Application of Genetic Algorithm in Multi-objective Optimization

List of Illustrations
Figure 3.1: (a) Top view and (b) Isometric view of the indeterminate plate…………………….…45
Figure 3.2: (a) Balanced reactive forces with smaller enclosed area and (b) Bigger enclosed area with
unbalanced reactive forces………………………………………………………………………46
Figure 3.3: (a) Location of three supports which generates an area on the surface (b) heuristically
calculated maximum possible area with equal reaction forces in all
supports…………………………………………………………………………………...……50
Figure 3.4: Modified test case with circular discontinuities…………………………………...…..53
Figure 4.1: (a) Differences among reactive forces and (b) enclosed area by support locations for
“Continuous Method”………………………………………………………………………….58
Figure 4.2: Optimum objective value obtained by using “Continuous Method” from 30
runs…………………………………………………………………………………………….59
Figure 4.3: Solution space for (a) continuous method and (b) discretized method………………60
Figure 4.4: Optimum objective value obtained by using two
methods………………………….……………………………………………………………..64
Figure 4.5 (a) Distribution of optimal area value and (b) reaction differences by two
methods………………………………………………………………………………………...65
Figure 4.6: Graph of minimum (best) objective value vs generation number for continuous and
discretized method……………………………………………………………………………..67
Figure 4.7: Indeterminate structure with (a) previous discontinuous areas (b) 25% increased circular
discontinuities and (c) 50% increased circular discontinuities…………………………………..69
Figure 4.8: Results after applying three different penalty functions- flat, linear and nonlinear…………………………………………………………………………………………..70
Figure 4.9: Objective functions for the three penalty functions after increasing the discontinuous
space by (a) 25% and (b) 50%..................................................................................................................72
Figure 4.10: Steps followed in coded discretized algorithm……………………………………74
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