Progressively Interactive Evolutionary Multi-Objective Optimization ...

F2
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1
F1
Figure 28: Final archive solutions for
problemDS4.
F2
2
1.5
1
0.5
0
0 0.5 1
F1
1.5 2
Figure 30: Final archive solutions for
problemDS5.
F2
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1
F1
Figure 29: Attainment surfaces(0%, 50%
and100%)forproblemDS4from21runs.
F2
2
1.5
1
0.5
0
0 0.5 1
F1
1.5 2
Figure 31: Attainment surfaces(0%, 50%
and100%)forproblemDS5from21runs.
terminationcriterion(ǫu = 0.0001)andthesameneededexclusivelyforthelowerlevel
optimization task, which includes the local search. Table 1 shows these values for the
best, median and worst of 21 simulation runs for all eight problems. It is clear from
thetablethatthemostofthecomputationaleffortsarespentinthelowerlevelsolution
evaluations. Despite our efforts being differentfromanested algorithm in not solving
a lower level problem all the way for every upper level solution, the nature of bilevel
programming problem demands that the lower level optimization task must be emphasized.
The use of archive in sizing lower level subpopulations in a self-adaptive
mannerandtheuseofacoarseterminatingconditionforlowerleveloptimizationtask
enabled our algorithm to use comparatively smaller number of function evaluations
than that would be needed in a nested algorithm. We compare the function evalua-
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