Sampling Bias and Search Space Boundary Extension in Real Coded Genetic Algorithms

In Real coded genetic algorithms, some crossover operators do not work well on functions which have their optimum at the corner of the search space. To cope with this problem, we have proposed boundary extension methods 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 boundary extension methods from a view point of the sampling bias and perform a comparative study on the effect of applying boundary extension methods, namely the BEM boundary extension by mirroring, the BES (boundary extension with extended selection). We were able to confirm that to use sampling methods which have smaller sampling bias had good performance on both functions which have their optimum at or near the boundaries of the search space, and functions which have their optimum at the center of the search space. The BES/SD/A (BES by shortest distance selection with aging) had good performance on functions which have their optimum at or near the boundaries of the search space. We also confirmed that applying the BES/SD/A did not cause any performance degradation on functions which have their optimum at the center of the search space. This feature of the BES/SD/A is very useful because when we solve some function optimization problems, we do not know the position of their optimal point.