Genetic algorithms with a robust solution searching scheme

Abstract
A large fraction of studies on genetic algorithms (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.