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96
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 708 (19 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.
A Fast Elitist NonDominated Sorting Genetic Algorithm for MultiObjective Optimization: NSGAII
, 2000
"... Multiobjective evolutionary algorithms which use nondominated 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) nonelitism approach, and (iii) the need for specifying a sharing ..."
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Cited by 662 (15 self)
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Multiobjective evolutionary algorithms which use nondominated 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) nonelitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a nondominated sorting based multiobjective evolutionary algorithm (we called it the Nondominated Sorting GAII or NSGAII) which alleviates all the above three difficulties. Specifically, a fast nondominated 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 NSGAII is able to find much better spread of solutions in all problems compared to PAESanother elitist multiobjective EA which pays special attention towards creating a diverse Paretooptimal front. Because of NSGAII's low computational requirements, elitist approach, and parameterless sharing approach, NSGAII should find increasing applications in the years to come.
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 78 (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
Ideal Evaluation from Coevolution
 Evolutionary Computation
, 2004
"... In many problems of interest, performance can be evaluated using tests, such as examples in concept learning, test points in function approximation, and opponents in gameplaying. Evaluation on all tests is often infeasible. Identification of an accurate evaluation or fitness function is a difficult ..."
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Cited by 68 (6 self)
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In many problems of interest, performance can be evaluated using tests, such as examples in concept learning, test points in function approximation, and opponents in gameplaying. Evaluation on all tests is often infeasible. Identification of an accurate evaluation or fitness function is a difficult problem in itself, and approximations are likely to introduce human biases into the search process. Coevolution evolves the set of tests used for evaluation, but has so far often led to inaccurate evaluation. We show that for any set of learners, a Complete Evaluation Set can be determined that provides ideal evaluation as specified by Evolutionary MultiObjective Optimization. This provides a principled approach to evaluation in coevolution, and thereby brings automatic ideal evaluation within reach. The Complete Evaluation Set is of manageable size, and progress towards it can be accurately measured. Based on this observation, an algorithm named DELPHI is developed. The algorithm is tested on problems likely to permit progress on only a subset of the underlying objectives. Where all comparison methods result in overspecialization, the proposed method and a variant achieve sustained progress in all underlying objectives. These findings demonstrate that ideal evaluation may be approximated by practical algorithms, and that accurate evaluation for testbased problems is possible even when the underlying objectives of a problem are unknown.
Performance Scaling of MultiObjective Evolutionary Algorithms
, 2002
"... 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 57 (5 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.
Multiobjective Genetic Programming: Reducing Bloat Using SPEA2
 In Proceedings of the 2001 Congress on Evolutionary Computation CEC2001
, 2001
"... This study investigates the use of multiobjective techniques in Genetic Programming (GP) in order to evolve compact programs and to reduce the effects caused by bloating. The proposed approach considers the program size as a second, independent objective besides the program functionality. In combina ..."
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Cited by 46 (3 self)
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This study investigates the use of multiobjective techniques in Genetic Programming (GP) in order to evolve compact programs and to reduce the effects caused by bloating. The proposed approach considers the program size as a second, independent objective besides the program functionality. In combination with a recent multiobjective evolutionary technique, SPEA2, this method outperforms four other strategies to reduce bloat with regard to both convergence speed and size of the produced programs on a evenparity problem.
On The Effects of Archiving, Elitism, And Density Based Selection in Evolutionary MultiObjective Optimization
 In
, 2001
"... . This paper studies the influence of what are recognized as key issues ..."
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Cited by 33 (7 self)
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. This paper studies the influence of what are recognized as key issues
Parallel estimation of distribution algorithms
, 2002
"... The thesis deals with the new evolutionary paradigm based on the concept of Estimation of Distribution Algorithms (EDAs) that use probabilistic model of promising solutions found so far to obtain new candidate solutions of optimized problem. There are six primary goals of this thesis: 1. Suggestion ..."
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Cited by 26 (4 self)
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The thesis deals with the new evolutionary paradigm based on the concept of Estimation of Distribution Algorithms (EDAs) that use probabilistic model of promising solutions found so far to obtain new candidate solutions of optimized problem. There are six primary goals of this thesis: 1. Suggestion of a new formal description of EDA algorithm. This high level concept can be used to compare the generality of various probabilistic models by comparing the properties of underlying mappings. Also, some convergence issues are discussed and theoretical ways for further improvements are proposed. 2. Development of new probabilistic model and methods capable of dealing with continuous parameters. The resulting Mixed Bayesian Optimization Algorithm (MBOA) uses a set of decision trees to express the probability model. Its main advantage against the mostly used IDEA and EGNA approach is its backward compatibility with discrete domains, so it is uniquely capable of learning linkage between mixed continuousdiscrete genes. MBOA handles the discretization of continuous parameters as an integral part of the learning process, which outperforms the histogrambased
Evolutionary Multiobjective Clustering
 In Proceedings of the Eighth International Conference on Parallel Problem Solving from Nature
, 2004
"... Clustering is a core problem in datamining with innumerable applications spanning many fields. A key di#culty of e#ective clustering is that for unlabelled data a `good' solution is a somewhat illdefined concept, and hence a plethora of valid measures of cluster quality have been devised. Mos ..."
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Cited by 23 (3 self)
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Clustering is a core problem in datamining with innumerable applications spanning many fields. A key di#culty of e#ective clustering is that for unlabelled data a `good' solution is a somewhat illdefined concept, and hence a plethora of valid measures of cluster quality have been devised. Most clustering algorithms optimize just one such objective (often implicitly) and are thus limited in their scope of application. In this paper, we investigate whether an EA optimizing a number of di#erent clustering quality measures simultaneously can find better solutions. Using problems where the correct classes are known, our results show a clear advantage to the multiobjective approach: it exhibits a far more robust level of performance than the classic kmeans and averagelink agglomerative clustering algorithms over a diverse suite of 15 real and synthetic data sets, sometimes outperforming them substantially.
A New Multiobjective Evolutionary Optimisation Algorithm: The TwoArchive Algorithm
"... Many MultiObjective Evolutionary Algorithms (MOEAs) have been proposed in recent years. However, almost all MOEAs have been evaluated on problems with two to four objectives only. It is unclear how well these MOEAs will perform on problems with a large number of objectives. Our preliminary study [1 ..."
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Cited by 19 (4 self)
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Many MultiObjective Evolutionary Algorithms (MOEAs) have been proposed in recent years. However, almost all MOEAs have been evaluated on problems with two to four objectives only. It is unclear how well these MOEAs will perform on problems with a large number of objectives. Our preliminary study [1] showed that performance of some MOEAs deteriorates significantly as the number of objectives increases. This paper proposes a new MOEA that performs well on problems with a large number of objectives. The new algorithm separates nondominated solutions into two archives, and is thus called the TwoArchive algorithm. The two archives focused on convergence and diversity, respectively, in optimisation. Computational studies have been carried out to evaluate and compare our new algorithm against the best MOEA for problems with a large number of objectives. Our experimental results have shown that the TwoArchive algorithm outperforms existing MOEAs on problems with a large number of objectives. 1