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652
Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications
, 1999
"... Many realworld problems involve two types of problem difficulty: i) multiple, conflicting objectives and ii) a highly complex search space. On the one hand, instead of a single optimal solution competing goals give rise to a set of compromise solutions, generally denoted as Paretooptimal. In the a ..."
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Cited by 340 (13 self)
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Many realworld problems involve two types of problem difficulty: i) multiple, conflicting objectives and ii) a highly complex search space. On the one hand, instead of a single optimal solution competing goals give rise to a set of compromise solutions, generally denoted as Paretooptimal. In the absence of preference information, none of the corresponding tradeoffs can be said to be better than the others. On the other hand, the search space can be too large and too complex to be solved by exact methods. Thus, efficient optimization strategies are required that are able to deal with both difficulties. Evolutionary algorithms possess several characteristics that are desirable for this kind of problem and make them preferable to classical optimization methods. In fact, various evolutionary approaches to multiobjective optimization have been proposed since 1985, capable of searching for multiple Paretooptimal solutions concurrently in a single simulation run. However, in spite of this...
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 326 (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...
Indicatorbased selection in multiobjective search
 in Proc. 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII
, 2004
"... Abstract. This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection ..."
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Cited by 101 (9 self)
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Abstract. This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection process. To this end, we propose a general indicatorbased evolutionary algorithm (IBEA) that can be combined with arbitrary indicators. In contrast to existing algorithms, IBEA can be adapted to the preferences of the user and moreover does not require any additional diversity preservation mechanism such as fitness sharing to be used. It is shown on several continuous and discrete benchmark problems that IBEA can substantially improve on the results generated by two popular algorithms, namely NSGAII and SPEA2, with respect to different performance measures. 1
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 85 (9 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.
MOPSO : A Proposal for Multiple Objective Particle Swarm
, 2002
"... This paper introduces a proposal to extend the heuristic called "particle swarm optimization" (PSO) to deal with multiobjective optimization problems. Our approach uses the concept of Pareto dominance to determine the flight direction of a particle and it maintains previously found nondomi ..."
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Cited by 78 (3 self)
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This paper introduces a proposal to extend the heuristic called "particle swarm optimization" (PSO) to deal with multiobjective optimization problems. Our approach uses the concept of Pareto dominance to determine the flight direction of a particle and it maintains previously found nondominated vectors in a global repository that is later used by other particles to guide their own flight. The approach is validated using several standard test functions from the specialized literature. Our results indicate that our approach is highly competitive with current evolutionary multiobjective optimization techniques.
Covariance Matrix Adaptation for Multiobjective Optimization
 Evolutionary Computation
"... The covariance matrix adaptation evolution strategy (CMAES) is one of the most powerful evolutionary algorithms for realvalued singleobjective optimization. In this paper, we develop a variant of the CMAES for multiobjective optimization (MOO). We first introduce a singleobjective, elitist C ..."
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Cited by 57 (8 self)
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The covariance matrix adaptation evolution strategy (CMAES) is one of the most powerful evolutionary algorithms for realvalued singleobjective optimization. In this paper, we develop a variant of the CMAES for multiobjective optimization (MOO). We first introduce a singleobjective, elitist CMAES using plusselection and step size control based on a success rule. This algorithm is compared to the standard CMAES. The elitist CMAES turns out to be slightly faster on unimodal functions, but is more prone to getting stuck in suboptimal local minima. In the new multiobjective CMAES (MOCMAES) a population of individuals that adapt their search strategy as in the elitist CMAES is maintained. These are subject to multiobjective selection. The selection is based on nondominated sorting using either the crowdingdistance or the contributing hypervolume as second sorting criterion. Both the elitist singleobjective CMAES and the MOCMAES inherit important invariance properties, in particular invariance against rotation of the search space, from the original CMAES. The benefits of the new MOCMAES in comparison to the wellknown NSGAII and to NSDE, a multiobjective differential evolution algorithm, are experimentally shown.
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
An EMO Algorithm Using the Hypervolume Measure as Selection Criterion
 2005 Int’l Conference, March 2005
, 2005
"... The hypervolume measure is one of the most frequently applied measures for comparing the results of evolutionary multiobjective optimization algorithms (EMOA). The idea to use this measure for selection is selfevident. A steadystate EMOA will be devised, that combines concepts of nondominated sor ..."
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Cited by 45 (8 self)
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The hypervolume measure is one of the most frequently applied measures for comparing the results of evolutionary multiobjective optimization algorithms (EMOA). The idea to use this measure for selection is selfevident. A steadystate EMOA will be devised, that combines concepts of nondominated sorting with a selection operator based on the hypervolume measure. The algorithm computes a well distributed set of solutions with bounded size thereby focussing on interesting regions of the Pareto front(s). By means of standard benchmark problems the algorithm will be compared to other well established EMOA. The results show that our new algorithm achieves good convergence to the Pareto front and outperforms standard methods in the hypervolume covered.
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