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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

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After using evolutionary techniques for single-objective optimization during more than two decades, the incorporation of more than one objective in the fitness function has finally become a popular area of research. As a consequence, many new evolutionary-based approaches and variations of existing techniques have recently been published in the technical literature. The purpose of this paper is to summarize and organize the information on these current approaches, emphasizing the importance of analyzing the operations research techniques in which most of them are based, in an attempt to motivate researchers to look into these mathematical programming approaches for new ways of exploiting the search capabilities of evolutionary algorithms. Furthermore, a summary of the main algorithms behind these approaches is provided, together with a brief criticism that includes their advantages and disadvantages, degree of applicability, and some known applications. Finally, future trends in this area and some possible paths for further research are also addressed.

In this paper, we propose an algorithm based on the clonal selection principle to solve multiobjective optimization problems (either constrained or unconstrained). The proposed approach uses Pareto dominance and feasibility to identify solutions that deserve to be cloned, and uses two types of mutation: uniform mutation is applied to the clones produced and non-uniform mutation is applied to the "not so good" antibodies (which are represented by binary strings that encode the decision variables of the problem to be solved). We also use a secondary (or external) population that stores the nondominated solutions found along the search process. Such secondary population constitutes the elitist mechanism of our approach and it allows it to move towards the true Pareto front of a problem over time. Our approach is compared with three other algorithms that are representative of the state-of-the-art in evolutionary multiobjective optimization. For our comparative study, three metrics are adopted and graphical comparisons with respect to the true Pareto front of each problem are also included. Results indicate that the proposed approach is a viable alternative to solve multiobjective optimization problems.