Hybrid Evolutionary Multi-Objective Optimization with Enhanced Convergence and Diversity

Sindhya, Karthik Hybrid Evolutionary Multi-Objective Optimization with Enhanced Convergence and Diversity Jyväskylä: University of Jyväskylä, 2011, 64 p.(+included articles) (Jyväskylä Studies in Computing ISSN 1456-5390; 131) ISBN 978-951-39-4372-1 Finnish summary Diss. Evolutionary multi-objective optimization (EMO) algorithms, commonly used to find a set of solutions representing the Pareto optimal front, are often criticized for their slow convergence, the lack of a theoretical convergence proof and for having no efficient termination criterion. In this thesis, the main focus is to improve EMO algorithms by addressing the criticisms. Hybrid EMO algorithms defined as hybrids of EMO algorithms and a local search procedure are proposed to overcome the criticisms of EMO algorithms. In the local search procedure, a local search operator originating from the field of multiple criteria decision making (involving solving an achievement scalarizing function based optimization problem using an appropriate mathematical optimization technique) is used to enhance the convergence speed of a hybrid EMO algorithm. A hybrid framework, a base on which hybrid EMO algorithms can be built, is also proposed incorporating a local search procedure, an enhanced diversity preservation technique and a termination criterion. As a case study, a hybrid EMO algorithm based on the hybrid framework is successfully used to find Pareto optimal solutions desirable to a decision maker in the optimal control problem of a continuous casting of steel process. In addition, a hybrid mutation operator consisting of both non-linear curve tracking mutation and linear differential evolution mutation operators is proposed to handle various interdependencies between decision variables in an effective way. The efficacy of the hybrid operator is demonstrated with extensive numerical experiments on a number of test problems. Furthermore, a new progressively interactive evolutionary algorithm (PIE) is proposed to obtain a single solution desirable to the decision maker. Here an evolutionary algorithm is used to solve scalarized problems formulated using the preference information of the decision maker. In PIE, the decision maker moves progressively towards her/his preferred solution by exploring and examining different solutions and does not have to trade-off between the objectives.