA-III</th><th>Two_Arch2</th></tr></thead><tbody><tr><td rowspan="3">DTLZ5(2,15)</td><td rowspan="3">Without reduction</td><td>1.134 E-2</td><td>1.641 E-3</td><td>2.034 E-3</td><td>1.344 E-3</td></tr><tr><td>1.326 E-2</td><td>3.195 E-3</td><td>4.085 E-3</td><td>2.786 E-3</td></tr><tr><td>1.667 E-2</td><td>4.034 E-3</td><td>9.031 E-3</td><td>4.239 E-3</td></tr><tr><td rowspan="6">DTLZ5(3,5)</td><td rowspan="3">Using L-PCA / NL-MVU-PCA</td><td>0.962 E-2</td><td>2.498 E-3</td><td>3.262 E-3</td><td>2.093 E-3</td></tr><tr><td>0.967 E-2</td><td>2.632 E-3</td><td>3.647 E-3</td><td>2.243 E-3</td></tr><tr><td>1.460 E-2</td><td>6.703 E-3</td><td>4.053 E-3</td><td>2.511 E-3</td></tr><tr><td rowspan="3">Without reduction</td><td>1.194 E-4</td><td>0.634 E-4</td><td>1.985 E-4</td><td>0.736 E-4</td></tr><tr><td>1.265 E-4</td><td>3.056 E-4</td><td>3.192 E-4</td><td>0.925 E-4</td></tr><tr><td>1.703 E-4</td><td>6.238 E-4</td><td>8.054 E-4</td><td>2.362 E-4</td></tr><tr><td rowspan="3">Using L-PCA / NL-MVU-PCA</td><td>0.934 E-4</td><td>2.838 E-4</td><td>2.360 E-4</td><td>0.602 E-4</td></tr><tr><td>1.027 E-4</td><td>2.923 E-4</td><td>2.786 E-4</td><td>0.659 E-4</td></tr><tr><td>1.175 E-4</td><td>3.037 E-4</td><td>2.837 E-4</td><td>1.231 E-4</td></tr></tbody></table>

Table 4.34 demonstrates that the IGD values decrease when the dimensionality reduction is used, which reveals the effectiveness of using the dimensionality reduction. Regarding the improvement rate before and after the reduction, the MOEA/DD surpasses other algorithms for DTLZ5(2,15), while the NSGA-III surpasses other algorithms for DTLZ5(3,5).

### 4.3.6 Testing the effect of hybriding the EMOs with dimensionality reduction and user preferences

In this section, we investigate the effect of incorporating both dimensionality reduction and user preferences in our approach. The used scalarizing function (for MOEA/D and MOEA/DD) is PBI (5.0). The mutation probability is 1/400 with an index of 50, and the recombination probability is 0.9 with an index of 5. The size of the population is set to 1000. Neighbor mating and adaptive recombination are used. We apply 250 reference points for NSGA-III. Preference approaches suppose that no redundant objective exists in the given problem (Saxena et al. 2013). Thus, dimensionality reduction procedure is always performed before applying the DM preferences.

After employing the reduction approach, the preference is applied on a reduced set of objectives. Table 4.35 shows the final solutions characteristics on the DTLZ5(3,5) problem. Each run has a different initial population which is the result of applying our reduction procedure on the concerned EMO. As mentioned before, $d_s$ (the expected improvement in solutions from the current best solution) = 0.01 and TDMax (the maximum number of calls of the preference information from the DM) = 30.

<table><caption>Table 4.35 Median distance between the obtained solutions and the most preferred solutions for $d_s = 0.01$</caption><thead><tr><th></th><th>MOEA/D</th><th>NSGA-III</th><th>Two_Arch2</th><th>MOEA/DD</th></tr></thead><tbody><tr><td>Accuracy</td><td>0.203</td><td>0.396</td><td>0.409</td><td>0.009</td></tr><tr><td>Number of function evaluations</td><td>6132</td><td>8038</td><td>8036</td><td>5981</td></tr><tr><td>Number of required DM calls</td><td>19</td><td>26</td><td>25</td><td>22</td></tr></tbody></table>
## 4.4 Simulations: Modeling the used protocols, simulation with small and large instances

### 4.4.1 Network protocol modeling

#### 4.4.1.1 Modeling the 3D location

Although 3D location is more realistic and accurate, most existing location systems focus on the 2D plane. Like 2D localization, two types of location can be distinguished in 3D environments: range-based localization and range-based localization. This classification is based on the fact that the actual distance between the nodes must be measured or not. Free-range 3D locating algorithms measure the exact orientation and distance between neighboring nodes, and use this information to locate the nodes. While locating algorithms based on free range have a certain hardware requirement. Therefore, they are more expensive to implement in practice. The Landscape 3D algorithm (Zhang et al. 2006) for example, is a 3D location algorithm according to the scope. Different 3D localization algorithms exist as free range 3DDVHOP algorithm (He et al. 2003), the 3D centroid algorithm (Bulusu et al. 2000) and 3D MDS-MAP (Tan et al. 2010).

To compensate for the deficit of the two types of localization algorithms mentioned, we propose to implement a localization based on rssi and iron exchanges hybridized with the DV-HOP protocol. Indeed, we propose a hybrid localization method based on the combination of the jump distance and the RSSI data for the 3D location. We propose a hybrid localization system that improves the free-range location technique (DV-HOP) in 3D by introducing an RSSI datum to revise the jump distance. First, 3D DV-HOP uses network connectivity information to estimate node locations in 3D space. Then, the RSSI value can be easily collected to correct the position of the nodes found by the DV-HOP depending on the signal strength. The RSSI value is measured in both directions: from the mobile node, we measure the received RSSI value of the other nodes (fixed, nomad or mobile); And from each fixed, nomad or mobile node, the RSSI value received from the mobile node is measured. The final permissible value of the RSSI between the mobile node and each other node corresponds to the higher value of the two values already mentioned.

Indeed, the different localization algorithms require that each normal node (which is not anchored) must have at least three neighboring anchor points, the 3DDV-Hop algorithm does not require 3 neighbor anchors per node. When applying the DVHOP algorithm, we need three nodes (which are not necessarily anchors) to locate each node. In our proposed model (3DDVHOP + RSSI), four nodes are required: three nodes of the 2D plane that the DVHOP algorithm requires and a node for the height. Figure 4.1 shows the location using the 3DDVHop and RSSI algorithm with a network topology with 3 anchors and 4 normal nodes. A1, A2 and A3 are anchors whereas Nx, N1, N2, N3 are normal nodes.

<figure><img src="image_38.png" /><figcaption>Figure 4.1: localization algorithm with 3D DV-HOP + RSSI</figcaption></figure>

The RSSI value can be influenced by various factors other than distance, such as node movement, environment, antenna orientation, or energy level. Thus, a detailed modeling of the physical environment, data binding and routing, greatly improves the obtaining of a precise distance from the RSSI value.
4.4.1.2 Physical layer (radio)

In our simulations, the physical layer uses a frequency set at 433 Mhz. Other parameters are
initialized with significant values. Some values are set according to standard protocols such as
802.15.4 and some other values are derived from empirical values of our experiments.

The following parameters are considered in our simulations:

- Transmit power = default (60 mW);

- Reception gain = default (50 mA);

- Operating temperature = default (25 c);

- Bit rate = default (256 kbps);

- RSSI = by default (140);

- Bit error rate = default (0.01);

- Range inside = by default (15m);

- Maximum number of nodes = by default (65000) according to protocol 802.15.4;

- Power supply = default (3.6 v);

4.4.1.3 Data Link Layer: CSMA / CA of 802.15.4

IEEE 802.15.4 is considered a promising technology for WSN, and a great deal of research
has been conducted to study the access and detection of collision avoidance multiple access
(CSMA / CA) carrier in 802.15 protocol .4. When more than one station tries to transmit one
frame at a time, a collision occurs, and eventually all data can be damaged. The standard
mechanism for resolving conflicts in computer networks is called multiple access carrier
(CSMA) detection. Indeed, the CSMA algorithms attempt to break the symmetries of faulty
transmissions restarting at the same time, using random binary explicit backoff
procedures. While wired devices can listen during their own transmissions and use CSMA
with collision detection (CSMA / CD), stations in wireless networks generally cannot listen to
their own broadcasts, and therefore collision transmissions cannot be detected after they have
been completed. Thus wireless devices use CSMA with collision avoidance (CSMA/CA or
CSMA-CA). For the data link layer, a problem of access priority to the channel arises if two
nodes within range (of them) speak simultaneously. We are interested in the modeling of the
802.15.4 CSMA / CA protocol. A non-coordinated CSMA is used (not slotted, without
acknowledgment and without RTS/CTS).

4.4.1.4 Routing Layer: Reactive AODV

To model the routing layer, the reactive AODV protocol is used. The AODV (Ad-hoc on
request Distance Vector) is a routing protocol for ad-hoc networks. It is designed to self-start
in a mobile node environment, and to withstand a variety of network behaviors such as node
mobility, link failure, and packet loss. At each node, the AODV maintains a routing table. The
entry of the routing table for a destination contains three essential fields: the next hop node, a
sequence id and a hop count. All packets destined for the destination are sent to the next hop
node. The sequence number acts as a timestamp form, and is a measure of the freshness of a
route. The number of hops represents the current distance to the destination node. In the
AODV, nodes discover roads in demand-response cycles. A node requests a route to a
destination by broadcasting a RREQ message to all its neighbors. When a node receives a
RREQ message but does not have a route to the requested destination, it in turn transmits the
RREQ message. This node also remembers a path inversion to the requesting node, which can
be used to transmit subsequent responses to this RREQ. This process repeats until the RREQ
reaches a node that has a valid route to the destination. This node (which can be the
destination itself) responds with a RREP message. This RREP is a unicast along the reverse
routes of the intermediate nodes until it reaches the originating node. Thus, at the end of this
request-response cycle, a bidirectional path is established between the requesting node and the
destination. When a node loses connectivity to its next hop, this node cancels its route by
sending a RERR to all nodes that have potentially received its RREP.
In our case, each node, by receiving a RREQ, it returns it to all these neighbors even the
source that absorbs. A TTL is also used which is the maximum time at the end of which a new
RREQ with a higher sequence number is sent if no response is received from the destination
node or a node that knows a valid path to the destination. The destination receiving the RREQ
chooses a new source from these neighbors; this destination node becomes the source and
starts a new cycle by sending a new RREQ message. This process of request-response cycles
stops after 4280 seconds of simulations (~72 minutes).

4.4.1.5 Energy modeling and network lifetime

A deployed active sensor dissipates energy during transmission, detection, reception of a message or period of inactivity. Therefore, energy efficiency is an essential key in designing a network of wireless sensors. The optimization of energy consumption then becomes an essential factor for the optimization of the operation of a WSN. To model the energy consumption in our simulations, using an initial energy E<sub>0</sub> indicator in each node. Given that following the 802.15.4 protocol, the reception is more expensive than sending energy, E<sub>0</sub> will be reduced by 'i' units if you send a message, and it will decrease 2×i units if it receives a message. The energy consumption is linked to another indicator which is the lifetime of the network. Typically, the lifetime of the WSN is represented by the time after which the first node is out of service. Thus, for each variant of the algorithm, the time corresponding to the lifetime of the network is measured so as to have an idea of the influence of the choice of the locations of the new nomad nodes added over the lifetime of the network.

4.4.2 Small-scale simulations of the network with OMNet++

In our simulations, we use OMNeT++ 4.6 (Omnetpp 2018) which is a free platform for simulation and development of network protocols. OMNeT++ IDE is based on the Eclipse platform and contains a simulation kernel library, a topology description language called NED, and a graphical user interface for running the simulation, it also provides a component architecture For modules programmed in C++.

For small-scale simulations, the 3D case is considered. Four objectives were considered incrementally (two objectives, then three objectives, then four objectives): cost in nodes, coverage, location, and optimization of energy consumption.

In small scale simulations, we try to imitate our experiments conducted at the IUT
University (see section 4.5). The network architecture is based on a fixed number (11) of
nodes having known positions. The number of nomad nodes to be added is also fixed at
three. Their positions are determined with the algorithms tested. Similarly for mobile nodes,
only one node is used as trigger for the first message. The positions of the initially deployed
fixed nodes are chosen according to the distribution law used by OMNet++ which tries to
distribute uniformly the nodes from the center of the region of interest, this leads to the non-
coverage of certain zones at the borders if the number of nodes Fixed is too small.

The runtime scenario is: An initial message is sent from the mobile node to a random destination 'd'; once d is found by the AODV routing protocol, 'd' becomes the source and a new destination is selected ... etc. This cycle is repeated until a stop condition is satisfied, among other things a maximum simulation time. In order to imitate our experiments, the small scale simulations follow a fixed scenario in which the number of nodes is fixed;

For connectivity to nodes in this small scale scenario, a connectivity matrix is used between
nodes that are deducted from the empirical results derived from our experiments (Mnasri et al,
2017a). The same connectivity links of the experiments are thus used initially. Subsequently,
in order to model the dynamism of the network, these connectivity links are set to a
perturbation which makes it possible to modify these links of initial connectivity. This
perturbation concerns the calculation of the RSSI rates between the nodes. Indeed, a matrix of
RSSI rates extracted from experiments is used initially. Then, this matrix is set to a
Chapter 4. Numerical results, simulations and experimentations on testbeds perturbation (+/- 30 for each value) in order to have new connectivity relations between the nodes.

In the case of small scale simulations, we adopt the same architecture (number and type of nodes) 3D deployment used in the experiments (see Figures in the section 4.5).

Figure 4.2 represents the distribution of the nodes according to the OMNet++ interface in the small-scale simulations. Nodes named initial-i represents the fixed nodes and nodes named nomad-i represents the nomad nodes.

<figure><img src="image_39.png" /><figcaption>Figure 4.2 small-scale simulation scenario</figcaption></figure>

### 4.4.2.1 Variations in RSSI rates in small-scale simulations

To measure the location, we use the RSSI metric since the localization model used is based on a hybridization between the RSSI and the DVHop protocol. As a result, the higher the RSSI, the better the localization. A neighbor can enter the neighborhood table of a node only if the RSSI value of the detected node is greater than a predefined threshold. The theoretical value of this threshold is set at 100. Initially, RSSI levels are based on our empirical experiments and to guarantee dynamism within the network, disruption of the value of RSSI is introduced via a random function (+ -30).

Figure 4.3 shows, for different number of objectives considered by the algorithms tested, the average of the RSSI rates measured for all the nodes in connection with (detected by / detecting) the mobile node.

<figure><img src="image_40.png" /><figcaption>Figure 4.3 Average RSSI rates during small-scale simulations</figcaption></figure>

### 4.4.2.2 Variations in FER rates in small-scale simulations

To measure coverage, we use the Frame Error Rate (FER) as a measure to assess the quality of links between nodes. As a result, the lower the RMF, the better the coverage. Although the values of the FER are less variable than those of the RSSI, we take, for each pair of nodes (node i - node C); i ∈ [1, 14]; an average value extracted from four values taken with an interval of 10 seconds between the two. Initially, FER rates are based on our empirical experiments and to guarantee a dynamism within the network, disruption of the value of the FER is introduced via a random function (+ -0.04 to + - 0.2). Figure 4.4 shows the mean FER rates measured for all the nodes in connection with (detected by / detecting) the mobile node.
<figure><img src="image_41.png" /><figcaption>Figure 4.4 Average FER rates in small-scale simulations</figcaption></figure>

### 4.4.2.3 Variations in the number of neighbors in small-scale simulations

To get an idea about the connectivity of the network, one measures the number of neighbors of the target (the mobile node). Figure 4.5 represents the average of the number of neighbors of the mobile node per objective.

<figure><img src="image_42.png" /><figcaption>Figure 4.5 Average number of neighbors in small-scale simulations</figcaption></figure>

### 4.4.2.4 Variations in energy and network lifetime in small-scale simulations

Figures 4.6 and 4.7 show the variations of the energy level of the network in the small-scale simulations for different number of objectives. Indeed, for the different algorithms tested, an average of the energy indicator of the nodes of the network is measured after the addition of the nomad nodes, this according to the number of fixed nodes.

<figure><img src="image_43.png" /><figcaption>Figure 4.6 Variation of energy in relation to the number of fixed nodes, for 2 objectives</figcaption></figure>
<figure><img src="image_44.png" /><figcaption>Figure 4.7 Variation of energy in relation to the number of fixed nodes, for 4 objectives</figcaption></figure>

Figure 4.8 shows the time after which the first node of the network is switched off for different number of objectives, which gives us an idea of the lifetime of the network.

<figure><img src="image_45.png" /><figcaption>Figure 4.8 Change in lifetime in relation to the time</figcaption></figure>

### 4.4.2.5 Comparison of experiments and simulations for small scale instances

Figure 4.9 illustrates similar results of experiments and simulations for small scale instances.

<figure><img src="image_46.png" /><figcaption>Figure 4.9 Experiments vs. simulations for small scale instances</figcaption></figure>

### 4.4.3 Large scale network simulations with OMNet++

Large-scale simulations are carried out in order to prove the scalability and robustness of the proposed approach. Like simulations on a small scale, the OMNet++ 4.6 simulator is used. The 3D case is considered. The same objectives and the same execution scenario are used. In contrast, the network architecture, connectivity, range and mining with which the RSSI are different from those used in small-scale simulations.

The network architecture used is based on a number of fixed nodes determined by the user at the beginning of the simulations. The positions of these fixed nodes are random and chosen by the OMNet++ simulator. In our simulations, we usually choose more than 100 fixed nodes. For the nomad nodes to be added, their number is variable and fixed by the
algorithms tested. This number depends on the region of interest, the number of nodes initially deployed and the optimization algorithm tested. For mobile nodes, a single node is used to trigger the simulations.

Connectivity in large-scale simulations is more dynamic than that of small-scale simulations. It is deduced from the radio range of the nodes. This range can be either fixed for all nodes, or deduced from the transmit power and gain. In our simulations, we use the second alternative based on transmission power and gain. To calculate RSSI, using the formula of frees which include the distance and power:

$$RSSI(d)[dBm] = RSSI_{ref} - 10n \log_{10}(d / d_{ref})$$

Figure 4.10 shows an example of large-scale simulation with 85 fixed nodes, 36 nomad nodes, and a mobile trigger node.

<figure><img src="image_47.png" /><figcaption>Figure 4.10 Large-scale simulation scenario (85 fixed nodes and 36 nomad nodes)</figcaption></figure>

### 4.4.3.1 Variations in the number of nomad nodes added in large-scale simulations

Figures 4.11 and 4.12 show the variations in the average number of nomad nodes added to the network in the small-scale simulations for different number of objectives. Indeed, for the different algorithms, an average of the necessary number of nomad nodes to be added to the network is measured, according to the number of fixed nodes.

<figure><img src="image_48.png" /><figcaption>Figure 4.11 Variations in the number of nomad nodes added for two objectives</figcaption></figure>

<figure><img src="image_49.png" /><figcaption>Figure 4.12 Variations in the number of nomad nodes added for four objectives</figcaption></figure>
### 4.4.3.2 Changes in RSSI rates in large-scale simulations

Figures 4.13 and 4.14 represent, for different number of objectives considered by the different algorithms, the average of the RSSI rates measured for all the nodes in connection with (detected by / detecting) the mobile node.

<figure><img src="image_50.png" /><figcaption>Figure 4.13 Average RSSI rates for different number of objectives</figcaption></figure>

<figure><img src="image_51.png" /><figcaption>Figure 4.14 Average RSSI rates according to the number of initial nodes</figcaption></figure>

### 4.4.3.3 Variations in FER rates in large-scale simulations

Figures 4.15 and 4.16 show, for different number of objectives considered by the various algorithms, the FER average rates measured for all the nodes in connection with (detected by/detecting) the mobile node.

<figure><img src="image_52.png" /><figcaption>Figure 4.15 Average FER rates for different number of objectives</figcaption></figure>

<figure><img src="image_53.png" /><figcaption>Figure 4.16 Average FER rates according to the number of initial nodes</figcaption></figure>
#### 4.4.3.4 Variations in the number of neighbors in large-scale simulations

Figures 4.17 and 4.18 represent, for different number of objectives considered by the various algorithms, the average numbers of neighbors of the mobile node.

<figure><img src="image_54.png" /><figcaption>Figure 4.17 Average numbers of neighbors for three objectives</figcaption></figure>

<figure><img src="image_55.png" /><figcaption>Figure 4.18 Average numbers of neighbors for nine objectives</figcaption></figure>

#### 4.4.3.5 Variations in energy consumption and network lifetime in large-scale simulations

Figures 4.19 and 4.20 represent the variations of the energy level of the network in the small-scale simulations for different number of objectives. Indeed, for the various algorithms, one measures an average of the energy indicator of the nodes of the network after the addition of the nomad nodes, according to the number of fixed nodes.

<figure><img src="image_56.png" /><figcaption>Figure 4.19 Variation of energy in relation to the number of fixed nodes, for two objectives</figcaption></figure>
<figure><img src="image_57.png" /><figcaption>Figure 4.20 Variation of energy in relation to the number of fixed nodes, for four objectives</figcaption></figure>

Figure 4.21 shows the time after which the first node of the network is switched off for different number of objectives, which gives us an idea of the lifetime of the network.

<figure><img src="image_58.png" /><figcaption>Figure 4.21 Change in lifetime in relation to the number of targets</figcaption></figure>

### 4.4.4 Discussion and interpretations

After the analysis of the simulations, different interpretations can be envisaged:

- In some cases, lower RSSI averages are recorded after adding the nomad nodes. Despite this decrease indicating that the RSSI rates of the new (nomad) nodes are lower than the RSSIs of the installed (fixed) nodes, the location rate, the coverage rate and the number of neighbors are improved. Given the objectives set by our approach, this decrease in RSSI averages is understandable, since adding a node in a $x_1$ location so that it will be close to several nodes with a lower RSSI value will be better than adding it in a location $x_2$ with a higher RSSI value but a smaller number of neighbors.

- By comparing small and large scale simulation results, large-scale simulation results are more stable (at the level of convergence and the monotony of the curves) and give a clearer idea of the efficiency of the simulations. New deployment positions proposed in the improvement of objectives. This is explained by the fact that large-scale simulations give the possibility of having a larger population of individuals, which improves the selection of the best individuals thereafter. Similarly, mutation and crossing operators have the option of covering a larger search space, which allows identifying the most ideal solutions (deployment locations).

- Simulation results in small scale (Figures 4.3, 4.4, 4.5 and 4.6) show conformity with the experimental results during the day, the level of increased coverage and localization, which proves the effectiveness of the proposed approach in different contexts.

- By comparing the efficiency of the different algorithms tested, the simulation results show that this efficiency is relative to the number of objectives to be met. For example, Figures 4.11 and 4.12 (also 4.15 and 4.16) show that if the number of goals is less than three, the $\in$-NSGA-II is more efficient, while the NSGA-III is more effective than if $\in$-NSGA-II Number of objectives exceeds three. This is explained by the fact that the $\in$-NSGA-II is dedicated to multi-objective problems, while the authors of the NSGA-III propose it as an adaptation of
the NSGA-II for problems having more than four objectives (many-objective problems). Our study constitutes a proof by experimentation and simulations of this observation which has been proved by the authors of the tested algorithms (MOEA/DD and NSGA-III) only by tests on instances of theoretical problems (benchmarks).

## 4.5 Experimentations on real testbeds

To evaluate the robustness and the efficiency of the protocols, technologies and models in real environments, real platforms called testbeds can be used. Indeed, simulations and theoretical calculations fail to reproduce the physical characteristics of the real-world environments; hence the current tendency to reduce the differences between theory and practice by testing the new algorithms and solutions in real environments with experiments carried out on testbeds.

In this study, we propose a testbed composed of TeensyWiNo nodes. Using this personal testbed, different advantages are envisaged:

- **Conformity to reality:** A personal testbed like ours is based on tests in a real context of use unlike test platforms such as FIT/IoT-Lab (IoTLab 2017) which offers tests with a large number of nodes that are aligned or uniform on a grid.

- **Reproducibility:** since our testbed relies on open-source tools, such as OpenWiNo and Arduino, it is easy to manage and reproduce the obtained results by other research teams. Indeed, Ophelia supports different physical layers and various types of sensors, which facilitates the deployment of nodes and the prototyping task.

- **Heterogeneity of nodes:** Our testbed supports three different types of nodes (DecaWino, WiNoLoRa and TeensyWiNo). Thanks to its compliance with open hardware and software, the WiNo architecture allows integrating foreign libraries to manage the deployed nodes, which enables it to support a wide variety of nodes.

- **A distributed deployment:** Our testbed consists of more than 30 nodes deployed in several buildings and locations in a campus of 200 × 200 m².

- **Easy use and deployment:** The nodes in our testbed are manipulated (erasing data, updating) using OpenWino and the execution of the protocols stack is done via the usb interface of the nodes or by executing a command line from the console. Moreover, WiNo nodes are compatible with revolutionary transmission modes (UWB, LoRa,..etc) and most standard physical layers, which makes the design and customization of the network as well as the replacement of the physical layer easier and more realistic.

- **Real life usage:** WiNos nodes have small size, low power consumption rate and easy attachment to a mobile system or a person, which makes them an ideal component for the IoT and the prototyping of communicating objects.

### 4.5.1 Experimental parameters and used tools

An Intel Core i5-6600K 3.5 GHz computer is used to test the algorithms. Physical layer is based on a 433 MHz implementation. The applied access method is the non-coordinated CSMA/CA of the IEEE 802.15.4 protocol, and the routing layer relies on the reactive Ad-hoc On-demand Distance Vector protocol. The parameters considered in our experiments are illustrated in Table 4.36.

<table><caption>Table 4.36 Parameters of the experiments</caption><tr><td>Nodes repartition</td><td>6 sites on 200 * 200 m²</td></tr><tr><td>Nodes number</td><td>36 (29 fixed, 6 nomad, 1 mobile)</td></tr><tr><td>Sensing range</td><td>8m</td></tr><tr><td>Transmission range</td><td>7m</td></tr><tr><td>FER (Frame Error Rate)</td><td>0.01 (initially)</td></tr><tr><td>RSSI (Received Signal Strength Indicator)</td><td>100 (initially)</td></tr><tr><td>Average number of runs</td><td>25 experiments</td></tr><tr><td>Bit rate</td><td>256 kbps</td></tr><tr><td>Modulation model</td><td>125 kbit/s GFSK</td></tr></table>
<table><tr><td>Antenna model</td><td>transceiver RFM22</td></tr><tr><td>Modem configuration</td><td>12 # GFSK_Rb2Fd5</td></tr><tr><td>Frequency</td><td>434.79 MHz</td></tr><tr><td>Tx power</td><td>7 (the max of RFM22)</td></tr><tr><td>Message-number</td><td>1000</td></tr><tr><td>Message-length</td><td>16</td></tr><tr><td>Message-wait</td><td>5</td></tr><tr><td>Reception gain</td><td>50 mA</td></tr><tr><td>Transmission power</td><td>100 mW</td></tr></table>

**The deployed TeensyWiNo nodes:** are WiNoRF22 nodes equipped with brightness and temperature sensors to which other sensors are added (gyrometer, acceleration or pressure). They give access to low layers in order to manage the access time to the medium, the sleep, the awakening time, the CPU time and the management of the restricted memory. WiNo nodes represent a hardware platform able to host different protocols with real-time constraints (several months of use using two AAA batteries). The installed TeensyWiNo nodes are shown in Figure 4.22 and their technical characteristics are illustrated in Table 4.37.

<figure><img src="image_59.png" /><figcaption>Figure 4.22 The Teensy WiNo used nodes</figcaption></figure>

<table><caption>Table 4.37 Technical characteristics of the used TeensyWiNo nodes</caption><tr><td>CPU/RAM/Flash</td><td>CPU/RAM/Flash ARM Cortex M4 (32bit) 72MHz, 64kB RAM, 256kB Flash (PJRC Teensy 3.1)</td></tr><tr><td>Transceiver (Arduino libraries)</td><td>HopeRF RFM22b: 200-900MHz, 1-125kbps, GFSK/FSK/OOK, +20dBm RadioHead</td></tr><tr><td>Use</td><td>IoT, WSN</td></tr></table>

These nodes, incorporated in the Arduino ecosystem, facilitate the integration of hardware and software components (interaction devices, actuators, sensors, processing algorithms, etc.), which allows obtaining the feedback from the user's experience. The following tools are used:

- **Arduino 1.6.1** (Arduino 2018): is an open software/hardware platform employed by the WiNo nodes to prototype modules and transfer the sketches via serial links. Teensyduino is an Arduino add-on to run these sketches.

- **OpenWiNo** (Van Den Bossche et al. 2016): is a free development environment for protocol engineering in WSN and DL-IoT. It permits rapid prototyping of protocols (MAC, NWK and other layers) and pragmatic evaluation of their performances in C language. It also allows them to be run on testbed via real WiNo nodes relying on the Arduino environment and developed in Open Hardware. Coupled with the OpenWiNo software, the WiNo nodes form a self-organized open-protocol mesh network. This approach allows a great versatility on the hardware. Thus, OpenWiNo, associated with the WiNo hardware, has certain advantages compared with the other platforms and testbeds. The main advantage of OpenWiNo is its simplicity. For example, to change the Physical layer on a WiNo node, it is enough to change the transceiver and the associated driver. This is recommended in an open-hardware environment. Different transceivers enabling several PHY layers have been tested successfully with the OpenWiNo: Classical IEEE 802.15.4 2.4GHz DSSS (Freescale), IEEE 802.15.4-2011 UWB (DecaWave DW1000), LoRa mode 868MHz (HopeRF RFM95) and Proprietary 433MHz FSK/GFSK (HopeRF RFM22b).
### 4.5.2 Scenario 1: Testing with 11 nodes

In this section, we will shed the light on the fact that the proposed contributions are tested on a real-world problem by deploying nodes in the research building of the University Institute of Technology of Blagnac (IUT Blagnac), University of Toulouse, France.

The proposed genetic algorithms are implemented on an Intel core i3-3217U CPU 1.80GHz computer and the following parameters are used. The number of constraints is determined based on our formulation. Length, width and height are determined based on the 3D space of the real experiments:

- Maximum number of generation = 350.

- Number of individuals per generation = 300.

- Probability of mutation = 0.15.

- Probability of crossover = 0.5.

- Number of constraints = 14.

- Length of the area (x) = 23.21 meters.

- Width of the area (y) = 13.95 meters.

- Height of the area (z) = 6.75 meters.

- Maximum execution time = 5400 seconds.

Besides, the theoretical estimated relations (RSSI and FER values) between the fixed nodes are not taken theoretically according to the hardware characteristics of the nodes. Indeed, these relations are based on the average values of a set of practical measures (real ranges). To give those algorithms more ability to reflect the reality when computing the RSSI and FER values, then better estimating the relations between the fixed nodes and the nomad nodes or between fixed nodes and the mobile node), the corresponding RSSI and FER values are calculated based on the average value of two parameters: a theoretical threshold (we choose between two values of this threshold, according to the existence or not of closed doors between the two concerned nodes) and the measures (RSSI and FER) of the nearest fixed node to the concerned nomad/mobile node.

#### 4.5.2.1 Network architecture

The proposed network is composed of 11 fixed nodes initially deployed, 3 nomad nodes (named 'D', 'E' and 'F'), and a mobile node (named 'C'). The mobile node is attached to a person moving within the 3D space of the building. Figure 4.23 illustrates the power of the RSSI links between the different nodes. The RSSI value of each node is indicated on the arcs (a value between 0 and 255 which is convertible in dBm values (RSSI, 2016) as shown in Figures 4.25, 4.26, 4.27 and 4.28). Blue arcs indicate links with excellent RSSI connections in terms of quality of the received signal, green arcs indicate links with good connections, orange arcs indicate less good connection links, and red arcs indicate weak RSSI connections.

<figure><img src="image_60.png" /><figcaption>Figure 4.23 The logical network architecture</figcaption></figure>

Although the number of all deployed nodes does not exceed twenty in our experimentations, the use of meta-heuristics as a resolution approach in our work is justified,
since; according to Cheng et al. (2008); the 3D deployment problem is considered as an NP-hard problem starting from two nodes to deploy. Figure 4.24 illustrates the deployment schema in 2D and 3D plans. The origin of the local taken coordinate system is set at the point $P_0(0,0,0)$ indicated in Figure 4.24(a). The red nodes represent the fixed nodes and the blue nodes represent the nomad added nodes<fnref n="1" />. We note here that our deployment is considered as a 3D deployment (not a 2D multistage deployment) since there is connections between nodes situated in different floors of the building. Besides, the variation in height of the deployed nodes is not negligible as compared to length and width of the deployment field. Consequently, it is recommended to consider the indoor area as a continuous 3D space.

<figure><img src="image_61.png" /><figcaption>Figure 4.24 The 2D and 3D architecture of the real deployed indoor network</figcaption></figure>

Technical and localization characteristics of the installed nodes are listed in Table 4.38. Table 4.39 illustrates a set of chosen positions taken by the mobile node 'C' on the 3D space to assess coverage and localization before and after the redeployment. These positions are dispersed uniformly in different regions of the 3D space. In both mentioned tables, the x-axis represents the horizontal axis, the y-axis represents the vertical axis, and the z-axis represents the height. The point $P_0(0,0,0)$ corresponds to the following WGS84 GPS coordinates expressed in sexagesimal degrees (in degrees, minutes and seconds): latitude = 43°38′57.4″E; longitude = 1°22′28.4″E and altitude = 164 meters. These GPS coordinates can be easily converted into the local coordinates using appropriate formulas.

<table><caption>Table 4.38 Technical and localization characteristics of the installed nodes</caption><thead><tr><th rowspan="2">N°</th><th rowspan="2">Decimal nomenclature</th><th rowspan="2">Short address (the node's 16-bit address)</th><th rowspan="2">Type</th><th colspan="3">Position according to the local coordinate</th></tr><tr><th>X</th><th>Y</th><th>Z</th></tr></thead><tbody><tr><td>N1</td><td>01</td><td>0x0001</td><td>Teensy 3.0 mk20dx128</td><td>278</td><td>545</td><td>523</td></tr><tr><td>N2</td><td>02</td><td>0x0002</td><td>Teensy 3.0 mk20dx128</td><td>1063</td><td>525</td><td>521</td></tr><tr><td>N3</td><td>03</td><td>0x0003</td><td>Teensy 3.0 mk20dx128</td><td>683</td><td>498</td><td>526</td></tr><tr><td>N4</td><td>14</td><td>0x0004</td><td>Teensy 3.1 mk20dx256</td><td>663</td><td>414</td><td>206</td></tr><tr><td>N5</td><td>05</td><td>0x0005</td><td>Teensy 3.0 mk20dx128</td><td>2093</td><td>305</td><td>519</td></tr><tr><td>N6</td><td>06</td><td>0x0006</td><td>Teensy 3.0 mk20dx128</td><td>1237</td><td>1256</td><td>443</td></tr><tr><td>N7</td><td>15</td><td>0x0007</td><td>Teensy 3.1 mk20dx256</td><td>450</td><td>00</td><td>290</td></tr><tr><td>N8</td><td>1c*</td><td>0x0008</td><td>Teensy 3.1 mk20dx256</td><td>1114</td><td>1252</td><td>422</td></tr><tr><td>N9</td><td>31*</td><td>0x0009</td><td>Teensy 3.1 mk20dx256</td><td>416</td><td>495</td><td>336</td></tr><tr><td>N10</td><td>1F*</td><td>0x000A</td><td>Teensy 3.1 mk20dx256</td><td>1813</td><td>306</td><td>356</td></tr><tr><td>N11</td><td>34*</td><td>0x000B</td><td>Teensy 3.1 mk20dx256</td><td>672</td><td>270</td><td>291</td></tr></tbody></table>

<footnote n="1">¹ Color should be used for this figure in print version</footnote>
<table><caption>Table 4.39 Locations of selected positions taken by the mobile node 'C'</caption><tr><td>N12</td><td>58</td><td>0x000D</td><td>Teensy 3.1 mk20dx256</td><td>-</td><td>-</td><td>-</td></tr><tr><td>N13</td><td>59</td><td>0x000E</td><td>Teensy 3.1 mk20dx256</td><td>-</td><td>-</td><td>-</td></tr><tr><td>N14</td><td>60</td><td>0x000F</td><td>Teensy 3.1 mk20dx256</td><td>-</td><td>-</td><td>-</td></tr><tr><td>N15</td><td>C</td><td>0x000C</td><td>Teensy 3.1 mk20dx256</td><td>-</td><td>-</td><td>-</td></tr></table>

<table><thead><tr><th>No</th><th></th><th>P1</th><th>P2</th><th>P3</th><th>P4</th><th>P5</th><th>P6</th><th>P7</th><th>P8</th><th>P9</th><th>P10</th><th>P11</th><th>P12</th><th>P13</th><th>P14</th><th>P15</th><th>P16</th><th>P17</th></tr></thead><tbody><tr><td rowspan="3">Positions according to the local reference</td><td>X</td><td>943</td><td>938</td><td>624</td><td>345</td><td>1152</td><td>1393</td><td>1814</td><td>1646</td><td>2148</td><td>1904</td><td>1748</td><td>1167</td><td>1693</td><td>865</td><td>362</td><td>1142</td><td>2321</td></tr><tr><td>Y</td><td>265</td><td>422</td><td>870</td><td>1175</td><td>992</td><td>1197</td><td>1072</td><td>435</td><td>985</td><td>648</td><td>25</td><td>858</td><td>584</td><td>520</td><td>342</td><td>0</td><td>0</td></tr><tr><td>Z</td><td>392</td><td>386</td><td>343</td><td>518</td><td>478</td><td>462</td><td>394</td><td>502</td><td>413</td><td>517</td><td>383</td><td>187</td><td>10</td><td>100</td><td>28</td><td>140</td><td>165</td></tr></tbody></table>

### 4.5.2.2 Objectives

Our purpose is to add nomad nodes in the indicated locations guaranteeing a set of objectives. These objectives can be either **network objectives** or **application objectives**. The applicative objectives represent the metrics to measure: they are mainly linked to existing sensors measuring physical parameters such as brightness, temperature or opening and closing doors. The network objectives generally concern the measurement of the link's strength between nodes over time: the quality of link (thus the radio coverage quality) is evaluated by measuring the FER, the localization quality is evaluated by measuring the RSSI, while the number of neighbors is evaluated by measuring the both mentioned metrics. OpenWiNo uses the following concept to define a neighbor: a node 'b' is considered as a neighbor in the neighbors table of another node 'a' only if the RSSI signal of 'b', received by 'a' is sufficient (greater than a predefined tunable threshold). In our works we define also a predefined tunable empirical threshold for the FER, below it, a node is not considered as a neighbor. Thus, a neighbor enters to the neighbors table only if the two mentioned thresholds are respected. Indeed, to ensure the 3D coverage, each node must have at least one neighbor and should be monitored by at least one node. In general, to be ensured, the localization requires that all nodes must have at least one neighbor. However, in our case, we use a hybrid 3D localization model based on 3D DV-Hop and RSSI protocol which requires that each node must have four neighbors. We take measures by day and by night. This is explained by the fact that the existence of a large number of people by day implies that the majority of the doors are opened which improve the quality of the received signals. Overnight, the majority of the doors are closed. The anti-fire doors installed in the IUT prevent a good transmission of the signal.

### 4.5.2.3 Variation of the localization

To measure the localization, a localization model based on RSSI and 3D DV-Hop hybridization is used. Indeed, the localization quality is proportional to the RSSI value. A neighbor may be included in the neighbors table of a node only if it's received RSSI value is greater than the predefined threshold. This threshold is tunable via the command `"phy rssith set"` (Van den Bossche et al 2017). In our case, its value is fixed to 100. Based on the obtained numerical results, we study the effect of the value of the RSSI threshold and its relationship with the FER. The value of the RSSI can change over time and the period of its stability can be less than one second. Given this instability, we take an average value of RSSI extracted from four values taken with an interval of 20 seconds of waiting between these four values; for each pair of nodes (node *i* - node C); *i* ∈ [1,14]. The RSSI value (noted R<sub>ci</sub>) that represents the relationship between the mobile node 'C' and each node 'i' is taken as the maximum value between the detection value of 'C' by 'i' (signal generated by 'C'), and the detection value of 'i' by 'C' (signal detected by 'C'). The average of the R<sub>ci</sub> values between 'C' and all other nodes reaching the fixed threshold in each position Pi is represented by the ordinate axis in Figure 4.25, expressed in the negative value of the dBm (the RSSI values between 0 and 255 are converted (RSSI 2016) into values expressed in dBm), according to the proposed algorithms, by day. The horizontal axis in Figure 4.25 represents the Pi positions indicated in Table 4.39. Figure 4.26 shows the variation of the same RSSI averages overnight. Table A.1 (in Appendix
1) illustrates the average values, in different positions Pi, of the RSSI classified by neighbors of the node 'C', by day. Table A.2 (in Appendix 1) illustrates the average values, in different positions Pi, of the RSSI classified by neighbors of the node 'C', overnight.

<figure><img src="image_62.png" /><figcaption>Figure 4.25 Variations on the localization (RSSI), by day, for different positions</figcaption></figure>

<figure><img src="image_63.png" /><figcaption>Figure 4.26 Variations on the localization (RSSI), by night, for different positions</figcaption></figure>

#### 4.5.2.4 Variation of the coverage

The frame error rate (FER) is used as a metric to measure the coverage and to evaluate the quality of links between nodes. The above-mentioned threshold of FER (used to introduce neighbors) is fixed to 40%. The following concept using counters is used to compute the FER: We calculate the couples of exchanged frames (received and lost ones) for each pair of neighbors. These couples are calculated using internal counters which are represented by values between 0 and 255. The use of multiple counters is explained by the fact that if one counter is used, a large number of values can be accumulated, and the historic of the old values can be lost. To calculate the FER for each pair of neighbors, 10 counters of received frames and 10 counters of lost frames are calculated each $10^{-4}$ seconds. Indeed, in each reception of a new beacon carrying a sequence number noted 's', the received frame counter is increased by one and the lost frame counter is increased by a number 'x' according to the sequence number 's'. 'x' is the difference between the old sequence value and the new received sequence number 's'. The sum of the values of lost frames divided by the total amount of frames (those received and lost) gives the FER for the considered couple. The sliding window phenomenon may appear if the first counter is older. The OpenWiNo command "neighb fer counters" (Van den Bossche et al 2017) displays the details of internal counters and the sliding windows used to calculate the FER. This principle allows keeping the historic of the exchanged frames and calculating the error rate between each two neighbors. The coverage quality is proportional to the FER value. Despite the FER values vary less than those of the RSSI, we take an average value of the FER extracted from four values taken with an interval of 10 seconds of waiting between these four values; for each pair of nodes (node i - node C); i ∈ [1,14]. The FER value (noted CovCi) that represents the relationship between the mobile node 'C' and each node 'i' is taken as the average value between the detection value of 'C' by 'i' (signal generated by 'C'), and the detection value of 'i' by 'C' (signal detected by 'C'). The average of the CovCi values between 'C' and all other nodes reaching the fixed threshold in each position Pi is represented by the ordinate axis in Figure 4.27, using the proposed algorithms, by day. The horizontal axis in Figure 4.27 represents the Pi positions indicated in Table 4.39. Figure 4.28 shows the variation of the same FER averages overnight. Table A.3 (in Appendix 1) illustrates the average values, in different positions Pi, of the FER, classified
by neighbors of the node 'C', by day. Table A.4 (in Appendix 1) illustrates the average values, in different positions Pi, of the FER, classified by neighbors of the node 'C', overnight.

<figure><img src="image_64.png" /><figcaption>Figure 4.27 Variations of the coverage (FER), by day, in different positions</figcaption></figure>

<figure><img src="image_65.png" /><figcaption>Figure 4.28 Variations of the coverage (FER), overnight, in different positions</figcaption></figure>

4.5.2.5 Variation of the number of neighbors

Figure 4.29 shows the variation of the number of neighbors, using the proposed algorithms, by day, for the Pi positions. Figure 4.30 shows the variation on the number of neighbors overnight, for the Pi positions.

<figure><img src="image_66.png" /><figcaption>Figure 4.29 Variation of the number of neighbors, by day</figcaption></figure>

<figure><img src="image_67.png" /><figcaption>Figure 4.30 Variation of the number of neighbors, by night</figcaption></figure>
### 4.5.2.6 Discussion

The improvement of the coverage (FER), the localization (RSSI) and the number of neighbors compared to the initial deployment are summarized by day in Table 4.40 and by night Table 4.41.

<table><caption>Table 4.40 The improvement of RSSI and FER rates compared to the initial deployment, by day</caption><thead><tr><th></th><th>NSGA-IIr</th><th>NSGA-IIa</th><th>cNSGA-IIIr</th><th>cNSGA-IIIa</th><th>U-NSGA-IIIr</th><th>U-NSGA-IIIa</th></tr></thead><tbody><tr><th>Average RSSI's improvement</th><td>+3,0929<br>(+1,2081%)</td><td>+3,5258<br>(+1,3772%)</td><td>+4,7547<br>(+1,8573%)</td><td>+5,8252<br>(+2,2754%)</td><td>+7,5488<br>(+2,9487%)</td><td>+9,5194<br>(+3,7185%)</td></tr><tr><th>Average FER's improvement</th><td>-2,019%</td><td>-3,463%</td><td>-3,247%</td><td>-4,307%</td><td>-6,087%</td><td>-8,175%</td></tr><tr><th>Average number of added neighbors in all Pi positions</th><td>+0,5294</td><td>+1,6071</td><td>+1,375</td><td>+1,353</td><td>+1,5076</td><td>+2,94</td></tr></tbody></table>

<table><caption>Table 4.41 The improvement of RSSI and FER rates compared to the initial deployment, by night</caption><thead><tr><th></th><th>NSGA-IIr</th><th>NSGA-IIa</th><th>cNSGA-IIIr</th><th>cNSGA-IIIa</th><th>U-NSGA-IIIr</th><th>U-NSGA-IIIa</th></tr></thead><tbody><tr><th>Average RSSI's improvement</th><td>+1,627<br>(+0,6355%)</td><td>+3,774<br>(+1,4742%)</td><td>+4,205<br>(+1,6425%)</td><td>+4,727<br>(+1,8464%)</td><td>+8,7211<br>(+3,4066%)</td><td>+10,132<br>(+3,9578%)</td></tr><tr><th>Average FER's improvement</th><td>-2,018%</td><td>-3,463%</td><td>-3,247%</td><td>-4,307%</td><td>-6,087%</td><td>-8,1754%</td></tr><tr><th>Average number of neighbors in all the Pi positions</th><td>+0,3529</td><td>+1,647</td><td>+0,9411</td><td>+1,7647</td><td>+2,1176</td><td>+2,8823</td></tr></tbody></table>

After the analysis of the experiment results, several findings can be considered:

- In the majority of the instances, the average of RSSI signal strength is greater at day than night because of the opened doors during day while the average of FER signal strength is greater at night than day due to less human activities at night involving less perturbations and signal interference.

- When comparing the variation of the FER and the RSSI rates between day and night, it is noted that the FER rate is higher by day than night although the RSSI rate is also higher by day than night: this indicates that the introduction of neighbors according to the highest RSSI does not always give the lowest error rate. By comparing the error rate before and after deployment, we conclude that our approach has allowed minimizing the error rates and subsequently maximizing coverage.

- The node range is not spherical: according to measures, some nodes can be detected by a set of nodes while some other further near nodes cannot detect them. For instance, the node 'N4' is the only one detecting the node 'C' which is in the location P1 although there is other nodes which are less distant from the location P1. This assumption has been considered when implementing the proposed algorithms.

- When capturing measures on the same position over several periods, it is noted that after a period of initializing the links between nodes, the RSSI increases (stronger signal) and the FER decreases (less error rate).

- The nature of the relationship between the RSSI and the FER is investigated: each neighbor is introduced in the neighbors table based on a high RSSI rate but after a moment, the rate of lost frames may be very high. Thus, increasing the RSSI value may not decrease the FER value. So, the FER indicates the quality of links better than the RSSI.

- When comparing the two methods of selecting the mutation operators (random vs adaptive), we conclude that the adaptive method is always better than the random one due to its intelligent process. Thus, the adaptive method can be considered as an upper bound for the random method.

- According to experimentations, the U-NSGA-III proposed versions are more efficient in resolving our problem than the NSGA-II proposed versions. This can be explained by the fact that the NSGA-III selection procedure which is based on reference points and niching (U-NSGA-III) allows more diversity among the members of the population.

- Although this selection procedure used on the cNSGA-III (based on reference points), the NSGA-II seems to be (in several positions) more efficient than the cNSGA-III: this can be
explained by the fact that the cNSGA-III is dedicated to resolve many objective problems and
may have some difficulties when resolving single or bi-objective problems.

**4.5.3 Scenario 2: Ophelia testbed (Testing with 36 nodes)**

Ophelia is a platform based on Arduino, OpenWiNo and the installed TeensyWiNo nodes, to which a web interface is added. This interface allows remote access to Ophelia testbed, programming and executing experimental sketches (in python language) on the nodes. In what follows, we detail the execution scenario of our experiments using Ophelia.

**4.5.3.1 Experimental scenario and results**

30 fixed nodes initially deployed with known positions (chosen according to the users application needs) are used. The number of nomad nodes to be added is limited to six. The positions of the latter nodes are to be determined by the tested optimization algorithms. Only one mobile node is applied.

In order to study the impact of the selected positions of the nomad nodes on the network performance, the following scenario of the experiments is repeated several times: At the beginning, all the nodes are flashed and the parameters of the initial configuration (power of transmission, etc.) are sent. Then, the mobile node sends a broadcast to all other nodes. The RSSI and FER rates issued from and received by each node are considered. After a predefined waiting time, another transmitter is chosen and the other nodes become receivers. This process is repeated until 36 experiments are achieved. At the end, two connectivity matrices, combining the RSSI and FER means between the nodes, are created. The average number of neighbors of each node is deduced from these two matrices. In our experiments, two nodes are considered neighbors if and only if the mean rate of the RSSI (and FER, respectively) recorded between these two nodes is greater (lower, respectively) than a pre-defined threshold equal to 100 (0.1, respectively). Due to the stochastic nature of the used evolutionary optimization algorithms, the use of a statistical test with several executions is necessary to assess their behavior. Therefore, the mean values in our tests are calculated based on 25 runs of the algorithms.

**Comparing the RSSI values:** To assess different objectives, like the localization, the connectivity or the quality of links, the RSSI metric is calculated. Our experiments are based on a hybrid localization model which combines the RSSI information and the Distance-VectorHop protocol. Indeed, the higher the RSSI value, the better the localization will be. Figure 4.31 shows the average RSSI values (a convertible to dBm value in [0, 256]) exchanged between nodes for different numbers of objectives.

<figure><img src="image_68.png" /><figcaption>Figure 4.31 The average RSSI values, for different number of objectives</figcaption></figure>

**Comparing the FER rates:** To assess the coverage and the quality of links between nodes, the FER metric is calculated. Indeed, the lower the FER value, the better the coverage will be. To assess FER values for each pair of nodes, an average value deduced from four values is considered with an interval of 10 seconds between the four values. Figure 4.32 shows the average FER values between nodes for different numbers of objectives.
<figure><img src="image_69.png" /><figcaption>Figure 4.32 The average FER values, for different number of objectives</figcaption></figure>

**Comparing the number of neighbors:** To evaluate the connectivity and the utilization of the network, the average number of each node neighbors is computed. Indeed, the previous definition of the neighbor based-on RSSI and FER is used. Figure 4.33 shows the average number of neighbors for all nodes and for different numbers of objectives.

<figure><img src="image_70.png" /><figcaption>Figure 4.33 Average number of neighbors, for different number of objectives</figcaption></figure>

**Comparing the network lifetime:** Figure 4.34 indicates, for different number of objectives, the network lifetime considered as the time in which the first node of the network has no energy.

<figure><img src="image_71.png" /><figcaption>Figure 4.34 Average lifetime of the network, for different number of objectives</figcaption></figure>

**Comparing the energy consumption:** Figure 4.35 illustrates the variation of the network energy consumption as a function of time. Indeed, the average of the energy rates of all nodes is calculated after adding the nomad nodes.

<figure><img src="image_72.png" /><figcaption>Figure 4.35 Average energy consumption levels, as a function of time</figcaption></figure>
### 4.5.3.2 Interpretations and discussion

After performing the experiments, several findings can be considered:

- This study is a proof of the applicability of the optimization approaches in real-world contexts using real experiments. It shows the theoretical findings obtained by applying the tested algorithms.

- Our experiments show that a link between two nodes can have a high FER and an excellent RSSI at the same time. Thus, the RSSI and FER rates are not always inversely proportional.

- By studying the performance and behavior of the tested algorithms before and after the application of the proposed hybridization scheme, the experimental results demonstrate that NSGA-III is generally better than MOEA/DD in the RSSI and FER rates. Thus, the NSGA-III is considered more efficient in satisfying the localization, the coverage and the link quality, while MOEA/DD is better used to satisfy the average number of neighbors and the network lifetime.

- Consistent with our numerical results (see sections 4.2 and 4.3), the experiments assert that the effectiveness of the algorithms depends on the number of objectives to be optimized. Indeed, figures 4.31, 4.32, 4.33 and 4.34 show that if the objective number does not exceed three, the behavior of the MOEA/D will be better than that of the NSGA-III. In the case of four objectives or more, the behavior of the NSGA-III becomes better than that of the MOEA/D. This finding can be explained by the fact that, unlike MOEA/DD and Two_Arch2, the NSGA-III is only dedicated to many-objective problems.

- Contrary to different studies such as (Li et al. 2015) showing that the decomposition-based methods are generally more efficient than the NSGA-III, our results prove that MOEA/DD is not always better than NSGA-III because our problem is a real-world one having some features which are different from those characterizing the theoretical problems used to evaluate these algorithms.

- Finally, it is proven that the incorporation of the dimensionality reduction and the user preferences improves the results (higher HV, higher coverage and localization) and enhance the behavior of the tested algorithms.

- The Two_Arch2 has an almost stable behavior that is generally not influenced by varying the number of objectives.

### 4.5.4 Results of experimentations on PI-NSGA-III

**Comparing the RSSI rates:** To assess the connectivity ($f_8$ in our modeling, see section 3.2.2), the quality of links ($f_{10}$) and the localization ($f_5$), the RSSI metric is used since the used localization model is based on RSSI and Distance-VectorHop protocol. Thus, the higher the RSSI rate is, the better the localization is. Figure 4.36 illustrates the average of RSSI (a value in [0, 256] convertible to dBm) between nodes (for each node $i \in [1, 36]$ with other ones).

<figure><img src="image_73.png" /><figcaption>Figure 4.36 Comparing the average rates of RSSI</figcaption></figure>

**Comparing the FER rates:** To measure the coverage ($f_6$), we use the FER as a metric to evaluate the quality of links between nodes. Hence, the lower the FER is, the better the coverage is. Figure 4.37 shows the average measured FER for each node with other ones.
<figure><img src="image_74.png" /><figcaption>Figure 4.37 Comparing the average rates of FER</figcaption></figure>

*Comparing the number of neighbors:* To measure the network connectivity (f8) and the utilization of the network (f4), the average number of neighbors of each node is measured. The same definition of neighborhood (previously explained in the experiment scenario) is used. Figure 4.38 illustrates the average number of neighbors for each node.

<figure><img src="image_75.png" /><figcaption>Figure 4.38 Comparing the average number of neighbors</figcaption></figure>

**Discussion and interpretations of PI-NSGA-III results:** After evaluating the experiments, different interpretations can be deduced:

- The rates of RSSI and FER are not necessarily inversely proportional: a link between two nodes may have an excellent RSSI and high FER in the same time.

- The FER values are more relevant during day than overnight. This can be explained by the activities of persons in the building during day such as opening and closing doors, which generates perturbations on the signal.

- By comparing the efficiency of the tested algorithms, the experimental results show that the NSGA-III generally outperforms the MOEA/DD in the RSSI and FER rates (Thus, it is better in satisfying the coverage, the quality of links and the localization), while the latter algorithm is generally more efficient than NSGA-III in optimizing the number of neighbors of each node (Thus, it is better in satisfying the utilization of the network).

- Contrary to the results of different studies (see (Li et al 2015) and (Yuan et al 2016)) showing that the decomposition-based methods are better than NSGA-III, our results prove that the MOEA/DD does not always outperforms the NSGA-III (PI-NSGA-III-VF in our case). This can be explained by the fact that our problem is a real world one which is different from theoretical problems used to test the algorithms. It is also explained and by the contribution of the incorporation of preferences on the NSGA-III.

- Since the tested algorithms (NSGA-III and MOEA/DD) are tested by their authors only on instances of theoretical test problems, our study is a proof of the applicability of the optimization approaches in real world contexts using real experimentations.

# 4.6 Results on hybridizing ACO and NSGA-III (AcNSGA-III)

## 4.6.1 Numerical results of the algorithms

When resolving a particular problem, the parameters setting has a major influence on the algorithm behavior. In this section, we present the parameters setting of the algorithms and the results using the HV metric. The used parameters are as follows:
- The size of the population (NS): 300 (Thus, Npop =150).

- The operators of reproduction: It would be best to perform a recombination operation using near parent solutions in the case of MaOPs. Therefore, a large distribution index SBX operator (simulated binary crossover) is used. The recombination probability is PrOx=0.8 using a distribution index $τ_r$ = 45. The mutation probability using the bit-flip operator, is PrMt=2*10⁻³ using a distribution index $τ_m$ = 25.

- The number of runs: in order to guarantee statistical confident results, each algorithm is executed 25 runs using a different initial population in each execution.

- The constraints number: 5.

- The number of ants (NbA): 350

- The pheromone minimum threshold (MaxTP): 1

- The pheromone maximum threshold (MinTP): 15

- The pheromone exponent (ExP): 0.4

- The pheromone evaporation coefficient (EvP): 0.25

- The number of objectives and the termination condition (the maximum number of generations) are as shown in Table 4.42. For each instance, the best performance is demonstrated using shaded background.

<table><caption>Table 4.42 HV (Best, average and worst values)</caption><thead><tr><th>Obj Nbr</th><th>Max nbr of generations</th><th>ACO</th><th>NSGA-III</th><th>AcNGSA-III</th></tr></thead><tbody><tr><td rowspan="3">3</td><td rowspan="3">1300</td><td>0.984682</td><td>0.902458</td><td>0.903168</td></tr><tr><td>0.983561</td><td>0.901896</td><td>0.902375</td></tr><tr><td>0.982327</td><td>0.898023</td><td>0.987653</td></tr><tr><td rowspan="3">4</td><td rowspan="3">1800</td><td>0.885236</td><td>0.974685</td><td>0.976687</td></tr><tr><td>0.884381</td><td>0.974233</td><td>0.975986</td></tr><tr><td>0.884003</td><td>0.973612</td><td>0.975124</td></tr><tr><td rowspan="3">5</td><td rowspan="3">2600</td><td>0.878847</td><td>0.972892</td><td>0.973382</td></tr><tr><td>0.872324</td><td>0.972716</td><td>0.972899</td></tr><tr><td>0.871456</td><td>0.972684</td><td>0.972633</td></tr></tbody></table>

The AcNGSA-III outperforms the ACO and the NSGA-III in the most of the instances which proves its efficiency. Another observation is that the ACO is better than the NSGA-III for three objectives, while the latter one is better when the number of objectives is higher than three. This is congruent with the observation of its authors (Deb and Jain 2014) which asserts that the NSGA-III is dedicated to resolve many-objectives problems. Also, due to the increasing complexity of the problem when the number of objectives increases, for all algorithms, better HV values are obtained with smaller number of objectives.

### 4.6.2 Comparing simulations and experimentations

This section aims to provide a comparison between the simulation and the experimental tests of the 3D deployment scheme in indoor WSN while satisfying different objectives. We are interesting in testing the behavior the tested evolutionary optimization algorithms (ACO, NSGA-III) and the new suggested one (AcNSGA-III). The same above mentioned simulation/experiments parameters and working environment are used.

**Experimental/simulation scenario:** In experiments, 30 fixed nodes with known positions are used. Six nomad nodes are to be added. Their positions are determined with the tested optimization algorithms. For mobile nodes, only one node is used. The positions of the initially deployed fixed nodes are chosen according to the users applicative needs. The execution scenario is as following: At the beginning, all the nodes are flashed. Then, the initial configuration parameters (transmission power, etc.) are sent. Then, a first node sends a broadcast to other nodes. The measurements are taken in two directions: the sender records his RSSI and FER rates with each node and each receiving node returns these same measurements. After a fixed waiting time, the sender finishes the process. Then, the sender is
changed and all other nodes become receivers. The same process is repeated until 36 experiments are performed which give us two connectivity matrices with the RSSI and FER values between all nodes. The neighbors of each node are deduced from the two matrices. In our case, a node *i* is considered as neighbor to another node *j* if the average of the RSSI emitted from *i* to *j* and the one from *j* to *i*, is greater than a fixed threshold (100); and the FER average is also lower than a fixed threshold (0.1).

To study the impact of the new positions of the nomad nodes on the network performance and to evaluate the behaviors of the suggested algorithm (acNSGA-III), this latter is compared to the ACO and the NSGA-III (Deb and Jain 2014) which is another recent many-objective optimization algorithm. Because of the stochastic nature of evolutionary algorithms and the necessity of a statistical test to compare two algorithms, the average values in the experimental scenario are obtained using 25 executions. Thus, we obtain a well-based judgment concerning the performance of the algorithms.

For simulations, the same architecture (number and types of nodes) and scenario are used. Concerning the fixed nodes, its positions are identified using the distribution law of the OMNeT++. This distribution law aims to distribute nodes starting from the center of the RoI uniformly. Concerning the connectivity of nodes in simulations, a connectivity matrix based on empirical experiments is established between nodes using the same initial connectivity links of the experiments. To introduce dynamism on the network in simulations; the RSSI connectivity links are set to perturbations to modify the initial links. Indeed, the RSSI matrix is set to a perturbation (+/- 30 for each value) to have new connectivity relations between nodes each time. The simulation scenario is as follows: An initial message is sent from the trigger node (mobile node) to a random destination *d*. Once *d* is found by the AODV routing protocol, it becomes the source and a new destination is selected until the maximum time of simulation is reached.

Since comparing two algorithms is only possible through the use of a statistical test and due to the stochastic nature of the tested evolutionary algorithms, it is necessary to perform any test over many executions to obtain a well based judgment concerning their performance. Thus, all average values in this section, are computed based on 25 executions of the algorithms. In the following, the different measures (RSSI, FER, etc.) are taken in both simulation and experiments.

**Comparing the RSSI rates.** In order to measure the localization, the RSSI metric is used since the used localization model is based on hybridization between the RSSI and the DVHop (Distance-VectorHop) localization protocol. Thus, the higher the RSSI, the better the localization is. A neighbor can be added to the neighborhood table of a node only if the RSSI value of the detected node is greater than a predefined threshold. The value of this threshold is set to 90. Initially, RSSI levels are based on our empirical experiments. Then, as mentioned before, in order to guarantee dynamism within the network, disruption of the value of RSSI is introduced via a random function. Figure 4.39 shows, for different number of objectives, the average of the RSSI rates measured for all the nodes in connection with the mobile node.

<figure><img src="image_76.png" /><figcaption>Figure 4.39 Comparing the average RSSI rates</figcaption></figure>

**Comparing the FER rates.** To measure coverage, we use the FER as a metric to assess the quality of links between nodes. Thus, the lower the FER, the better the coverage is.
Although the FER values are less variable than those of the RSSI, for each node's pair {node C, node i}, an average value extracted from four values is taken with an interval of 10 seconds between the four values. Initially, FER rates are based on our empirical experiments. Afterwards, to guarantee dynamism within the network, disruption of the FER values is introduced via a random function (+/- 0.04 to +/- 0.2). Figure 4.40 shows the average FER rates measured for all nodes in connection with (detected by / detecting) the mobile node.

<figure><img src="image_77.png" /><figcaption>Figure 4.40 Comparing the average FER rates</figcaption></figure>

**Comparing the number of neighbors.** In order to assess the network connectivity, the number of neighbors of the target (the mobile node) is measured. Figure 4.41 shows the average of the number of neighbors of the mobile node per objective.

<figure><img src="image_78.png" /><figcaption>Figure 4.41 Comparing the average number of neighbors</figcaption></figure>

**Comparing the energy consumption and the network lifetime.** Figure 4.42 shows the variation of the energy level of the network according to the time. Indeed, for the different tested algorithms, according to the number of the fixed nodes, an average of the energy indicator of all nodes of the network is measured after adding nomad nodes.

<figure><img src="image_79.png" /><figcaption>Figure 4.42 Comparing the average energy consumption levels</figcaption></figure>

Figure 4.43 illustrates the lifetime of the network. It shows for different number of objectives, the time in which the first node of the network is switched off.
<figure><img src="image_80.png" /><figcaption>Figure 4.43 Comparing the average lifetime</figcaption></figure>

## Discussion and interpretations

After comparing the simulations and the experiments, different interpretations can be considered:

- The obtained results (Figures 4.39 to 4.43) show conformity with the results of experimentation, notably with regard to the coverage and localization rates. This proves the accuracy of the models of simulation and the effectiveness of the proposed approach in different contexts. Indeed, our work represents a proof by experimentation and simulations of the observations which has been proved by the authors of the tested algorithms (NSGA-III for example) only by tests on instances of theoretical test problems.

- In several cases, lower RSSI averages are recorded after adding the nomad nodes. Despite this decrease indicating that the RSSI rates of the added nodes are lower than the RSSI values of the fixed nodes, the localization rate, the coverage rate and the number of neighbors are improved. Given the objectives set by our approach, this decrease in RSSI averages is understandable, since adding a node in a location x1 so that it will be close to several nodes with a lower RSSI value will be better than adding it in a location x2 with a higher RSSI value but smaller number of neighbors.

- The error rates (FER) are more important in experiments than in simulations. This is due to the influence of the activities of persons in the building during experiments (for example opening and closing doors) which generates the perturbation of the signal.

- By comparing the efficiency of the tested algorithms, as proved by numerical results (section 4.3), the simulation/experimental results show that this efficiency is relative to the number of objectives to be optimized. Table 4.42 shows that for less than three objectives, the ACO is more efficient than NSGA-III, while the latter is more effective than ACO if the number of objectives exceeds three. This is explained by the fact that the ACO is dedicated for multi-objective problems, while the authors of NSGA-III propose this latter as an adaptation of the NSGA-II for many-objective problems having more than three objectives. However, the AcNSGA-III has an almost stable behavior and is not influenced by the variation of the number of objectives.

# 4.7 Results on accentBirdsPSO and on hybridizing PSO and MAS

## 4.7.1 Numerical results

In this section, the algorithms parameters and the obtained numerical results are presented.

### 4.7.1.1 PSO and NSGA-III parameters

The used setting parameters are detailed in Table 4.43.

<table><caption>Table 4.43 Setting parameters of the algorithm</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Population size</td><td>300</td></tr><tr><td>Number of independent runs</td><td>25, on different initial populations</td></tr><tr><td>Number of constraints</td><td>7</td></tr></tbody></table>
<table><tbody><tr><td></td><td>Number of objectives</td><td colspan="2">Variable, see Table 4.44</td></tr><tr><td></td><td>Maximum number of generations</td><td colspan="2">Variable, see Table 4.44</td></tr><tr><td rowspan="7">PSO parameters</td><td>Number of particles per swarm</td><td colspan="2">10-50</td></tr><tr><td>Number of swarms</td><td colspan="2">Identified by the used clustering algorithm</td></tr><tr><td>C1(cognitive components)</td><td colspan="2">2.8 to 2.2</td></tr><tr><td>C2 (social components)</td><td colspan="2">1.2 to 1.8</td></tr><tr><td>Inertial weight</td><td colspan="2">0.95 to 0.4</td></tr><tr><td>Maximum particle velocity</td><td colspan="2">According to the formula (5.1)</td></tr><tr><td>Initial swarm particle velocity</td><td colspan="2">Randomly uniformly distributed in [-4, 4]</td></tr><tr><td></td><td>Initial minimum number of clusters</td><td colspan="2">4</td></tr><tr><td rowspan="10">NSGA-III parameters</td><td rowspan="3">Recombination</td><td>Operator</td><td>SBX</td></tr><tr><td>probability</td><td>0.8</td></tr><tr><td>distribution index</td><td>45</td></tr><tr><td rowspan="3">Mutation</td><td>Operator</td><td>Bit-flip</td></tr><tr><td>probability</td><td>1/400</td></tr><tr><td>distribution index</td><td>25</td></tr></tbody></table>

The sum of cognitive and personal components is generally set to four as recommended in (Shi and Eberhart 1999). In (Jason et al., 2004), they are set to 2.8 and 1.3, respectively. Although, based on our experiments, we adopt the values of 1.75 and 1.35, respectively. According to (Shi and Eberhart 1999), the linear inertia weight value decreasing from 0.95 to 0.4. If the maximum velocity of the particle is too low, the algorithm becomes too slow; else if it is too high, the algorithm becomes too unstable. Thus, the maximum particle velocity is set according to the formula 5-4*(i/I) (5.1) where i is the current iteration and I is the maximum number of iterations.

### 4.7.1.2 Results on our real-world problem

Given the random behavior of the optimization algorithms and aiming at obtaining a statistically reliable comparison results, an average of 25 executions of the algorithms is performed. Table 4.44 demonstrates the obtained HV values for different numbers of objectives and generations. Best performances (having higher HV) are shown with shaded backgrounds.

<table><caption>Table 4.44 Hypervolume values (Best, average and worst)</caption><thead><tr><th>ObjNbr</th><th>Max nbr of generations</th><th>NSGA-III</th><th>MaOPSO</th><th>acMaPSO</th><th>acMaMaPSO</th></tr></thead><tbody><tr><td rowspan="3">3</td><td rowspan="3">1300</td><td>0.902231</td><td>0.903458</td><td>0.903631</td><td>0.903774</td></tr><tr><td>0.901658</td><td>0.902896</td><td>0.903036</td><td>0.903039</td></tr><tr><td>0.898235</td><td>0.898023</td><td>0.902563</td><td>0.901088</td></tr><tr><td rowspan="3">4</td><td rowspan="3">1800</td><td>0.974892</td><td>0.976985</td><td>0.977331</td><td>0.977329</td></tr><tr><td>0.974743</td><td>0.976833</td><td>0.977098</td><td>0.977243</td></tr><tr><td>0.973897</td><td>0.975612</td><td>0.976892</td><td>0.976838</td></tr><tr><td rowspan="3">5</td><td rowspan="3">2600</td><td>0.972983</td><td>0.972892</td><td>0.972985</td><td>0.973324</td></tr><tr><td>0.972563</td><td>0.972116</td><td>0.972728</td><td>0.972984</td></tr><tr><td>0.972126</td><td>0.971084</td><td>0.972436</td><td>0.972356</td></tr></tbody></table>

Obtained results show that for different numbers of objectives, acMaPSO and acMaMaPSO are often more efficient than other algorithms. Moreover, although the MaOPSO is more efficient than the NSGA-III, it has higher relative degradation when the number of objectives increases compared to other algorithms.

### 4.7.1.3 Results of DTLZ test problems

To prove its scalability, we test the performance of our approach on the theoretical test suite (DTLZ (Deb et al 2005)) after assessing it on real testbeds. The quality of the obtained non-dominated solution sets generated by the tested algorithms is assessed using the IGD metric (Coello et al 2002) and 15 independent runs in each test. IGD allows measuring both the diversity and the convergence of the non-dominated obtained solutions. Table 4.45 shows best, average and worst IGD values of the DTLZ1-4 test suite. Best performances (having lower IGD values) are shown with shaded backgrounds.
<table><caption>Table 4.45 Best, average and worst IGD values on DTLZ1-4 test suite</caption><thead><tr><th>Test Pb</th><th>ObjNbr</th><th>Number of generations</th><th>MaOPSO</th><th>NSGA-III</th><th>acMaPSO</th><th>acMaMaPSO</th></tr></thead><tbody><tr><td rowspan="6">DTLZ1</td><td rowspan="3">3</td><td rowspan="3">400</td><td>3.458E-4</td><td>4.880 E-4</td><td>3.566 E-4</td><td>3.238E-4</td></tr><tr><td>1.231 E-3</td><td>1.308 E-3</td><td>1.209E-3</td><td>1.298E-3</td></tr><tr><td>4.783 E-3</td><td>4.880 E-3</td><td>3.844E-3</td><td>4.257E-3</td></tr><tr><td rowspan="3">5</td><td rowspan="3">600</td><td>0.635E-4</td><td>5.116 E-4</td><td>0.642E-4</td><td>0.637E-4</td></tr><tr><td>0.684E-4</td><td>0.980 E-4</td><td>0.649E-4</td><td>0.648E-4</td></tr><tr><td>1.323E-3</td><td>1.979 E-3</td><td>1.589E-3</td><td>1.635E-3</td></tr><tr><td rowspan="6">DTLZ2</td><td rowspan="3">3</td><td rowspan="3">250</td><td>5.663 E-4</td><td>1.262 E-3</td><td>3.856 E-4</td><td>5.734 E-4</td></tr><tr><td>6.102 E-4</td><td>1.357 E-3</td><td>5.897 E-4</td><td>5.023 E-4</td></tr><tr><td>7.029 E-4</td><td>2.114 E-3</td><td>8.014 E-4</td><td>6.298 E-4</td></tr><tr><td rowspan="3">5</td><td rowspan="3">350</td><td>1.302 E-3</td><td>4.254 E-3</td><td>1.279 E-3</td><td>1.243 E-3</td></tr><tr><td>1.534 E-3</td><td>4.982 E-3</td><td>1.432 E-3</td><td>1.412 E-3</td></tr><tr><td>1.896 E-3</td><td>5.862 E-3</td><td>1.982 E-3</td><td>1.786 E-3</td></tr><tr><td rowspan="6">DTLZ3</td><td rowspan="3">3</td><td rowspan="3">1000</td><td>7.235 E-4</td><td>9.751 E-4</td><td>6.088 E-4</td><td>6.320 E-4</td></tr><tr><td>3.028 E-3</td><td>4.007 E-3</td><td>3.011 E-3</td><td>2.875 E-3</td></tr><tr><td>6.657 E-3</td><td>6.665 E-3</td><td>6.234 E-3</td><td>4.657 E-3</td></tr><tr><td rowspan="3">5</td><td rowspan="3">1000</td><td>1.432 E-3</td><td>3.086 E-3</td><td>1.533 E-3</td><td>1.512 E-3</td></tr><tr><td>2.569 E-3</td><td>5.960 E-3</td><td>2.167 E-3</td><td>2.247 E-3</td></tr><tr><td>6.233 E-2</td><td>1.196 E-2</td><td>5.798 E-3</td><td>6.064 E-3</td></tr><tr><td rowspan="6">DTLZ4</td><td rowspan="3">3</td><td rowspan="3">600</td><td>2.846 E-1</td><td>2.915 E-4</td><td>4.321 E-1</td><td>3.654 E-1</td></tr><tr><td>6.280 E-1</td><td>5.970 E-4</td><td>7.194 E-1</td><td>6.025 E-1</td></tr><tr><td>6.685 E-1</td><td>4.286 E-1</td><td>8.632 E-1</td><td>6.309 E-1</td></tr><tr><td rowspan="3">5</td><td rowspan="3">1000</td><td>3.093 E-1</td><td>9.849 E-4</td><td>6.058 E-2</td><td>8.052 E-2</td></tr><tr><td>4.834 E-1</td><td>1.255 E-3</td><td>0.381 E-1</td><td>0.352 E-1</td></tr><tr><td>4.992 E-1</td><td>1.721 E-3</td><td>2.984 E-1</td><td>2.554 E-1</td></tr></tbody></table>

For DTLZ1-3, the same results as our real world problem are found: acMaPSO and acMaMaPSO are more efficient than other algorithms while MaOPSO is better than NSGA-III. For DTLZ4, NSGA-III is more efficient than acMaPSO, acMaMaPSO and MaOPSO. There is no significant difference between the results of three and five objectives.

### 4.7.2 Experimental and simulation results

In this section, a comparison between the simulation and the experimental tests is provided. The performance and the behavior of the suggested algorithms (acMaPSO, acMaMaPSO) are compared to those of MaOPSO and NSGA-III. Indeed, theoretical analysis and simulators are not entirely able to reproduce all the technical and physical characteristics of the real environment. Also, nowadays, there is a tendency to face protocol and algorithmic proposals with real environments. In this context, through the experiments over our testbed, we aim to reduce the gaps between theory and practice in WSN and IoT deployment issues.

#### 4.7.2.3 Comparing the simulations to the experimental results on Ophelia testbeds

* Experimental/simulation scenario

The same scenario in the section 4.6.2 is used, with average values of 25 executions of the algorithms.

* Comparing the RSSI rates: To assess the connectivity (f8 in our modeling (see section 3.2.2)), the quality of links (f10) and the localization (f5), the RSSI metric is used since localization is based on RSSI and Distance-Vector Hop protocol. So, the higher the RSSI rate, the better the localization. Figure 4.44 illustrates, for different numbers of objectives (to be satisfied by the tested algorithms), the average of the RSSI rates measured for all nodes in connection with (detected by/detecting) the mobile node. This average of RSSI is a value in [0, 256] convertible to dBm.
<figure><img src="image_81.png" /><figcaption>Figure 4.44 RSSI average rates of nodes in connection with the mobile node</figcaption></figure>

* **Comparing the FER rates:** To measure the coverage (f6), FER is used as a metric to evaluate the quality of links between nodes. Thus, the lower the FER is, the better the coverage is. Figure 4.45 illustrates, for different numbers of objectives to satisfy by the tested algorithms, the average of the FER rates measured for all nodes in connection with (detected by/detecting) the mobile node.

<figure><img src="image_82.png" /><figcaption>Figure 4.45 FER average rates of nodes in connection with the mobile node</figcaption></figure>

* **Comparing the number of neighbors:** To measure the network connectivity (f8) and the utilization of the network (f4), the average number of neighbors of nodes in connection with the mobile node is measured. We use the same notion of neighbor previously explained in the experiment scenario. Figure 4.46 illustrates, for different numbers of objectives, the average number of neighbors measured for all nodes in connection with the mobile node.

<figure><img src="image_83.png" /><figcaption>Figure 4.46 Average number of neighbors of nodes in connection with the mobile node</figcaption></figure>

* **Comparing the energy consumption and the network lifetime:** Figure 4.47 shows the energy variations of the network according to the time. Indeed, the average of the energy indicator of all the nodes is measured after adding the nomad nodes.
<figure><img src="image_84.png" /><figcaption>Figure 4.47 Comparing the average energy consumption levels</figcaption></figure>

Table 4.46 shows the lifetime of the network. It illustrates for two numbers of objectives, the time in which the first node is dead.

<table><caption>Table 4.46 Comparing the average lifetime</caption><thead><tr><th rowspan="2">Nbr of objectives</th><th colspan="2">MaOPSO</th><th colspan="2">NSGA-III</th><th colspan="2">acMaPSO</th><th colspan="2">acMaMaPSO</th></tr><tr><th>simulations</th><th>experiments</th><th>simulations</th><th>experiments</th><th>simulations</th><th>experiments</th><th>simulations</th><th>Experiments</th></tr></thead><tbody><tr><td>2</td><td>3546</td><td>3502</td><td>3485</td><td>3487</td><td>3543</td><td>3549</td><td>3572</td><td>3583</td></tr><tr><td>5</td><td>3478</td><td>3469</td><td>3528</td><td>3546</td><td>3540</td><td>3553</td><td>3568</td><td>3571</td></tr></tbody></table>

### 4.7.2.4 Discussion and interpretations

After evaluating the experiments, different interpretations can be deduced:

- The rates of RSSI and FER are not necessarily inversely proportional: a link between two nodes may have an excellent RSSI and a high FER at the same time.

- The FER values are more relevant during the day than overnight. This can be explained by the activities of persons in the building during experiments such as opening and closing doors, which generates perturbations on the signal.

- In agreement with the findings of different other studies (such as (Figueiredo et al 2016)) showing that the MaOPSO is better than the NSGA-III, our numerical results based on HV and IGD metrics prove that the NSGA-III does not outperforms the MaOPSO. However, experimental results show that our PSO new variants generally outperforms the NSGA-III in the RSSI and FER rates (Thus, it is better in satisfying the coverage, the quality of links and the localization), while the latter is generally more effective than PSO for the number of neighbors of each node (So, it is better in satisfying the utilization of the network). This difference between numerical and experimental results can be explained by the fact that our problem is a real-world one which is different from the theoretical benchmarks used to test the algorithms.

- Since the NSGA-III algorithm is tested by their authors only on instances of theoretical test problems, our study is a proof of the applicability of this algorithm in a real-world context, using real experimentations.

- In contrast with other tested algorithms, the NSGA-III in simulations has higher RSSI values than in experiments.

- In comparison with RSSI, the FER rates are more important in experiments than in simulations.

## 4.8 Conclusion

In this chapter, we proposed a set of evaluations based on numerical tests, on simulations and on experimentations with different scenarios to prove the effectiveness of the proposed hybridizations on different contexts. To sum up the findings, these evaluations proves that the proposed hybrid algorithms achieve (and surpasses for specific evaluation metrics such as the number of neighbors), the performance of the standard versions of the PSO, MOEA/DD and the NSGA-III algorithms. These findings are summarized in the next chapter (see the section *Findings and results*). Nevertheless, our evaluations can be enhanced by scaling up and testing the deployment proposed by the hybrid algorithms using a larger number of nodes.
# Conclusions and future research directions

In this thesis, we addressed and studied the problem of 3D indoor deployment of nodes in collection networks using a multi-objective optimization approach. In fact, when solving real-world problems known by a large number of objectives, the performance of EMOs deteriorates and different outcomes are encountered such as the dependency on the number of objectives, the exponential increase in the number of needed solutions and the size of the population. As a solution to issues, we have studied then modified different hybrid meta-heuristics to improve their performance. We proposed the hybridization of these meta-heuristics both with a dimensionality reduction method, with a method of incorporating user preferences and with the MAS. We tested the positioning solution proposed by these hybrid algorithms with simulations and experiments following different scenarios.

## 1 Findings and results

The main contributions and corresponding findings of our research work could be summarized as follows:

- An in-depth literature review of methods for optimizing deployment in WSN, particularly the algorithms that take into account 3D indoor deployment. This study covers swarm-based meta-heuristics (Optimization by Particle Swarm, ant colony optimization), genetic algorithms, taboo search, simulated annealing. The study also deals with the single-objective and multi-objective case; the static and dynamic case of deployment.

- A mathematical formulation that aims at modeling the problematic. It is about fixing the objective function to be optimized, the decision variables and the different constraints to take into consideration. Our objective is to minimize the number of used sensor nodes and the consumption of energy. Simultaneously, maximizing the network lifetime, the coverage, the localization and the connectivity.

- We also propose an adaptive mutation and recombination operators that encourages mating with the neighborhood, integrate a concept of multiple scalarizing functions in pareto-based EMOs to overcome the inefficiency of recombination and to increase costs in time and space in the case of many-objective real problems. The obtained results show that for most cases, the aggregation algorithm (MOEA/DD) is more efficient than tested other algorithms (NSGA-II and NSGA-III) to solve the 3D indoor deployment. Moreover, the results prove that the adaptive method of selecting recombination and mutation operators with neighborhood restrictions improves the algorithm performance.

- A first justified hybridization is proposed. It combines two procedures based on user preferences (PI-EMO-PC) and reduction of dimensionality (MVU-PCA) with optimization algorithms belonging to three classes: aggregation-based algorithms (Two_Arch2), reference points-based (MOEA/DD, NSGA-III) and decomposition-based (MOEA/D). To evaluate the proposed new hybrid algorithms, we used the HV metric on our deployment problem; and the IGD metric on theoretical test problems such as DTLZ. Then, to validate the theoretical observations, a set of prototypes were realized. The results show the superior performance of the modified hybrid algorithms over original ones. In addition, there have been other interesting findings such as the superior performance of MOEA/D over NSGA-III in the case of correlated objectives.

- A second hybridization is proposed. It combines an interactive approach of incorporating user preferences (PI-EMO-VF) with the NSGA-III algorithm. Results showed that the performance of the proposed hybrid algorithm exceeds the performance of another recent many-objective algorithm (MOEA/DD) for different evaluation metrics (such as the number of neighbors) although the literature (see (Li et al., 2015) and (Yuan et al., 2016)) states that MOEA/DD gives better results than the standard NSGA-III on theoretical problems.
- A third hybridization is proposed, which combines, for the first time, the ant colony optimization (ACO) algorithm with a recent variant of genetic algorithms (NSGA-III). The advantage of this hybridization scheme is that, unlike conventional hybridizations, the two hybridized algorithms run at the same time and can interact with the same population. From results, it has been deduced that the proposed algorithm (acNSGA-III) outperforms the traditional NSGA-III and the standard ACO.

- Another proposed modification consists in introducing a new concept of bird's accent in the particle swarm optimization algorithm. The new algorithm is named acMaPSO. This new accent concept is based on the idea of separating the swarm (the bird community) into different groups of regional dwellings according to their accents. Thus, to maintain the diversity of the population during the search process of the algorithm, this accent concept evaluates the local particle search capability and classifies particles into different accent groups according to their common way of singing. To escape the local optima, aged particles "die" and are replaced periodically by new randomly generated ones.

- A fourth proposed hybridization consists of distributing the acMaPSO algorithm by hybridizing it with a multi-agent system (MAS). The new algorithm (acMaMaPSO) benefits from the interactivity of particles (becoming agents) and the distribution. The proposed multi-agent architecture is based on three types of agents that have different knowledge and action plans: an environment agent, bird agents (or particle agents) and swarm agents. The acMaPSO and acMaMaPSO algorithms are very competitive compared with the MOPSO algorithm. The obtained results show that acMaPSO and acMaMaPSO exceed for specific evaluation metrics such as the number of neighbors, the performance of the standard PSO algorithm and the NSGA-III algorithm.

To sum up, the performance indicators used to assess our work, the simulations and the real prototyping highlight the good behavior of our proposed approaches on many-objective problems and show the effectiveness of the hybridization.

## 2 Future research directions

The perspectives of our work are multiple and several open questions remain to be explored. Our perspectives mainly concern two categories: The first category is interested in the development of new hybridization schemes between EMO and other deployment resolution approaches. The second one concerns issues that are related to the network, real experiments and prototyping.

### Hybridization perspectives:

- According to its authors (Deb et al. (2010), the PI-EMO-VF procedure contains a large number of parameters to be initialized by the user from the beginning. This makes PI-EMO-VF sensitive to the initial setting. Hence, it is important to propose a parameter-less version of the PI-EMO-VF.

- Although our reduction and preferences platform reduces the number of objectives and the complexity of the problem, it seems to be complex to implement. Hence, to show the contribution of its use, a study of the algorithmic complexity of our hybrid approach can be conducted.

- To evaluate their performances, different recent MOEA and other reduction procedures (rather than the MVU-PCA already used) can be integrated into our platform. In this regard, we propose to incorporate the KnEA algorithm (Zhang et al., 2015) and the FS (Feature Selection) reduction procedure (Mitra et al., 2002).

- The integration of preferences into metaheuristics other than EAs is a promising research direction since different population-based metaheuristics have proven their performance in resolving MOPs. The PSO and the Artificial Immune System (AIS) can be used in this regard.
- In order to help the DM navigate on multidimensional spaces of many-objective problems, researches can be provided regarding the development of better visualization tools.

- A comparative study between all the proposed schemes of hybridization can be implemented.

- As a continuation of this work, we are actually proposing a new optimization algorithm based on the imitation of the behaviors of wild animals in their territories, and its application on our problematic.

## Network Application and prototyping Perspectives:

- One of the advantages of our Ophelia testbed is that it is more realistic in terms of constraints and conditions of use than a platform with a large number of uniform nodes such as SmartSantander (Sanchez et al., 2014), IoTLab (Fleury et al., 2015) or INDRIYA (Doddavenkatappa et al., 2011). These platforms allow us to test our algorithms using a larger number of nodes (up to 1024 nodes). In future studies, in order to compare our Ophelia results with other prototyping platforms and to prove the scalability of our approach, tests on the IoTLab platform are possible since it allows to test the same metrics of our experiences (link quality, RSSI, ... etc)

- Other directions of research can be investigated such as the resolution of dynamic redeployment of nodes with consideration of other objectives. We also aim to intensify the deployed network by adding new nodes to better satisfy the localization constraint that requires four neighbors for each target. We should then redo our experiences to investigate the influence of the network density on the results.

- Another future contribution concerns the implementation of a more realistic energy model with OMNeT++, based on the BO and SO management values (Farhad et al., 2016) of the CSMA/CA 802.15.4 protocol for example.

- Despite its effectiveness, OpenWiNo lacks libraries that implement standard protocols. Hence the interest of implementing other transmission protocols and technologies in OpenWiNo.

Finally, given the success of multi-objective optimization in solving several real-world problems, often with conflicting goals, the time has come to push its use in different dynamic and complex application domains.
Publications (within this thesis)

**International Journals**

* IRJIE'15 MNASRI S., NASRI N., VAN DEN BOSSCHE A., VAL T. The 3D Deployment Multi-objective Problem in Mobile WSN: Optimizing Coverage and Localization. International Research Journal of Innovative Engineering. ISSN 2395-0560, Vol. 1 N. issue 5, Mai 2015.

* AJSE'17 MNASRI S., NASRI N., VAN DEN BOSSCHE A., VAL T. Resolving the 3D indoor deployment problem using hybrid modified many-objective optimization algorithms. Arabian Journal for Science and Engineering. ISSN: 2193-567X (Print) 2191-4281 (Online), https://link.springer.com/journal/13369. (**Impact Factor= 0.865**), [in review, submitted on March 31th, 2017].

* NACOJ'18 MNASRI S., NASRI N., VAN DEN BOSSCHE A., VAL T. Enhanced hybrid many-objective evolutionary algorithms for real world problems: application to the 3D indoor redeployment problem. Natural Computing. ISSN 0305-054. (https://link.springer.com/journal/11047) ISSN: 1567-7818 (Print) 1572-9796 (Online). (**Impact Factor= 0.778**), [in review, submitted on February 14th, 2018].

* ISATRANS'18 MNASRI S., NASRI N., VAN DEN BOSSCHE A., VAL T. A new multi-agent particle swarm algorithm based on birds accents for the 3D indoor deployment problem. ISA Transactions. ISSN:0019-0578. (https://www.journals.elsevier.com/isa-transactions) (**Impact Factor:3.39, 5Y-IF: 3.4**), [in revision, submitted on February 07th, 2018].

**International Conferences**

* PEMWN'14 MNASRI S., NASRI N., VAL T. An Overview of the deployment paradigms in Wireless Sensor Networks. International Conference on Performance Evaluation and Modeling in Wired and Wireless Networks (PEMWN 2014), Tunisie – 04-07 Novembre 2014.

* ISNCC'15 MNASRI S., THALJAOUI A., NASRI N., VAL T. A genetic algorithm-based approach to optimize the coverage and the localization in the wireless audiosensors networks. IEEE International Symposium on Networks, Computers and Communications (ISNCC 2015), Hammamet, Tunisie, IEEExplore digital library, 13-15 Mai 2015.

* IINTEC'17 Mnasri S., Nasri N., VAN DEN BOSSCHE A., Val T. "A Comparative analysis with validation of NSGA-III and MOEA/D in resolving the 3D indoor redeployment problem in DL-IoT". IEEE International Conference on Internet of Things, Embedded Systems and Communications (IINTEC'17), Gafsa, Tunisia, October 20-22th, 2017(Among best six papers).

* AdHocNow'17(a) Mnasri S., Nasri N., VAN DEN BOSSCHE A., Val T., "A hybrid ant-genetic algorithm to solve a real deployment problem: a case study with experimental validation". International Conference on Ad Hoc Networks and Wireless (AdHoc-Now 2017), Messina, Italy, September 20-22 th, 2017, SPRINGER (Eds.), **(Ranked B)**.

* AdHocNow'17(b) Mnasri S., VAN DEN BOSSCHE A., Nasri N., Val T., " The 3D redeployment of nodes in Wireless Sensor Networks with real testbed prototyping". International Conference on Ad Hoc Networks and Wireless (AdHoc-Now 2017), Messina, Italy, September 20-22 th, 2017, SPRINGER (Eds.), **(Ranked B)**.

* IWCMC'18(a) MNASRI S., NASRI N., VAN DEN BOSSCHE A., VAL T. The 3D indoor redeployment process in DL-IoT: a real testbed prototyping using an hybrid PI-NSGA-III-VF optimization strategy. The 14th International Wireless Communications and Mobile Computing Conference (http://iwcmc.org/2018/) **(Ranked B)**.
* IWCMC'18(b) MNASRI S., NASRI N., VAL T. The deployment in 3D indoor DL-IoT with experimental validation using a multi-agent particle swarm optimization algorithm based on birds accents. The 14th International Wireless Communications and Mobile Computing Conference (http://iwcmc.org/2018/) (Ranked B).

National Conferences

* **JNCT'14** MNASRI S., NASRI N., VAL T. Contribution au déploiement optimisé des réseaux de capteurs sans fil. Journées Nationales des Communications Terrestres (JNCT 2014), ISBN 978-3-8417-3468-6, Toulouse-Blagnac, France - 22,23 Mai 2014.

* **JNCT'16** MNASRI S., NASRI N., VAN DEN BOSSCHE A., VAL T. Simulation d'un réseau sans fil d'intérieur et des algorithmes NSGA-II et NSGA-III modifiés pour la résolution de la problématique de couverture et de localisation 3D. Journées Nationales des Communications Terrestres (JNCT 2016), Montbéliard – France, 01-02 Septembre 2016.
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# Appendix 1
## RSSI and FER measures of in our experimental tests (Scenario 1)

<table><caption>Table A1 Averages of RSSI values by neighbours of 'C' in different positions during day</caption><thead><tr><th></th><th></th><th>N1</th><th>N2</th><th>N3</th><th>N4</th><th>N5</th><th>N6</th><th>N7</th><th>N8</th><th>N9</th><th>N10 (A)</th><th>N11 (B)</th><th>VMR(Initial deployment)</th><th>VMR(e-NSGA-II-AxN-AmN)</th><th>VMR(U-NSGA-III-AxN-AmN)</th><th>VMR(mMOEA/DD-AxN-AmN)</th></tr></thead><tbody><tr><td rowspan="2">P1</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>130</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>163</td><td>158,5</td><td>163,2</td><td>166,5</td></tr><tr><td>RSSI detected by 'C'</td><td>79</td><td>96</td><td>81</td><td>163</td><td>88</td><td></td><td>75</td><td>75</td><td>81</td><td>88</td><td>88</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P2</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>135</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>128</td><td>132,8</td><td>134,2</td><td>138,2</td></tr><tr><td>RSSI detected by 'C'</td><td>106</td><td>105</td><td>77</td><td>168</td><td>101</td><td>78</td><td>91</td><td>99</td><td>77</td><td>97</td><td>80</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P3</td><td>RSSI generated by 'C'</td><td>128</td><td></td><td></td><td>116</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>123,5</td><td>124,9</td><td>132,7</td><td>139,4</td></tr><tr><td>RSSI detected by 'C'</td><td>101</td><td>91</td><td>109</td><td>132</td><td>79</td><td>78</td><td>88</td><td>105</td><td>86</td><td>80</td><td>87</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P4</td><td>RSSI generated by 'C'</td><td>151</td><td></td><td></td><td>115</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>125,37</td><td>127,6</td><td>138,5</td><td>140,1</td></tr><tr><td>RSSI detected by 'C'</td><td>142</td><td>95</td><td>125</td><td>144</td><td>118</td><td>105</td><td>97</td><td>139</td><td>101</td><td>112</td><td>88</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P5</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>111</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>120</td><td>124,8</td><td>126,6</td><td>129,6</td></tr><tr><td>RSSI detected by 'C'</td><td>91</td><td>89</td><td>94</td><td>134</td><td>104</td><td>108</td><td>82</td><td>138</td><td>93</td><td>104</td><td>88</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P6</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>109</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>128,25</td><td>131,5</td><td>128,8</td><td>134,5</td></tr><tr><td>RSSI detected by 'C'</td><td>93</td><td>90</td><td>94</td><td>136</td><td>117</td><td>98</td><td>74</td><td>141</td><td>71</td><td>119</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P7</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>113</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>123,4</td><td>125,57</td><td>129</td><td>132,8</td></tr><tr><td>RSSI detected by 'C'</td><td>93</td><td>87</td><td>84</td><td>141</td><td>120</td><td>107</td><td>80</td><td>133</td><td>81</td><td>116</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P8</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>109</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>112,5</td><td>119,5</td><td>119,5</td><td>125,6</td></tr><tr><td>RSSI detected by 'C'</td><td>77</td><td>88</td><td>91</td><td>129</td><td>102</td><td>91</td><td></td><td>113</td><td>83</td><td>106</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P9</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>106</td><td>99</td><td>83</td><td></td><td>89</td><td></td><td>89</td><td></td><td>106</td><td>117</td><td>121</td><td>124,5</td></tr><tr><td>RSSI detected by 'C'</td><td>78</td><td>83</td><td>89</td><td>106</td><td>99</td><td>83</td><td></td><td>89</td><td></td><td>89</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P10</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>97</td><td>125</td><td></td><td></td><td></td><td></td><td></td><td></td><td>119,33</td><td>123</td><td>126,3</td><td>129,6</td></tr><tr><td>RSSI detected by 'C'</td><td>93</td><td>86</td><td>98</td><td>109</td><td></td><td></td><td></td><td>120</td><td></td><td>113</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P11</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>129</td><td>123</td><td>98</td><td>101</td><td>74</td><td></td><td></td><td></td><td>119,66</td><td>124,14</td><td>127,8</td><td>133,3</td></tr><tr><td>RSSI detected by 'C'</td><td>75</td><td>76</td><td>99</td><td>129</td><td>123</td><td>98</td><td>101</td><td>74</td><td></td><td>124</td><td>103</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P12</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>134</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>129</td><td>133</td><td>131</td><td>133,4</td></tr><tr><td>RSSI detected by 'C'</td><td>93</td><td>91</td><td>95</td><td>146</td><td>99</td><td>90</td><td>92</td><td>112</td><td>88</td><td>95</td><td>90</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P13</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>120</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>124,66</td><td>132,2</td><td>130,5</td><td>132,2</td></tr><tr><td>RSSI detected by 'C'</td><td>87</td><td>91</td><td>96</td><td>153</td><td>99</td><td>93</td><td>115</td><td>99</td><td></td><td>106</td><td>81</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P14</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>131</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>130</td><td>127,6</td><td>129,9</td><td>134,9</td></tr><tr><td>RSSI detected by 'C'</td><td>81</td><td>83</td><td>85</td><td>173</td><td>86</td><td></td><td>113</td><td>98</td><td>84</td><td>93</td><td>104</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P15</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>122</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>121</td><td>127</td><td>127</td><td>128,8</td></tr><tr><td>RSSI detected by 'C'</td><td>94</td><td>83</td><td>111</td><td>135</td><td>79</td><td></td><td>123</td><td></td><td>97</td><td></td><td>98</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P16</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>128</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>128</td><td>131</td><td>133,2</td><td>133,8</td></tr><tr><td>RSSI detected by 'C'</td><td>91</td><td>87</td><td>84</td><td>112</td><td>93</td><td></td><td>98</td><td>79</td><td>84</td><td>84</td><td>89</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P17</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>106</td><td>79</td><td></td><td>87</td><td>88</td><td></td><td>89</td><td>82</td><td>106</td><td>107,5</td><td>107,5</td><td>112,3</td></tr><tr><td>RSSI detected by 'C'</td><td>80</td><td>98</td><td></td><td>106</td><td>79</td><td></td><td>87</td><td>88</td><td></td><td>89</td><td>82</td><td></td><td></td><td></td><td></td></tr><tr><td colspan="2">Average values</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>123,98</td><td>127,506</td><td>129,805</td><td>133,5</td></tr></tbody></table>

* VMR (A): Let Vi be the upper value between the RSSI value of detecting 'C' by the node Ni and the RSSI value of detecting Ni by the node 'C' in a given position Pi considering the new nomad node's positions given by the algorithm A. VMR(A) is the average value of the RSSI, it is defined by dividing the sum of Vi by the total number of nodes detected by or detecting the node 'C'.

* The positions of nomad nodes and their corresponding values of RSSI in each location Pi are not mentioned in Tables A1 and A2. RSSI values in Table A1 and Table A2 are expressed in values between 0 and 255, not in dBm.
Appendix 1. RSSI and FER measures of in our experimental tests (Scenario 1)

<table><caption>Table A2 Averages of RSSI values by neighbours of 'C' in different positions overnight.</caption><thead><tr><th>vs</th><th></th><th>N1</th><th>N2</th><th>N3</th><th>N4</th><th>N5</th><th>N6</th><th>N7</th><th>N8</th><th>N9</th><th>N10 (A)</th><th>N11 (B)</th><th>VMR(Initial deployment)</th><th>VMR(e-NSGA-II-AxN-AmN)</th><th>VMR(U-NSGA-III-AxN-AmN)</th><th>VMR(mMOEA/DD-AxN-AmN)</th></tr></thead><tbody><tr><td rowspan="2">P1</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td>135</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>120,5</td><td>116,4</td><td>118,9</td><td>126,7</td></tr><tr><td>RSSI detected by 'C'</td><td>89</td><td>106</td><td>104</td><td>170</td><td>102</td><td>91</td><td>91</td><td>98</td><td>79</td><td>99</td><td>93</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P2</td><td>RSSI generated by 'C'</td><td>129</td><td>129</td><td></td><td>134</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>121,125</td><td>121,125</td><td>121</td><td>129,5</td></tr><tr><td>RSSI detected by 'C'</td><td>107</td><td>104</td><td>103</td><td>169</td><td>104</td><td></td><td>93</td><td>118</td><td>100</td><td>117</td><td>98</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P3</td><td>RSSI generated by 'C'</td><td>131</td><td>132</td><td>130</td><td>109</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>133,4</td><td>134,28</td><td>131,4</td><td>139,2</td></tr><tr><td>RSSI detected by 'C'</td><td>104</td><td>118</td><td>120</td><td>156</td><td>85</td><td>81</td><td>89</td><td>118</td><td>90</td><td>94</td><td>81</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P4</td><td>RSSI generated by 'C'</td><td>128</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>114,5</td><td>114,5</td><td>115</td><td>119,8</td></tr><tr><td>RSSI detected by 'C'</td><td>118</td><td>87</td><td>101</td><td>123</td><td>93</td><td>90</td><td>82</td><td>106</td><td>82</td><td>82</td><td>81</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P5</td><td>RSSI generated by 'C'</td><td>129</td><td></td><td></td><td>137</td><td>118</td><td></td><td></td><td></td><td></td><td></td><td></td><td>125,5</td><td>126,09</td><td>128,4</td><td>132,9</td></tr><tr><td>RSSI detected by 'C'</td><td>117</td><td>110</td><td>125</td><td>148</td><td>112</td><td>102</td><td>81</td><td>150</td><td>87</td><td>116</td><td>97</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P6</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>106</td><td>108,66</td><td>107,2</td><td>111,8</td></tr><tr><td>RSSI detected by 'C'</td><td>76</td><td>82</td><td>68</td><td>110</td><td>76</td><td>85</td><td></td><td>102</td><td></td><td>77</td><td>72</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P7</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>117,2</td><td>117,33</td><td>121,6</td><td>126,3</td></tr><tr><td>RSSI detected by 'C'</td><td>95</td><td>106</td><td>82</td><td>111</td><td>128</td><td>92</td><td>75</td><td>124</td><td>77</td><td>109</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P8</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>112</td><td>114,5</td><td>118,8</td><td>124,4</td></tr><tr><td>RSSI detected by 'C'</td><td>73</td><td>82</td><td>79</td><td>118</td><td>106</td><td>83</td><td>75</td><td>98</td><td>77</td><td>98</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P9</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>105</td><td>107,75</td><td>110,7</td><td>116,6</td></tr><tr><td>RSSI detected by 'C'</td><td>92</td><td>76</td><td>75</td><td>100</td><td>96</td><td>80</td><td></td><td>110</td><td>72</td><td>98</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P10</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td>134</td><td></td><td></td><td></td><td></td><td></td><td></td><td>117,66</td><td>122,5</td><td>125,6</td><td>133,3</td></tr><tr><td>RSSI detected by 'C'</td><td>73</td><td>85</td><td>79</td><td>93</td><td>123</td><td>71</td><td></td><td>107</td><td>76</td><td>112</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P11</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>128</td><td>137,6</td><td>140,3</td><td>145,5</td></tr><tr><td>RSSI detected by 'C'</td><td>75</td><td>95</td><td>99</td><td>119</td><td>118</td><td></td><td></td><td>97</td><td></td><td>115</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P12</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>113</td><td>115,7</td><td>113,8</td><td>119,8</td></tr><tr><td>RSSI detected by 'C'</td><td>85</td><td>87</td><td>74</td><td>123</td><td>74</td><td>76</td><td>86</td><td>103</td><td>72</td><td>78</td><td>78</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P13</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td>123</td><td></td><td></td><td></td><td></td><td></td><td></td><td>110,25</td><td>120,28</td><td>112,5</td><td>118,5</td></tr><tr><td>RSSI detected by 'C'</td><td>31</td><td>90</td><td>118</td><td>157</td><td>104</td><td>92</td><td>85</td><td>111</td><td>90</td><td>108</td><td>82</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P14</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>118,66</td><td>128,75</td><td>133,4</td><td>131,9</td></tr><tr><td>RSSI detected by 'C'</td><td>102</td><td>80</td><td>102</td><td>185</td><td>74</td><td></td><td>106</td><td>111</td><td>94</td><td>79</td><td>106</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P15</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td>137</td><td></td><td></td><td>143</td><td></td><td></td><td></td><td>130,8</td><td>136,85</td><td>139,8</td><td>144,2</td></tr><tr><td>RSSI detected by 'C'</td><td>90</td><td>74</td><td>106</td><td>169</td><td>80</td><td></td><td>129</td><td>77</td><td>119</td><td>77</td><td>117</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P16</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>118</td><td>121,33</td><td>126,7</td><td>129,6</td></tr><tr><td>RSSI detected by 'C'</td><td>73</td><td>76</td><td>72</td><td>118</td><td>88</td><td></td><td>81</td><td>72</td><td>73</td><td>73</td><td>86</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P17</td><td>RSSI generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>118</td><td>120</td><td>120,8</td><td>127,8</td></tr><tr><td>RSSI detected by 'C'</td><td>73</td><td>75</td><td>74</td><td>118</td><td>91</td><td></td><td>79</td><td>79</td><td>82</td><td>94</td><td>79</td><td></td><td></td><td></td><td></td></tr><tr><td colspan="2">Average values</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>117,973</td><td>121,746</td><td>122,7</td><td>128,105</td></tr></tbody></table>

<table><caption>Table A3 Averages of FER values by neighbours of 'C' in different positions during day</caption><thead><tr><th>\</th><th></th><th>N1</th><th>N2</th><th>N3</th><th>N4</th><th>N5</th><th>N6</th><th>N7</th><th>N8</th><th>N9</th><th>N10 (A)</th><th>N11 (B)</th><th>VMF (Initial deployment)</th><th>VMR(e-NSGA-II-AxN-AmN)</th><th>VMR(U-NSGA-III-AxN-AmN)</th><th>VMR(mMOEA/DD-AxN-AmN)</th></tr></thead><tbody><tr><td rowspan="2">P1</td><td>FER generated by 'C'</td><td></td><td></td><td></td><td>0,244</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,1287</td><td>0,0878</td><td>0,0868</td><td>0,0785</td></tr><tr><td>FER detected by 'C'</td><td>0,661</td><td>0,037</td><td>0,459</td><td>0,013</td><td>0,684</td><td></td><td>0,684</td><td>0,49</td><td>0,581</td><td>0,105</td><td>0,045</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P2</td><td>FER generated by 'C'</td><td></td><td>0</td><td></td><td>0,115</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,35392</td><td>0,31194</td><td>0,3</td><td>0,28</td></tr><tr><td>FER detected by 'C'</td><td>0,356</td><td>0,171</td><td>0,196</td><td>0,006</td><td>0,144</td><td>0,8</td><td>0,464</td><td>0,168</td><td>0,891</td><td>0,21</td><td>0,74</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P3</td><td>FER generated by 'C'</td><td></td><td>0,507</td><td></td><td>0,292</td><td>0,929</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,32305</td><td>0,32305</td><td>0,301</td><td>0,268</td></tr><tr><td>FER detected by 'C'</td><td>0,048</td><td>0,1</td><td>0,7</td><td>0,006</td><td>0,057</td><td>0,972</td><td>0,121</td><td>0,051</td><td>0,784</td><td>0,141</td><td>0,847</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P4</td><td>FER generated by 'C'</td><td></td><td>0,051</td><td></td><td>0,203</td><td>0,857</td><td></td><td></td><td>0,877</td><td>0,052</td><td>0,314</td><td>0,069</td><td>0,333</td><td></td><td></td><td></td><td></td></tr><tr><td>FER detected by 'C'</td><td>0,060</td><td>0,855</td><td>0,097</td><td>0,082</td><td>0,049</td><td>0,126</td><td>0,877</td><td>0,052</td><td>0,314</td><td>0,069</td><td>0,333</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P5</td><td>FER generated by 'C'</td><td></td><td></td><td></td><td>0,914</td><td></td><td></td><td></td><td>0,352</td><td></td><td></td><td></td><td>0,21201</td><td>0,17811</td><td>0,145</td><td>0,102</td></tr><tr><td>FER detected by 'C'</td><td>0,218</td><td>0,208</td><td>0,260</td><td>0,028</td><td>0,198</td><td>0,553</td><td>0,912</td><td>0,024</td><td>0,31</td><td>0,172</td><td>0,936</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P6</td><td>FER generated by 'C'</td><td></td><td></td><td></td><td>0,977</td><td></td><td></td><td></td><td>0,913</td><td></td><td></td><td></td><td>0,379925</td><td>0,261708</td><td>0,2734</td><td>0,23481</td></tr><tr><td>FER detected by 'C'</td><td>0,043</td><td>0,66</td><td>0,132</td><td>0,016</td><td>0,030</td><td>0,224</td><td>0,956</td><td>0,017</td><td>0</td><td>0,031</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P7</td><td>FER generated by 'C'</td><td></td><td></td><td></td><td>0,968</td><td></td><td></td><td></td><td>0,951</td><td></td><td></td><td></td><td>0,20183</td><td>0,216775</td><td>0,18</td><td>0,12</td></tr><tr><td>FER detected by 'C'</td><td>0,202</td><td>0,215</td><td>0,5</td><td>0,009</td><td>0,017</td><td>0,108</td><td>0</td><td>0,009</td><td>0,666</td><td>0,023</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P8</td><td>FER generated by 'C'</td><td></td><td></td><td></td><td>0,948</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,129375</td><td>0,1048333</td><td>0,164</td><td>0,092</td></tr><tr><td>FER detected by 'C'</td><td>0,452</td><td>0,236</td><td>0,522</td><td>0,008</td><td>0,015</td><td>0,175</td><td></td><td>0,007</td><td>0,744</td><td>0,016</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P9</td><td>FER generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,0096</td><td>0,0087</td><td>0,0139</td><td>0,0084</td></tr><tr><td>FER detected by 'C'</td><td>0,8</td><td>0,59</td><td>0,866</td><td>0,009</td><td>0,017</td><td>0</td><td></td><td>0,052</td><td></td><td>0,042</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">P10</td><td>FER generated by 'C'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,1097</td><td>0,09468</td><td>0,078</td><td>0,083</td></tr></tbody></table>