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A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II

by Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, T. Meyarivan , 2000
"... Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN 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 param ..."
Abstract - Cited by 1815 (60 self) - Add to MetaCart
Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN 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(MN ) 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 a number of 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. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems eciently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint non-linear problem, are compared with another constrained multi-objective optimizer and much better performance of NSGA-II is observed. Because of NSGA-II's low computational requirements, elitist approach, parameter-less niching approach, and simple constraint-handling strategy, NSGA-II should find increasing applications in the coming years.
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A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II

by Kalyanmoy Deb, Samir Agrawal, Amrit Pratap, T Meyarivan , 2000
"... Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) -4 computational complexity (where is the number of objectives and is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing ..."
Abstract - Cited by 662 (15 self) - Add to MetaCart
Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) -4 computational complexity (where is the number of objectives and 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 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) solutions. Simulation results on five difficult test problems show that the proposed NSGA-II is able to find much better spread of solutions in all problems compared to PAES---another elitist multi-objective EA which pays 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.

Comparison of Multiobjective Evolutionary Algorithms: Empirical Results

by Eckart Zitzler, Lothar Thiele, Kalyanmoy Deb , 2000
"... 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 conver ..."
Abstract - Cited by 628 (41 self) - Add to MetaCart
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.

Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art

by David A. Van Veldhuizen, Gary B. Lamont , 2000
"... 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, ..."
Abstract - Cited by 440 (7 self) - Add to MetaCart
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 c...

A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques

by Carlos A. Coello Coello - Knowledge and Information Systems , 1998
"... . This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search cap ..."
Abstract - Cited by 292 (22 self) - Add to MetaCart
. This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described mentioning its advantages and disadvantages, their degree of applicability and some of their known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed. Keywords: multiobjective optimization, multicriteria optimization, vector optimization, genetic algorithms, evolutionary algorithms, artificial intelligence. 1 Introduction Since the pioneer work of Rosenberg in the late 60s regarding the possibility of using genetic-based search to deal with multiple objectives, this new area of research (now called evolutionary multiobjective optimization) has grown c...
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Scalable Test Problems for Evolutionary Multi-Objective Optimization

by Kalyanmoy Deb, Lothar Thiele, Marco Laumanns, Eckart Zitzler - Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH , 2001
"... After adequately demonstrating the ability to solve di#erent two-objective optimization problems, multi-objective evolutionary algorithms (MOEAs) must now show their e#cacy in handling problems having more than two objectives. In this paper, we have suggested three di#erent approaches for systema ..."
Abstract - Cited by 148 (21 self) - Add to MetaCart
After adequately demonstrating the ability to solve di#erent two-objective optimization problems, multi-objective evolutionary algorithms (MOEAs) must now show their e#cacy in handling problems having more than two objectives. In this paper, we have suggested three di#erent approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of exact shape and location of the resulting Pareto-optimal front, and introduction of controlled di#culties in both converging to the true Pareto-optimal front and maintaining a widely distributed set of solutions are the main features of the suggested test problems. Because of the above features, they should be found useful in various research activities on MOEAs, such as testing the performance of a new MOEA, comparing di#erent MOEAs, and better understanding of the working principles of MOEAs.
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Global Optimization Algorithms -- Theory and Application

by Thomas Weise , 2011
"... This e-book is devoted to Global Optimization algorithms, which are methods for finding solutions of high quality for an incredible wide range of problems. We introduce the basic concepts of optimization and discuss features which make optimization problems difficult and thus, should be considered ..."
Abstract - Cited by 97 (26 self) - Add to MetaCart
This e-book is devoted to Global Optimization algorithms, which are methods for finding solutions of high quality for an incredible wide range of problems. We introduce the basic concepts of optimization and discuss features which make optimization problems difficult and thus, should be considered when trying to solve them. In this book, we focus on
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Multiobjective Optimization Using Dynamic Neighborhood Particle Swarm Optimization

by Xiaohui Hu, Russell C. Eberhart , 2002
"... This paper presents a Particle Swarm Optimization (PSO) algorithm for multiobjective optimization problems. PSO is modified by using a dynamic neighborhood strategy, new particle memory updating, and one-dimension optimization to deal with multiple objectives. Several benchmark cases were tested and ..."
Abstract - Cited by 85 (2 self) - Add to MetaCart
This paper presents a Particle Swarm Optimization (PSO) algorithm for multiobjective optimization problems. PSO is modified by using a dynamic neighborhood strategy, new particle memory updating, and one-dimension optimization to deal with multiple objectives. Several benchmark cases were tested and showed that PSO could efficiently find multiple Pareto optimal solutions.

A Tutorial on Evolutionary Multiobjective Optimization

by Eckart Zitzler, Marco Laumanns, Stefan Bleuler - In Metaheuristics for Multiobjective Optimisation , 2003
"... Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. ..."
Abstract - Cited by 78 (0 self) - Add to MetaCart
Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. Meanwhil e evol utionary mul tiobjective optimization has become establ ished as a separate subdiscipl ine combining the fiel ds of evol utionary computation and cl assical mul tipl e criteria decision ma ing. This paper gives an overview of evol tionary mu l iobjective optimization with the focus on methods and theory. On the one hand, basic principl es of mu l iobjective optimization and evol tionary alA#xv hms are presented, and various al gorithmic concepts such as fitness assignment, diversity preservation, and el itism are discussed. On the other hand, the tutorial incl udes some recent theoretical resul ts on the performance of mu l iobjective evol tionaryalvDfifl hms and addresses the question of how to simpl ify the exchange of methods and appl ications by means of a standardized interface. 1
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M-PAES: A Memetic Algorithm for Multiobjective Optimization

by Joshua D. Knowles, David W. Corne , 2000
"... A memetic algorithm for tackling multiobjective optimization problems is presented. The algorithm employs the proven local search strategy used in the Pareto archived evolution strategy (PAES) and combines it with the use of a population and recombination. Verification of the new algorithm is carri ..."
Abstract - Cited by 76 (5 self) - Add to MetaCart
A memetic algorithm for tackling multiobjective optimization problems is presented. The algorithm employs the proven local search strategy used in the Pareto archived evolution strategy (PAES) and combines it with the use of a population and recombination. Verification of the new algorithm is carried out by testing it on a set of multiobjective 0/1 knapsack problems. On each problem instance, comparison is made between the new memetic algorithm, the (1+1)-PAES local searcher, and the strength Pareto evolutionary algorithm (SPEA) of Zitzler and Thiele. 1 Introduction In recent years, genetic algorithms (GAs) have been applied more and more to multiobjective problems. For a comprehensive overview, see [2]. Undoubtedly, as an extremely general metaheuristic, GAs are well qualified to tackle problems of a great variety. This asset, coupled with the possession of a population, seems to make them particularly attractive for use in multiobjective problems, where a number of solutions appro...