Search space boundary extension method in real-coded genetic algorithms

In real-coded genetic algorithms (GAs), some crossover operators do not wor k well on functions which have their optimum at the corner of the search sp ace. To cope with this problem, we have proposed a boundary extension metho d which allows individuals to be located within a limited space beyond the boundary of the search space. In this paper, we give an analysis of the bou ndary extension methods from the viewpoint of sampling bias and perform a c omparative study on the effect of applying two boundary extension methods, namely the boundary extension by mirroring (BEM) and the boundary extension with extended selection (BES). We were able to confirm that to use samplin g methods which have smaller sampling bias had good performance on both fun ctions which have their optimum at or near the boundaries of the search spa ce, and functions which have their optimum at the center of the search spac e. The BES/SD/A (BES by shortest distance selection with aging) had good pe rformance on functions which have their optimum at or near the boundaries o f the search space. We also confirmed that applying the BES/SD/A did not ca use any performance degradation on functions which have their optimum at th e center of the search space. (C) 2001 Elsevier Science Inc. All rights res erved.