OPTIMIZATION THROUGH GENETIC ALGORITHMS IN A CONTINUOUS SEARCH SPACE

Abstract

In different fields of science, real life problems are expressed into effective mathematical models that provide predictions for the behavior of the problem. Methods that serve this purpose are simulated annealing (SA), differential evolution (DE), particle swarm optimization (PSO), ant-colony optimization (ACO) and genetic algorithms (GAs) etc. These are collectively called the meta-heuristic algorithms that do not ensure the exact optimal solution rather to provide more near optimal results. Among these, GA is an intelligent optimization method to solve the non-convex, multi-modal optimization problems. The objective of this research is to use GA for optimization of complex nature, multi-modal and unconstrained optimization problems, represented in real encoding scheme. Operators are proposed to optimize the problem while maintaining an equilibrium of selection pressure and population diversity. Mimicking the natural biological process of evolution, GAs search for the global optima by retaining the fittest individuals at each generation. These healthy individuals undergo crossover process and thus better offspring are produced for next generation after matting. In this way, each generation possesses more good characteristic than the previous generation. Working with its three basic operators, i.e., selection, crossover and mutation, GA explores the search space of the most promising areas at each generation. Each operator plays a very important role in globally optimizing the problem in a way that selecting the best proportion of individuals, crossing among parents and mutation to bring diversity among individuals. This study mainly focuses the crossover operators but a significant contribution to a selection process is also given by proposing a selection operator. Their performance is evaluated and compared on the basis of multi-modal functions called the benchmark functions. Extensive simulation study is conducted and results are cross checked with the solutions given in peer reviewed literature. Other part of the thesis focuses on two crossover operators for function optimization. Results demonstrate the better performance of proposed operators as compared to other competing operators. The fifth chapter proposed the selection operator which is used in combination with traditional crossover and mutation operators. Analysis of the results through χ 2 goodness of fit test, the performance index and the statistics shows the ability of the proposed operator of not being trapped at the local optima. The MATLAB software is used to perform the study and obtain the results which are further compared with other studies