Then, solutions with the highest the site weighted objective from the obtained Pareto solutions are shown in Table 8. Table 8Results for MOEA with HDE, DE, and GA (w1 varies).Table 7 shows that values of each target F1 and F2 change correspondently when w1 varies, which means that different settings of the weight will result in different decisions. Moreover, when the weight of the first objective (total cost) equals 0.1, the solution is the best. When the difference between w1 and w2 becomes smaller, the solutions become worse. Table 8 implies a similar conclusion for HDE, DE, and GA.From the comparisons for specific solutions, the following conclusion can be easily drawn: (1) HDE is better than DE or GA no matter whether LP or MOEA is adopted: HDE and DE are more suitable than GA when LP is used; HDE and GA are better than DE when MOEA is used.

(2) Different weights for objectives will influence the solutions, for the conflicted objectives, and the assigned weights with large ratios (i.e., w1:w2 �� 3:1) may result in better solutions.5.3. Nondominated Solution Analysis of MOEAFor the MOP, there have several metrics to evaluate the quality of the nondominated solutions (Robi? and Filipi? [38]). However, the implementation of most metrics needs a prerequisite; that is, the true Pareto front must be known. In this study, it is impossible to find the true Pareto front because the MSJRD is a practical problem. So we adopt the metric (Spacing, SP) used by Esparcia-Alc��zar et al. [39, 40] to measure the distribution of solutions on the Pareto front by evaluating the variance of neighboring solutions.

The lower value of SP means that better nondominated solution is obtained.SP measures the relative distances between the members of Pareto front asSP=��i=1n(d??di)2(n?1),(21)where n is the number of the first nondominated solutions found. The distance di is given bydi=minj(|f1i(x)?f1j(x)|+|f2i(x)?f2j(x)|),??i,j=1,…,n,(22)where fNk(?) is the fitness of point k on objective N and d- is the mean of all di. Table 9 shows the mean and variance of SP by 10 runs using MOEA. Table 9Statistical analysis of SP by 10 runs.Table 9 shows that the mean and variance of SP obtained by HDE is the lowest, and corresponding values obtained by DE are biggest. That is to say, HDE is better than DE and GA for the MOEA method. The conclusion is consistent with Section 5.2.

At the same time, it verifies that the conversion using weights for the MSJRD is feasible.In order to have a better understanding of the solutions’ distribution of the last generation, the entire nondominated fronts found by HDE, DE, and GA are presented from Figure 2 to Figure 4.Figure 2Nondominated solutions of the final population Brefeldin_A obtained by HDE.Figure 4Nondominated solutions of the final population obtained by GA.Figures Figures2,2, ,3,3, and and44 show that HDE and GA are capable of obtaining Pareto solutions, while the effectiveness and distribution of solutions are much worse for DE.