Seminaire Bourbaki, 37, 1994-1995 - Exp.790-804 by Bourbaki N. PDF

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Note that Pareto subset sizes differ here. Needless to say, we are aware of the weaknesses of these test instances since they exploit only one type of symmetry and since they are defined only for two dimensions in search and objective space. But as can be seen shortly, these simple test problems can be used to demonstrate interesting phenomena occurring in standard EMOA and some special purpose EMOA presented here. 2 41 Experimental Investigation of Problem Hardness In the following sections, several EMOA are tested for their ability to reach and preserve many or all existing Pareto subsets.

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Fm (x) = ⎝ ... ⎠ = ⎝ ⎠ . 2 fm (x) (x − cm ) ⎛ (6) The c1 , . . , cm ∈ IRn are constant values. The special problem F2 (x), as defined in Equation (7), has constants c1 = (0, 0)T and c2 = (2, 0)T while F3 (x), see Equation (8), has constants c1 = (0, 0, 0)T , c2 = (2, 0, 0)T , and c3 = (0, 0, 2)T . Both problems are convex and the corresponding Pareto sets are defined by a single line given as 0 ≤ x1 ≤ 2 and x2 = 0 as well as a triangular shaped plain spanned between (0,0,0), (2,0,0), and (0,0,2) respectively.

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Seminaire Bourbaki, 37, 1994-1995 - Exp.790-804 by Bourbaki N.

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