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About this book

Researchers and practitioners alike are increasingly turning to search, op­ timization, and machine-learning procedures based on natural selection and natural genetics to solve problems across the spectrum of human endeavor. These genetic algorithms and techniques of evolutionary computation are solv­ ing problems and inventing new hardware and software that rival human designs. The Kluwer Series on Genetic Algorithms and Evolutionary Computation pub­ lishes research monographs, edited collections, and graduate-level texts in this rapidly growing field. Primary areas of coverage include the theory, implemen­ tation, and application of genetic algorithms (GAs), evolution strategies (ESs), evolutionary programming (EP), learning classifier systems (LCSs) and other variants of genetic and evolutionary computation (GEC). The series also pub­ lishes texts in related fields such as artificial life, adaptive behavior, artificial immune systems, agent-based systems, neural computing, fuzzy systems, and quantum computing as long as GEC techniques are part of or inspiration for the system being described. This encyclopedic volume on the use of the algorithms of genetic and evolu­ tionary computation for the solution of multi-objective problems is a landmark addition to the literature that comes just in the nick of time. Multi-objective evolutionary algorithms (MOEAs) are receiving increasing and unprecedented attention. Researchers and practitioners are finding an irresistible match be­ tween the popUlation available in most genetic and evolutionary algorithms and the need in multi-objective problems to approximate the Pareto trade-off curve or surface.

Table of Contents

Frontmatter

Chapter 1. Basic Concepts

Abstract
Problems with multiple objectives arise in a natural fashion in most disciplines and their solution has been a challenge to researchers for a long time. Despite the considerable variety of techniques developed in Operations Research (OR) to tackle these problems, the complexities of their solution calls for alternative approaches.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 2. Evolutionary Algorithm MOP Approaches

Abstract
Both researchers and practitioners certainly have a strong interest in knowing the state-of-the-art of a discipline in which they are interested to work. For researchers, this is the normal procedure to trigger original contributions. For practitioners, this knowledge of the area allows them to choose the most appropriate algorithm(s) for their specific application.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 3. MOEA Test Suites

Abstract
Why test MOEAs? To evaluate, compare, classify, and improve algorithm performance (effectiveness and efficiency)! What is an MOEA test? An MOP test function, an MOP test suite, pedagogical functions, or a real-world problem? How to find an appropriate MOEA test? MOEA literature, historical use, test generators, or well known real-world applications. When to test? Incremental algorithm and test development starting early or wait until end of development. How to design an MOEA test? Assumptions, computational platform selection, statistical tools, metric selection, experimental plan, and an on-going process. Therefore, considerable effort must be expended not only to define proper MOP tests and generate the proper design of MOEA experiments, but also to employ the honest selection of appropriate testing metrics and associated statistical evaluation and comparison. In this chapter, the development of various MOP test suites is addressed, and in the next chapter, their use in appropriate MOEA evaluations is discussed.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 4. MOEA Testing and Analysis

Abstract
Regarding the scientific method of experimentation, it is desirable to construct an accurate, reliable, consistent and non-arbitrary representation of MOEA architectures and performance over sets of MOPs. In particular, through the use of standard procedures and criteria, one should attempt to minimize the influence of bias or prejudice of the experimenter when testing an MOEA hypothesis. The design of each experiment must conform then to an accepted “standard” approach as reflected in any generic scientific method. When employing this approach, the detailed design of MOEA experiments can draw heavily from outlines presented by Barr et al. (1995), and Jackson et al. (1991). These generic articles discuss computational experiment design for heuristic methods, providing guidelines for reporting results and ensuring their reproducibility. Specifically, they suggest that a well-designed experiment follow these steps: (1) Define experimental goals; (2) Choose measures of performance (metrics); (3) Design and execute the experiment; (4) Analyze data and draw conclusions; and (5) Report experimental results. This chapter applies these concepts in developing experimental MOEA testing procedures using appropriate MOP test suites from Chapter 3.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 5. MOEA Theory and Issues

Abstract
Many MOEA development efforts acknowledge various facets of underlying MOEA theory, but make limited contributions when simply citing relevant issues raised by others. Some authors, however, exhibit significant theoretical detail. Their work provides basic MOEA models and associated theories. Table 5.1 lists contemporary efforts reflecting MOEA theory development. In essence, an MOEA is searching for optimal elements in a partially ordered set or in the Pareto optimal set. Thus, the concept of convergence to P true and PF true is integral to the MOEA search process.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 6. Applications

Abstract
Although the application of classical multiobjective optimization techniques to solve problems in different (management, engineering and scientific) areas started as early as 1951 (see Section 6.2 from Chapter 1), Multi-Objective Evolutionary Algorithms (MOEAs) were applied for the first time until the mid-1980s (Schaffer, 1985). However, since the late 1990s, there has been a considerable increase in the number of applications of MOEAs. This has been mainly originated by the success of MOEAs in solving real-world problems. MOEAs have generated either competitive or better results than those produced using other search techniques. This has made the task of classifying MOEA applications difficult and subjective. Trying to deal with this problem, it was decided to use a rather simple and general classification in this chapter, trying to fit each paper reviewed within the closest category according to the focus of the work. For example, a paper that is related to scheduling and naval engineering but is more focused on the second subject, is classified under “environmental, naval and hydraulic engineering”. This avoids overlapping to a certain extent, but can be confusing for some people. Therefore, it was decided to add as many entries as possible to the analytical index provided at the end of this book to facilitate the search. Additionally, italics characters are used throughout this chapter to indicate the specific name of an application, in an attempt to facilitate the search of specific information.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 7. MOEA Parallelization

Abstract
When solving optimization problems, parallelizing associated computer algorithms may result in more efficient, and possibly more effective, implementations. This is primarily due to the increased number of processors (and local memories) working on the problem, thus allowing investigation of more of the solution space in a given time period.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 8. Multi-Criteria Decision Making

Abstract
One aspect that most of the current research on evolutionary multiobjective optimization (EMO) often disregards is the fact that the solution of a multiobjective optimization problem (MOP) really involves three stages: measurement, search, and decision making.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 9. Special Topics

Abstract
Evolutionary Algorithms (EAs) are not the only search techniques that have been used to deal with multiobjective optimization problems. In fact, as other search techniques (e.g., tabu search and simulated annealing) have proved to have very good performance in many combinatorial (as well as other types of) optimization problems, it is only natural to think of extensions to such approaches to deal with multiple objectives.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Chapter 10. Epilog

Abstract
The intent of this monograph as indicated in the Preface is to provide as complete as possible a foundation for the development and use of multiobjective evolutionary algorithms. The previous chapters have provided a comprehensive framework for the study and extension of such stochastic search algorithms; the general goal being to generate the Pareto optimal front with a uniform density of points on the front along with the values of the associated decision variables. The classified variety of proposed MOEAs is presented in Chapter 2 along with their subjective advantages and disadvantages. Various generic test suites are presented in Chapter 3 across unconstrained numerical problems, constrained numerical problems, N P-complete problems and real-world applications. Viable metrics are presented in Chapter 4 to evaluate each proposed MOEA across a variety of evolutionary operators and performance visualizations for test suite functions. As in all chapters, areas of proposed research are presented at the end of each chapter along with MOEA discussion questions for the student as well as the practioner.
Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont

Backmatter

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