Optimization of multimodal continuous functions using a new crossover for the real-coded genetic algorithms

In this study, a new crossover approach to the real-coded genetic algorithm is proposed. The approach is simply based on efficiently tuned real-coded crossover operation using the probability distribution function of Gauss distribution to generate rather dissimilar strings which may be candidates of possible solutions. Also linear and quadratic mapping algorithms comparatively used both to constrain individuals in the given search spaces and to produce different individuals in order to increase average fitness relatively for the same population. Moreover, to refine genetically found optimum points the local search technique based on Newton's method was performed. The designed software was first implemented on 11 well-known test functions and their results were compared with previous findings as shown in tables. In few test functions, the elitism operator was put into effect to maintain fitness stability helping increase the search performance of the proposed algorithm. The results indicate that the solutions to the test functions were almost the same with theoretical ones and the number of function evaluations for each test function was less than that obtained from using previous approaches. © 2008 Elsevier Ltd. All rights reserved.