A large fraction of studies on GAs emphasize finding a globally optimal solution. Some other investigations have also been made for detecting multiple solutions. If a global optimal solution is very sensitive to noise or perturbations in the environment then there may be cases where it is not good to use this solution. In this paper, we propose a new scheme which extends the application of GAs to domains that require the discovery of robust solutions. Perturbations are given to the phenotypic features while evaluating the functional value of individuals, thereby reducing the chance of selecting sharp peaks (i.e., brittle solutions). A mathematical model for this scheme is also developed. Guidelines to determine the amount of perturbation to be added is given. We also suggest a scheme for detecting multiple robust solutions. The effectiveness of the scheme is demonstrated by solving different one-and two-dimensional functions having broad and sharp peaks.

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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 a 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 the view point of sampling bias and perform a comparative 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 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.