MULTIMODAL OPTIMIZATION USING NICHING GENETIC ALGORITHMS

Abstract

Interest in multimodal optimization is expanding rapidly since real-world optimization problems often require the location of multiple optima in the search space. Multimodal optimization provides multiple solutions for problems with multimodal search space. In this thesis, multimodal optimization using genetic algorithms with various niching methods is investigated. First, the performance of various niching methods of genetic algorithms is compared in the optimization of three categories of multimodal functions. This comparison shows that among the three niching methods investigated in this research, sharing, crowding and clearing, the clearing method outperforms the other two niching methods for the test functions. The portfolio optimization problem serves as the case study for this research to do multimodal optimization. It is addressed by using genetic algorithms with the clearing method. Quadratic programming, the traditional method for portfolio optimization, can produce only one optimal portfolio, whereas clearing genetic algorithms are able to produce multiple portfolios. There are three main observations from this study. 1) The portfolio optimization problem constructed based on mean variance analysis is shown to be multimodal; that is besides the optimal portfolio there is a family of near optimal portfolios with similar performance but different constituents. 2) With respect to the transaction costs incurred by portfolio turnover, after portfolio adjustment the resulting portfolio that is most similar to the previous portfolio is considered preferable. An investor is allowed to choose such a portfolio from a pool of portfolios with similar performance. 3) Genetic algorithms with specially designed operators such as crossover and mutation can handle general constraints involved in portfolio optimization effectively. Additionally, issues on setting niching parameters and large-size optimization are discussed. As the size of the optimization problem is always an important concern, the fine local tuning technique is tailored to allow genetic algorithms to handle largescale numerical optimization problems. In this research, the portfolio optimization problem is selected to serve us the case study; most of the techniques used and proposed in this research can be modified and then employed to address other optimization problems with similar properties.