Evolutionary Algorithms for Solving Multi-Objective Problems


The solving of multi-objective problems (MOPs) has been a continuing effort by humans in many diverse areas including computer science, engineering, economics, finance, industry, physics, chemistry, and ecology, among others. Many powerful deterministic and stochastic techniques for solving these large dimensional optimization problems have risen out of operations research, decision science, engineering, computer science and other related disciplines. The explosion in computing power continues to arouse extraordinary interest in stochastic search algorithms that require high computational speed and very large memories. A generic stochastic approach is that of evolutionary algorithms (EAs). Such algorithms have been demonstrated to be very powerful and generally applicable for solving difficult single objective problems. Their fundamental algorithmic structures can also be applied to solving many multi-objective problems. In this book, the various features of multi-objective evolutionary algorithms (MOEAs) are presented in an innovative and unique fashion, with detailed customized forms suggested for a variety of applications. Also, extensive MOEA discussion questions and possible research directions are presented at the end of each chapter.

Based upon the original contributions of Darwin and Mendel, evolution occurs through natural selection and adaptation. Using this basic biological model, various evolutionary algorithm structures have been developed. Single objective EAs and in particular genetic algorithms (GAs), evolutionary programming (EP) and evolution strategies (ES) have been shown to find if not the optimal solution something that is satisfactory; i.e. "satisfices'' the user. The goal of course is to search the associated objective/fitness function landscape (phenotype space) through exploration and exploitation for the "optimal'' solution. Such activity is controlled through the use of biologically inspired "mating'', "mutation'' and "selection'' operators. Specific evolutionary algorithm development involves the encoding of the independent variables (genotype) and the structuring of specific parametric mating, mutation, and selection operators. These operators manipulate each genotype individual appropriately as the search proceeds through the phenotype landscape.

The design of innovative evolutionary algorithmic approaches for multi-objective problems is built upon the research and development for single objective functions. Understanding this body of knowledge lends insight to the design and implementation of MOEAs. The use of MOEAs requires insight not only of the algorithmic domain, but also knowledge of the application problem domain. This monograph addresses such variations in the development of multi-objective evolutionary algorithms (MOEA), associated theory, appropriate multi-objective problems (MOPs) for MOEA testing, and experience with real-world applications. Many references are included and suggested for further reading.

Applying the fundamental concepts of MOEAs to real-world problems was initially a curiosity, but today is a common trend. By using the concepts and techniques presented in this book one can obtain insight into the selection of an MOEA software platform and associated tuning of the various operator parameters for complex applications. Moreover, most complex real-world applications have side constraints which requires MOEA tailoring in searching the fitness landscape. This book attempts to address all these issues through the following features:

The flow of material in each chapter is intended to present a natural and comprehensive development of MOEAs from basic concepts to complex applications. As previously stated, at the end of each chapter a list of possible research topics is given along with a number of pertinent discussion questions.