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Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach
 IEEE Transactions on Evolutionary Computation
, 1999
"... Abstract—Evolutionary algorithms (EA’s) are often wellsuited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in ..."
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Cited by 490 (17 self)
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Abstract—Evolutionary algorithms (EA’s) are often wellsuited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EA’s are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the Strength Pareto EA (SPEA), that combines several features of previous multiobjective EA’s in a unique manner. It is characterized by a) storing nondominated solutions externally in a second, continuously updated population, b) evaluating an individual’s fitness dependent on the number of external nondominated points that dominate it, c) preserving population diversity using the Pareto dominance relationship, and d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proofofprinciple results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware–software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Paretooptimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EA’s on the 0/1 knapsack problem. Index Terms — Clustering, evolutionary algorithm, knapsack problem, multiobjective optimization, niching, Pareto optimality.
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 300 (11 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 283 (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...
Balance between Genetic Search and Local Search in Memetic Algorithms for Multiobjective Permutation Flowshop Scheduling
 IEEE Trans. on Evolutionary Computation
, 2002
"... This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by the hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Paretofront. On the other hand, the main negative ..."
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Cited by 58 (14 self)
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This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by the hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Paretofront. On the other hand, the main negative effect is the increase in the computation time per generation. Thus the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: SPEA and NSGAII. Finally, we demonstrate that local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.
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
A multiobjective evolutionary algorithm based on decomposition
 IEEE Transactions on Evolutionary Computation, Accepted
, 2007
"... 1 Decomposition is a basic strategy in traditional multiobjective optimization. However, this strategy has not yet widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a MOP into a number o ..."
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Cited by 33 (12 self)
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1 Decomposition is a basic strategy in traditional multiobjective optimization. However, this strategy has not yet widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a MOP into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and NSGAII. Experimental results show that it outperforms or performs similarly to MOGLS and NSGAII on multiobjective 01 knapsack problems and continuous multiobjective optimization problems. Index Terms multiobjective optimization, decomposition, evolutionary algorithms, memetic algorithms, Pareto optimality, computational complexity. I.
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 30 (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 ...
MultiObjective Optimization Using Genetic Algorithms: A Tutorial
"... abstract – Multiobjective formulations are a realistic models for many complex engineering optimization problems. Customized genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In many reallife problems, objectives under consid ..."
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Cited by 27 (0 self)
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abstract – Multiobjective formulations are a realistic models for many complex engineering optimization problems. Customized genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In many reallife problems, objectives under consideration conflict with each other, and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives. A reasonable solution to a multiobjective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. In this paper, an overview and tutorial is presented describing genetic algorithms developed specifically for these problems with multiple objectives. They differ from traditional genetic algorithms by using specialized fitness functions, introducing methods to promote solution diversity, and other approaches. 1.