Generation of Pareto Frontier by Genetic Algorithms

Abstract

Recently, multiobjective optimization methods using evolutionary methods such as genetic algorithms have been studied actively by many researchers [4, 23, 24, 30, 33, 37, 44, 49, 58, 107–109, 127, 145, 157, 158, 165]. These approaches are useful for generating Pareto frontiers in particular with two or three objective functions, and decision making can be easily performed on the basis of visualized Pareto frontier. In generating Pareto frontiers by evolutionary methods, there are two main issues of the convergence and the diversity (1) how to guide individuals to the real Pareto frontier as close and fast as possible and (2) how to keep the diversity of individuals spreading over the whole of Pareto frontier at the final generation. The convergence and the diversity of individuals are closely related to fitness evaluation for each individual and density estimation in a population. In this chapter, we describe several techniques for fitness evaluation and density estimation, and introduce representative algorithms using genetic algorithm.