and many others for their assistance in generating computational results and reviewing various aspects of the material. We also thank to all those researchers who agreed to send us some of their research papers and theses to enrich the material contained in this book. We express our sincere appreciation to Prof. David E. Goldberg for including this book as a volume in Kluwer's International Series on Genetic Algorithms and Evolutionary Computation. Also, it has been a pleasure working with Kluwer's professional editorial and production staff. We particularly thank Ana Bozicevic, Ann Bolotin and Christopher Kula for their prompt and kind assistance at all times during the development of this book.We would also like to thank the other primary MOEA researchers not only for their innovative papers but for various conversations providing more insight to developing better algorithms. Such individuals include David Come, Dragan

Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of current research and applications. Recommended MOEA designs are presented, along with conclusions and recommendations for future work.

Solving optimization problems with multiple (often conflicting) objectives is generally a quite difficult goal. Evolutionary Algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade a multiplicity of Multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define and execute a quantitative MOEA performance comparison methodology. Almost all comparisons cited in the current literature visually compare algorithmic results, resulting in only relative conclusions. Our methodology gives a basis for absolute conclusions regarding MOEA performance. Selected results from its execution with four MOEAs are presented and described.

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