# A Multi-Objective Harmony Search Algorithm for Sustainable Design of Floating Settlements +
## 4 Computational Results and Discussion  
The MOHS algorithm is run on an Intel (R) Core (TM) i5-3210M CPU @2.50 GHz computer with 4 GB of RAM. We compare the MOHS algorithm to the JDE algorithm in [6] as mentioned before. The population size is taken as 100 for both algorithms. Both algorithms performed 100 generations for each run. We took five runs for each algorithm with a different seed number. In order to analyze the performance of algorithms, we employ the hypervolume (HV), measuring the volume of the non-dominated portion of the objective space, as a performance metric [18]. Among the five replications with different numbers (S), we report the best, median, worst, and standard deviation values at generation 100 as given in Table 1 for JDE and MOHS algorithms, respectively. In addition, the line plot of HV values for both algorithms is given in Figure 9.  
As seen in Table 1 and Figure 9, both algorithms have a good performance in 100 generations for the best, median, worst, and Std values of HV. In addition, the proportions of non-dominated solutions are similar. The MOHS algorithm was slightly more robust than the JDE algorithm because the standard deviation was slightly smaller. These values are very close to each other because both algorithms employ the non-dominated sorting procedure and constrained-domination principle borrowed and adopted for JDE and MOHS algorithms from NSGA-II.  
The chart of the non-dominated solutions (\(f_{1}\ front\)) for the JDE algorithm at generation 100 and MOHS at generation 100 can be seen in Figures 10 and 11, respectively. Since we have a feasible set of solutions, the seed number 3 is selected for the JDE algorithm, and seed number 2 is selected for the MOHS algorithm. Additionally, in each figure, we pick three solutions. They represent different design alternatives generated by the algorithms for the decision-maker.  
In the first selected solution from the JDE algorithm in Figure 12, wind protection for houses is satisfied but it is not valid for the visibility of the yacht marina. On the other hand, accessibility is very high and the visibility of the yacht club is satisfying. For the second selected solution in Figure 13, privacy is good for both houses and the yacht marina, but there is an interesting placement between houses since different modules of houses are far away from each other. Although the visibility value is higher in this solution, one housing module prevents the visibility of the yacht club. The third selected solution from the JDE algorithm shown in Figure 14 has very poor wind protection. However, the yacht club is very noticeable and accessibility is satisfactory.  
Figure 11: 3D Scatter plot of the MOHS algorithm.  
Figure 12: The first selected solution from the JDE algorithm.  
Figure 10: Scatter plot of the JDE algorithm.  
If we consider the selected solutions from the MOHS algorithm, the most accessible solution, which is the first one, represents a different configuration than the one in the JDE algorithm, as seen in Figure 15. This is because, in this design alternative, all functions are coming together. For the second one chosen from the MOHS alternatives (Figure 16), all objectives are highly desirable. However, the third solution chosen from the MOHS algorithm is very similar to the second selected one, with only the location of one house unit seriously changed (Figure 17).  
Figure 14: The third selected solution from the JDE algorithm.  
Figure 13: The second selected solution from the JDE algorithm.  
Figure 16: The second selected solution from the MOHS algorithm.  
Figure 17: The third selected solution from the MOHS algorithm.  
Figure 15: The first selected solution from the MOHS algorithm.