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24
SPEA2: Improving the Strength Pareto Evolutionary Algorithm
, 2001
"... The Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler and Thiele 1999) is a relatively recent technique for finding or approximating the Paretooptimal set for multiobjective optimization problems. In different studies (Zitzler and Thiele 1999; Zitzler, Deb, and Thiele 2000) SPEA has shown very ..."
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Cited by 401 (16 self)
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The Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler and Thiele 1999) is a relatively recent technique for finding or approximating the Paretooptimal set for multiobjective optimization problems. In different studies (Zitzler and Thiele 1999; Zitzler, Deb, and Thiele 2000) SPEA has shown very good performance in comparison to other multiobjective evolutionary algorithms, and therefore it has been a point of reference in various recent investigations, e.g., (Corne, Knowles, and Oates 2000). Furthermore, it has been used in different applications, e.g., (Lahanas, Milickovic, Baltas, and Zamboglou 2001). In this paper, an improved version, namely SPEA2, is proposed, which incorporates in contrast to its predecessor a finegrained fitness assignment strategy, a density estimation technique, and an enhanced archive truncation method. The comparison of SPEA2 with SPEA and two other modern elitist methods, PESA and NSGAII, on different test problems yields promising results. 1
Multiobjective Evolutionary Algorithms: Analyzing the StateoftheArt
, 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 mideighties in an attempt to stochastically solve problems of this generic class. During the past decade, ..."
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Cited by 285 (7 self)
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Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mideighties 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...
Approximating the nondominated front using the Pareto Archived Evolution Strategy
 EVOLUTIONARY COMPUTATION
, 2000
"... We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its ..."
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Cited by 236 (18 self)
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We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1 + 1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1 + 1)PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some realworld applications when local search seems superior to or competitive with populationbased methods. We introduce (1 + λ) and (μ  λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.
MultiObjective Genetic Algorithms: Problem Difficulties and Construction of Test Problems
 Evolutionary Computation
, 1999
"... In this paper, we study the problem features that may cause a multiobjective genetic algorithm (GA) difficulty in converging to the true Paretooptimal front. Identification of such features helps us develop difficult test problems for multiobjective optimization. Multiobjective test problems ..."
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Cited by 153 (12 self)
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In this paper, we study the problem features that may cause a multiobjective genetic algorithm (GA) difficulty in converging to the true Paretooptimal front. Identification of such features helps us develop difficult test problems for multiobjective optimization. Multiobjective test problems are constructed from singleobjective optimization problems, thereby allowing known difficult features of singleobjective problems (such as multimodality, isolation, or deception) to be directly transferred to the corresponding multiobjective problem. In addition, test problems having features specific to multiobjective optimization are also constructed. More importantly, these difficult test problems will enable researchers to test their algorithms for specific aspects of multiobjective optimization. Keywords Genetic algorithms, multiobjective optimization, niching, paretooptimality, problem difficulties, test problems. 1 Introduction After a decade since the pioneering wor...
The Pareto Envelopebased Selection Algorithm for Multiobjective Optimization
 Proceedings of the Parallel Problem Solving from Nature VI Conference
, 2000
"... . We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelopebased Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hypergrid based scheme. PESA's selection method is relatively unusual in comparison with current well ..."
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Cited by 57 (2 self)
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. We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelopebased Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hypergrid based scheme. PESA's selection method is relatively unusual in comparison with current well known multiobjective evolutionary algorithms, which tend to use counts based on the degree to which solutions dominate others in the population. The diversity maintenance method is similar to that used by certain other methods. The main attraction of PESA is the integration of selection and diversity maintenance, whereby essentially the same technique is used for both tasks. The resulting algorithm is simple to describe, with full pseudocode provided here and real code available from the authors. We compare PESA with two recent strongperforming MOEAs on some multiobjective test problems recently proposed by Deb. We find that PESA emerges as the best method overall on these problems...
MPAES: A Memetic Algorithm for Multiobjective Optimization
, 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 ..."
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Cited by 52 (5 self)
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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...
A Tutorial on Evolutionary Multiobjective Optimization
 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. ..."
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Cited by 41 (0 self)
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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
Using Unconstrained Elite Archives for MultiObjective Optimisation
 IEEE Transactions on Evolutionary Computation
, 2001
"... MultiObjective Evolutionary Algorithms (MOEAs) have been the subject of numer ous studies over the past 20 years. Recent work has highlighted the use of an active archive of elite, nondominated solutions to improve the optimisation speed of these algorithms. ..."
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Cited by 39 (12 self)
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MultiObjective Evolutionary Algorithms (MOEAs) have been the subject of numer ous studies over the past 20 years. Recent work has highlighted the use of an active archive of elite, nondominated solutions to improve the optimisation speed of these algorithms.
PESAII: Regionbased Selection in Evolutionary Multiobjective Optimization
 Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2001
, 2001
"... We describe a new selection technique for evolutionary multiobjective optimization algorithms in which the unit of selection is a hyperbox in objective space. In this technique, instead of assigning a selective fitness to an individual, selective fitness is assigned to the hyperboxes in object ..."
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Cited by 39 (7 self)
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We describe a new selection technique for evolutionary multiobjective optimization algorithms in which the unit of selection is a hyperbox in objective space. In this technique, instead of assigning a selective fitness to an individual, selective fitness is assigned to the hyperboxes in objective space which are currently occupied by at least one individual in the current approximation to the Pareto frontier. A hyperbox is thereby selected, and the resulting selected individual is randomly chosen from this hyperbox. This method of selection is shown to be more sensitive to ensuring a good spread of development along the Pareto frontier than individualbased selection. The method is implemented in a modern multiobjective evolutionary algorithm, and performance is tested by using Deb's test suite of `T' functions with varying properties. The new selection technique is found to give significantly superior results to the other methods compared, namely PAES, PESA, and SPEA; each is a modern multiobjective optimization algorithm previously found to outperform earlier approaches on various problems.
Performance Scaling of MultiObjective Evolutionary Algorithms
"... In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Paretooptimal. If none of the objectives have preference over the othe ..."
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Cited by 39 (3 self)
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In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Paretooptimal. If none of the objectives have preference over the other, none of these tradeoff solutions can be said to be better than any other solution in the set. Multiobjective Evolutionary Algorithms (MOEAs) can find these optimal tradeoffs in order to get a set of solutions that are optimal in an overall sense.