# A Novel Genetic Algorithm for the Synthetical Sensor-Weapon-Target Assignment Problem
## 4 Experimental Studies
### Experimental Settings  
The experiments are performed on a personal computer with i7-2.5 GHz CPU and 8 GB memory. All algorithms are written by Matlab. In our experiments, twenty-five S-WTA test instances are used for comparing GA-SWTA with MRBCH, Swt-opt and ds-GA. As these instances are carefully designed by [PERSON] et al. [28] and generated with different scales and features, they can comprehensively examine the performance of the proposed algorithm. These instances and their features are shown in Table 3. Detailed data of these instances, such as the threat value of target, the constrains of sensors cost, and so on, are available online [28].  
In these experimental studies, all parameters of the MRBCH algorithm and Swt-opt algorithm are the same as the by the authors of [28]. In addition, for our proposed algorithm, the population size is \(pop=100\), the selection method is the roulette wheel selection, the crossover probability is \(pc=0.8\), and the mutation probability is \(pm=0.4\). The crossover probability and the mutation probability are the recommended settings in the work by the authors of [13].  
For the ds-GA algorithm, the population size \(pop=100\), the crossover probability \(pc=0.1\), and the mutation probability \(pm=0.8\), \(a_{\max}=0.95\), \(a_{\min}=0.5\), \(\beta_{\max}=0.5\) and \(\beta_{\min}=0.05\). All the parameters are the recommended settings in paper [27]. Furthermore, in ds-GA, the penalty function is used for constraint handling. However, in this paper, as the proposed S-WTA model is different from the one in ds-GA, the penalty function should be redesigned to make it can be suitable for our proposed algorithm. We use the general constraint handling rules of the penalty function [39], which are also used in ds-GA, to redesign the penalty function. In this way, as the redesigned function can maintain the same characteristics as the original function, the performance of the algorithm is not greatly affected. The penalty function of the \(i\)th individual is shown as  
\[\left\{\begin{array}{l}{f^{\prime}}_{i}(x,y)=f_{i}(x,y)-g(x,y)\\ \\ {g(x,y)=\left\{\begin{array}{l}0,\text{ the constraints are satisfied}\\ \min\left\{F(x,y)\right\},\text{ otherwise}\\ \end{array}\right.}\\ \\ {F(x,y)=\left\{f_{1}(x,y),\cdots,f_{pop}(x,y)\right\},}\end{array}\right. \tag{7}\]  
where \(f_{i}(x,y)\) is the fitness of the \(i\)th individual, \(f^{\prime}_{i}(x,y)\) is the penalized fitness, and \(F(x,y)\) is the fitness set of the populations.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Instance** & **M** & **W** & **N** & **Instance** & **M** & **W** & **N** \\ \hline No. 1 & 5 & 4 & 3 & No. 14 & 26 & 23 & 17 \\ No. 2 & 4 & 5 & 7 & No. 15 & 24 & 22 & 21 \\ No. 3 & 6 & 6 & 6 & No. 16 & 28 & 23 & 19 \\ No. 4 & 9 & 8 & 8 & No. 17 & 23 & 19 & 30 \\ No. 5 & 10 & 7 & 12 & No. 18 & 25 & 20 & 28 \\ No. 6 & 13 & 11 & 9 & No. 19 & 40 & 40 & 40 \\ No. 7 & 17 & 14 & 12 & No. 20 & 62 & 50 & 30 \\ No. 8 & 19 & 14 & 15 & No. 21 & 67 & 72 & 54 \\ No. 9 & 15 & 18 & 21 & No. 22 & 85 & 72 & 67 \\ No. 10 & 19 & 23 & 16 & No. 23 & 100 & 90 & 80 \\ No. 11 & 20 & 22 & 15 & No. 24 & 150 & 130 & 120 \\ No. 12 & 21 & 18 & 20 & No. 25 & 180 & 170 & 160 \\ No. 13 & 20 & 28 & 23 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: The test instances and its features.  
As the MRBCH and Swt-opt algorithms are deterministic, the result is an invariable for the same instance. Therefore, both are performed only once. In addition, because our proposed algorithm and the ds-GA algorithm are GA-based algorithms, each run of the algorithms produces a different result. Therefore, we perform 30 independent runs on both of the algorithms for each instance. Meanwhile, we stop both of the algorithms until the best solutions found so far remain unchanged in 500 generations.