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209
A Fast and Elitist MultiObjective Genetic Algorithm: NSGAII
, 2000
"... Multiobjective evolutionary algorithms which use nondominated 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) nonelitism approach, and (iii) the need for specifying a sharing param ..."
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Cited by 805 (28 self)
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Multiobjective evolutionary algorithms which use nondominated 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) 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 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 NSGAII, in most problems, is able to find much better spread of solutions and better convergence near the true Paretooptimal front compared to PAES and SPEA  two other elitist multiobjective EAs which pay special attention towards creating a diverse Paretooptimal front. Moreover, we modify the definition of dominance in order to solve constrained multiobjective problems eciently. Simulation results of the constrained NSGAII on a number of test problems, including a fiveobjective, sevenconstraint nonlinear problem, are compared with another constrained multiobjective optimizer and much better performance of NSGAII is observed. Because of NSGAII's low computational requirements, elitist approach, parameterless niching approach, and simple constrainthandling strategy, NSGAII should find increasing applications in the coming years.
A Comprehensive Survey of EvolutionaryBased Multiobjective Optimization Techniques
 Knowledge and Information Systems
, 1998
"... . This paper presents a critical review of the most important evolutionarybased 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 ..."
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Cited by 211 (19 self)
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. This paper presents a critical review of the most important evolutionarybased 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 geneticbased search to deal with multiple objectives, this new area of research (now called evolutionary multiobjective optimization) has grown c...
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 152 (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...
PISA  A Platform and Programming Language Independent Interface for Search Algorithms
, 2003
"... This paper int roduces at ext based int rface (PISA)t hat allows t separat ty algorit hmspecific part of an op t mizer fromt he applicat ionspecific part . These part s are implement ed as independent programs forming freelycombinable modules. ..."
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Cited by 73 (8 self)
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This paper int roduces at ext based int rface (PISA)t hat allows t separat ty algorit hmspecific part of an op t mizer fromt he applicat ionspecific part . These part s are implement ed as independent programs forming freelycombinable modules.
Reducing Bloat and Promoting Diversity using MultiObjective Methods
, 2001
"... Two important problems in genetic programming (GP) are its tendency to find unnecessarily large trees (bloat), and the general evolutionary algorithms problem that diversity in the population can be lost prematurely. The prevention of these problems is frequently an implicit goal of basic GP. We exp ..."
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Cited by 67 (5 self)
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Two important problems in genetic programming (GP) are its tendency to find unnecessarily large trees (bloat), and the general evolutionary algorithms problem that diversity in the population can be lost prematurely. The prevention of these problems is frequently an implicit goal of basic GP. We explore the potential of techniques from multiobjective optimization to aid GP by adding explicit objectives to avoid bloat and promote diversity. The even 3, 4, and 5parity problems were solved efficiently compared to basic GP results from the literature. Even though only nondominated individuals were selected and populations thus remained extremely small, appropriate diversity was maintained. The size of individuals visited during search consistently remained small, and solutions of what we believe to be the minimum size were found for the 3, 4, and 5parity problems.
Feature Selection in Unsupervised Learning via Evolutionary Search
 In Proceedings of the Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
, 2000
"... Feature subset selection is an important problem in knowl edge discovery, not only for the insight gained from deter mining relevant modeling variables but also for the improved understandability, scalability, and possibly, accuracy of the resulting models. In this paper we consider the problem of ..."
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Cited by 54 (3 self)
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Feature subset selection is an important problem in knowl edge discovery, not only for the insight gained from deter mining relevant modeling variables but also for the improved understandability, scalability, and possibly, accuracy of the resulting models. In this paper we consider the problem of feature selection for unsupervised learning. A number of heuristic criteria can be used to estimate the quality of clusters built from a given featuresubset. Rather than combining such criteria, we use ELSA, an evolutionary lo cal selection algorithm that maintains a diverse population of solutions that approximate the Pareto front in a multi dimensional objectiv espace. Each evolved solution repre sents a feature subset and a number of clusters; a standard Kmeans algorithm is applied to form the given n umber of clusters based on the selected features. Preliminary results on both real and synthetic data show promise in finding Paretooptimal solutions through which we can identify the significant features and the correct number of clusters.
Running Time Analysis of a MultiObjective Evolutionary Algorithm on a Simple Discrete Optimization Problem
, 2002
"... For the first time, a running time analysis of a multiobjective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudoBoolean problem (Lotz: leading ones  trailing zeroes) is defined and a populationbased optimization algorithm (FEMO). We show, that the ..."
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Cited by 44 (7 self)
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For the first time, a running time analysis of a multiobjective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudoBoolean problem (Lotz: leading ones  trailing zeroes) is defined and a populationbased optimization algorithm (FEMO). We show, that the algorithm performs a black box optimization in #(n 2 log n) function evaluations where n is the number of binary decision variables. 1
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 38 (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.
A Short Tutorial on Evolutionary Multiobjective Optimization
, 2001
"... This tutorial will review some of the basic concepts related to evolutionary multiobjective optimization (i.e., the use of evolutionary algorithms to handle more than one objective function at a time). The most commonly used evolutionary multiobjective optimization techniques will be described and c ..."
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Cited by 36 (0 self)
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This tutorial will review some of the basic concepts related to evolutionary multiobjective optimization (i.e., the use of evolutionary algorithms to handle more than one objective function at a time). The most commonly used evolutionary multiobjective optimization techniques will be described and criticized, including some of their applications. Theory, test functions and metrics will be also discussed. Finally, we will provide some possible paths of future research in this area.