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Combining convergence and diversity in evolutionary multiobjective optimization
 Evolutionary Computation
, 2002
"... Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Paretooptimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms c ..."
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Cited by 121 (11 self)
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Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Paretooptimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Paretooptimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Paretooptimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept ofdominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modi�cations to the baseline algorithm are also suggested. The concept ofdominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.
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 50 (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
A MultiObjective Algorithm based upon Particle Swarm Optimisation, an Efficient Data Structure and Turbulence.
, 2002
"... This paper introduces a MultiObjective Algorithm (MOA) based upon the Particle Swarm Optimisation (PSO) heuristic. ..."
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Cited by 45 (1 self)
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This paper introduces a MultiObjective Algorithm (MOA) based upon the Particle Swarm Optimisation (PSO) heuristic.
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 41 (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.
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 41 (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 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 39 (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.
Convergence Properties of Some MultiObjective Evolutionary Algorithms
 IN CONGRESS ON EVOLUTIONARY COMPUTATION (CEC 2000
, 2000
"... We present four abstract evolutionary algorithms for multiobjective optimization and theoretical results that characterize their convergence behavior. Thanks to these results it is easy to verify whether a particular instantiation of these abstract evolutionary algorithms offers the desired limit b ..."
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Cited by 38 (6 self)
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We present four abstract evolutionary algorithms for multiobjective optimization and theoretical results that characterize their convergence behavior. Thanks to these results it is easy to verify whether a particular instantiation of these abstract evolutionary algorithms offers the desired limit behavior or not. Several examples are given.
A Unified Model for MultiObjective Evolutionary Algorithms with Elitism
 In Congress on Evolutionary Computation (CEC 2000
, 2000
"... Though it has been claimed that elitism could improve evolutionary multiobjective search significantly, a thorough and extensive evaluation of its effects is still missing. Guidelines on how elitism could successfully be incorporated have not yet been developed. This paper presents a unified model ..."
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Cited by 32 (6 self)
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Though it has been claimed that elitism could improve evolutionary multiobjective search significantly, a thorough and extensive evaluation of its effects is still missing. Guidelines on how elitism could successfully be incorporated have not yet been developed. This paper presents a unified model of multiobjective evolutionary algorithms, in which arbitrary variation and selection operators can be combined as building blocks, including archiving and reinsertion strategies. The presented model enables most specific multiobjective (evolutionary) algorithm to be formulated as an instance of it, which will be demonstrated by simple examples. We will further show how elitism can be quantified by the model's parameters and how this allows an easy evaluation of the effect of elitism on different algorithms. 1 Introduction The aim of this study is to provide a systematic approach to elitism in multiobjective evolutionary algorithms (MOEA). Multiobjective optimization can be seen as a ...
Evolutionary Search under Partially Ordered Fitness Sets
 IN PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON INFORMATION SCIENCE INNOVATIONS IN ENGINEERING OF NATURAL AND ARTIFICIAL INTELLIGENT SYSTEMS (ISI 2001
, 2001
"... The search for minimal elements in partially ordered sets is a generalization of the task of finding Paretooptimal elements in multicriteria optimization problems. Since there are usually many minimal elements within a partially ordered set, a populationbased evolutionary search is, as a matter o ..."
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Cited by 21 (4 self)
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The search for minimal elements in partially ordered sets is a generalization of the task of finding Paretooptimal elements in multicriteria optimization problems. Since there are usually many minimal elements within a partially ordered set, a populationbased evolutionary search is, as a matter of principle, capable of finding several minimal elements in a single run and gains therefore a steadily increase of popularity. Here, we present an evolutionary algorithm which population converges with probability one to the set of minimal elements within a finite number of iterations.
Archiving with Guaranteed Convergence and Diversity in MultiObjective Optimization
 In Proceedings of the Genetic and Evolutionary Computation Conference
, 2002
"... Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Paretooptimal solutions in a single simulation run. However, none of the multiobjective evolutionary algorithm ..."
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Cited by 18 (4 self)
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Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Paretooptimal solutions in a single simulation run. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Paretooptimal solutions with a wide diversity among the solutions. In this paper we discuss why a number of earlier MOEAs do not have such properties. A new archiving strategy is proposed that maintains a subset of the generated solutions. It guarantees convergence and diversity according to welldefined criteria, i.e. #dominance and #Pareto optimality.