Tackling multimodal problems in hybrid genetic algorithms

A method is proposed to address the issue of multimodality while using hybrid genetic algorithms (GAs). The hybrid GA is one in which the fitness of an individual is determined as the fitness of the best individual found under local search. A simple modification of commonly used phenotypic sharing is proposed for better performance in this learning environment. Further, it is shown how more information from the local search can be used to achieve speed-up by relaxing fitness evaluations. The method has been used on a structural design problem which shows promising results. INTRODUCTION Hybrid genetic algorithms (HGAs) have emerged as a popular choice for real-world optimization. Combining the robustness and global nature of a GA search with an efficient local searcher tuned to the problem provides HGAs the power for solving large real-world applications. Despite growing usage in practice and research on some of the theoretical aspects, HGAs have been less frequently analyzed and designed for performance in explicitly multimodal problems. This is an important issue as many realworld problems are multimodal. This paper addresses the issue of multimodality when using HGAs. The commonly used niching via phenotypic sharing was found to perform less efficiently an individual is assigned the fitness of the best point found under local search. This provides the motivation for studying how to adapt phenotypic sharing to HGAs. Fortunately, it turns out that the key problem is easily resolved and is a natural extension of the traditional algorithm for sharing. Besides making use of the fitness of the best individual from local search, other information from local search can be exploited to build models of basins of attraction for a problem. This information helps us relax or skip some function evaluations which in turn helps us solve a problem faster. A description of the hybrid GA environment is given in the next section. In section 3, we introduce phenotypic fitness sharing and how it should be tweaked to work more efficiently in HGAs. Section 4 describes a sharing method for HGAs which makes use of information from local search to enable evaluation relaxation. The real-world application is described in section 5 followed by results in section 6 and some extensions in section 7. The paper concludes by summarizing the work and analyzing the proposed method. HYBRID GA FRAMEWORK In nature, every individual learns during its lifetime to adapt to the environment and as a result increases its chances of survival. These adaptations are often the result of an exploratory search (Hinton and Nowlan, 1987). Hybrid GAs make use of this idea of