Proceedings Article•
Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms
01 Jan 2005-pp 0
TL;DR: This study illustrates how a technique such as the multiobjective genetic algorithm can be applied and exemplifies how design requirements can be refined as the algorithm runs, and demonstrates the need for preference articulation in cases where many and highly competing objectives lead to a nondominated set too large for a finite population to sample effectively.
Abstract: In this talk, fitness assignment in multiobjective evolutionary algorithms is interpreted as a multi-criterion decision process. A suitable decision making framework based on goals and priorities is formulated in terms of a relational operator, characterized, and shown to encompass a number of simpler decision strategies, including constraint satisfaction, lexicographic optimization, and a form of goal programming. Then, the ranking of an arbitrary number of candidates is considered, and the ef- fect of preference changes on the cost surface seen by an evolutionary algorithm is illustrated graphically for a simple problem. The formulation of a multiobjective genetic algorithm based on the pro- posed decision strategy is also discussed. Niche formation techniques are used to promote diversity among preferable candidates, and progressive articulation of preferences is shown to be possible as long as the genetic algorithm can recover from abrupt changes in the cost landscape. Finally, an application to the optimization of the low-pressure spool speed governor of a Pegasus gas turbine engine is described, which il- lustrates how a technique such as the Multiobjective Genetic Algorithm can be applied, and exemplifies how design requirements can be refined as the algorithm runs. The two instances of the problem studied demonstrate the need for pref- erence articulation in cases where many and highly competing objectives lead to a non-dominated set too large for a finite population to sample ef- fectively. It is shown that only a very small portion of the non-dominated set is of practical relevance, which further substantiates the need to sup- ply preference information to the GA.
Citations
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TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.
Abstract: Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN/sup 2/) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed.
37,111 citations
18 Sep 2000
TL;DR: Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA--two other elitist multi-objective EAs which pay special attention towards creating a diverse Paretimal front.
Abstract: Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN3) computational complexity (where M is the number of objectives and N is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN2) computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) N solutions. Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA--two other elitist multi-objective EAs which pay special attention towards creating a diverse Pareto-optimal front. Because of NSGA-II's low computational requirements, elitist approach, and parameter-less sharing approach, NSGA-II should find increasing applications in the years to come.
4,878 citations
Cites background from "Multiobjective Optimization and Mul..."
...Though there has been some work on dynamic sizing of the sharing parameter [4], a pa r meterless diversity preservation mechanism is desirable....
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TL;DR: This paper provides a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions and shows that elitism is shown to be an important factor for improving evolutionary multiobjectives search.
Abstract: In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.
4,867 citations
Cites methods from "Multiobjective Optimization and Mul..."
...Later, these approaches (and variations of them) were successfully applied to various multiobjective optimization problems (Ishibuchi and Murata, 1996; Cunha et al., 1997; Valenzuela-Rendón and UrestiCharre, 1997; Fonseca and Fleming, 1998; Parks and Miller, 1998)....
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TL;DR: An overview and tutorial is presented describing genetic algorithms (GA) developed specifically for problems with multiple objectives that differ primarily from traditional GA by using specialized fitness functions and introducing methods to promote solution diversity.
2,943 citations
Cites background from "Multiobjective Optimization and Mul..."
...Several survey papers [1-3, 12, 14, 22, 51, 54, 55] have been published on evolutionary...
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Book•
27 Dec 1999
TL;DR: The basic principles of evolutionary multiobjective optimization are discussed from an algorithm design perspective and the focus is on the major issues such as fitness assignment, diversity preservation, and elitism in general rather than on particular algorithms.
Abstract: Multiple, often conflicting objectives arise naturally in most real-world optimization scenarios. As evolutionary algorithms possess several characteristics due to which they are well suited to this type of problem, evolution-based methods have been used for multiobjective optimization for more than a decade. Meanwhile evolutionary multiobjective optimization has become established as a separate subdiscipline combining the fields of evolutionary computation and classical multiple criteria decision making. In this paper, the basic principles of evolutionary multiobjective optimization are discussed from an algorithm design perspective. The focus is on the major issues such as fitness assignment, diversity preservation, and elitism in general rather than on particular algorithms. Different techniques to implement these strongly related concepts will be discussed, and further important aspects such as constraint handling and preference articulation are treated as well. Finally, two applications will presented and some recent trends in the field will be outlined.
2,062 citations
Cites methods from "Multiobjective Optimization and Mul..."
...Later, these approaches (and variations of them) were successfully applied to various multiobjective optimization problems (Ishibuchi and Murata 1996; Cunha, Oliviera, and Covas 1997; Valenzuela-Rendón and Uresti-Charre 1997; Fonseca and Fleming 1998b; Parks and Miller 1998)....
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References
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Book•
01 Sep 1988
TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.
Abstract: From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required
52,797 citations
Book•
01 Jan 1992TL;DR: This book discusses the evolution of architecture, primitive functions, terminals, sufficiency, and closure, and the role of representation and the lens effect in genetic programming.
Abstract: Background on genetic algorithms, LISP, and genetic programming hierarchical problem-solving introduction to automatically-defined functions - the two-boxes problem problems that straddle the breakeven point for computational effort Boolean parity functions determining the architecture of the program the lawnmower problem the bumblebee problem the increasing benefits of ADFs as problems are scaled up finding an impulse response function artificial ant on the San Mateo trail obstacle-avoiding robot the minesweeper problem automatic discovery of detectors for letter recognition flushes and four-of-a-kinds in a pinochle deck introduction to biochemistry and molecular biology prediction of transmembrane domains in proteins prediction of omega loops in proteins lookahead version of the transmembrane problem evolutionary selection of the architecture of the program evolution of primitives and sufficiency evolutionary selection of terminals evolution of closure simultaneous evolution of architecture, primitive functions, terminals, sufficiency, and closure the role of representation and the lens effect Appendices: list of special symbols list of special functions list of type fonts default parameters computer implementation annotated bibliography of genetic programming electronic mailing list and public repository
13,487 citations
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...problem [20], grouping problems such as process-processor mapping [21] and nonlinear model term selection [22], or the evolution of computer programs [ 23 ]....
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...[13] L. Booker, \Improving search in genetic algorithms," in Genetic Algorithmsand Simulated Annealing (L. Davis, ed.)...
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...While such a designer-orientedformulation is very attractive, its practical usefulness depends heavily on theability to search and optimize cost surfaces in a class much broader than usual,as already provided to a large extent by the Genetic Algorithm (GA)....
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Proceedings Article•
01 Oct 1987
TL;DR: A sheet which is a blend of water-insoluble fibers and pieces of film of a dry material which converts to a gel quickly on contact with a large amount of water.
Abstract: Most implementations of genetic algorithms experience sampling bias and are unnecessarily inefficient. This paper reviews various sampling algorithms proposed in the literature and offers two new algorithms of reduced bias and increased efficiency. An empirical analysis of bias is then presented.
1,604 citations
"Multiobjective Optimization and Mul..." refers methods in this paper
...Selection uses Baker’s stochastic universal sampling (SUS) algorithm [ 11 ], which is optimal in terms of bias and spread....
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01 Jan 1998
TL;DR: In this article, a multiobjective genetic algorithm based on the proposed decision strategy is proposed, and a suitable decision making framework based on goals and priorities is subsequently formulated in terms of a relational operator, characterized and shown to encompass a number of simpler decision strategies.
Abstract: In optimization, multiple objectives and constraints cannot be handled independently of the underlying optimizer. Requirements such as continuity and differentiability of the cost surface add yet another conflicting element to the decision process. While "better" solutions should be rated higher than "worse" ones, the resulting cost landscape must also comply with such requirements. Evolutionary algorithms (EAs), which have found application in many areas not amenable to optimization by other methods, possess many characteristics desirable in a multiobjective optimizer, most notably the concerted handling of multiple candidate solutions. However, EAs are essentially unconstrained search techniques which require the assignment of a scalar measure of quality, or fitness, to such candidate solutions. After reviewing current revolutionary approaches to multiobjective and constrained optimization, the paper proposes that fitness assignment be interpreted as, or at least related to, a multicriterion decision process. A suitable decision making framework based on goals and priorities is subsequently formulated in terms of a relational operator, characterized, and shown to encompass a number of simpler decision strategies. Finally, the ranking of an arbitrary number of candidates is considered. The effect of preference changes on the cost surface seen by an EA is illustrated graphically for a simple problem. The paper concludes with the formulation of a multiobjective genetic algorithm based on the proposed decision strategy. Niche formation techniques are used to promote diversity among preferable candidates, and progressive articulation of preferences is shown to be possible as long as the genetic algorithm can recover from abrupt changes in the cost landscape.
1,175 citations