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250 Massimiliano Vasileproblems were taken from [4] and [3] and listed in Tab. 1. EPIC was compared to MPSO,NSGA-II and PAES in terms of number of function evaluations and of average distance fromthe optimal Pareto set (metric M 1 in [3]).Test function 1 is one-dimensional and has a disconnectedPareto set made of 2 subsets. EPIC was run with 5 exploring agents and a totalpopulation of 10 agents. The number of function evaluations was fixed to 600. Test function 2has a disconnected Pareto set made of 4 subsets. In this example, 5 exploring agents were usedover a total number of 10 agents in the population. The total number of function evaluationswas fixed to 3000. Test function 3 has 60 local Pareto fronts for q = 1 and n = 2 while has 21 9local Pareto fronts with n = 10 and q = 2. The maximum number of function evaluations wasfixed to 3000 for n = 2 and to 20000 for n = 10 and the number of exploring agents was 3 overa population of 5.Table 1.Multiobjective test functions8−x if x ≤ 1>:−4 + x if x > 4x ∈ [−5, 10]Deb f 1 = x 1h “ ”x 1, x 2 ∈ [0, 1]α ixf 2 = (1 + 10x 2) 1 − 11+10x 2−x 11+10x 2sin(2πqx 1)α = 2;. q = 4T4g = 1 + 10(n − 1) + P ni=2 [x2 i − 10cos(2πqx i)]; h = 1 −f 1 = x 1; f 2 = ghqf 1gx 1 ∈ [0, 1]; x i ∈ [−a, a]i = 2, . . . , nThe objective space for a typical run of EPIC is represented in Fig. 1 for all the three testfunctions. The results for the performance index M 1 averaged over 30 runs are summarisedin Tab. 2 and compared to MPSO, PAES and NSGA-II (the standard deviation is reportedin brackets). In [4] the three algorithms were run for a maximum of 4000, 1200 and 3200function evaluations respectively on case Deb, Scha and T4 with q = 1,n = 2 and a = 30.Then the average value µ M1 =1.542e-3 and the standard deviation σ M1 =5.19e-4 of M 1 over 20runs of EPIC on problem T4 with q = 2,n = 10 and a = 5 was compared to the results in [5]for NSGA-II(µ M1 =0.513053 σ M1 =0.118460),SPEA (µ M1 =7.340299 σ M1 =6.572516)and PAES(µ M1 =0.854816 σ M1 =0.527238). In should be underlined that, for this test function, in all the20 runs, EPIC converged to the global Pareto front.f 216128EPICOptimal Pareto Frontf 210.5EPICOptimalPareto Frontf 210.80.6Optimal Pareto FrontEPIC400.40.20−1 −0.5 0 0.5 1f 1−0.50 0.2 0.4 0.6 0.8 1f 100 0.2 0.4 0.6 0.8 1f 1Figure 1.Pareto fronts for the three test functions, Scha on the left, Deb in the middle, T4 on the right.5.1 Multi Gravity Assist TrajectoriesA common problem in space mission analysis is the optimal design of transfer trajectories exploitingone or more gravity assist manoeuvres (MGA) to change the orbital parameters of aspacecraft. Each gravity manoeuvre occurs at a planet and exploits the gravity action of the