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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 724 (22 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.
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 272 (22 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...
Scalable Test Problems for Evolutionary MultiObjective Optimization
 Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH
, 2001
"... After adequately demonstrating the ability to solve di#erent twoobjective optimization problems, multiobjective evolutionary algorithms (MOEAs) must now show their e#cacy in handling problems having more than two objectives. In this paper, we have suggested three di#erent approaches for systema ..."
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Cited by 144 (23 self)
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After adequately demonstrating the ability to solve di#erent twoobjective optimization problems, multiobjective evolutionary algorithms (MOEAs) must now show their e#cacy in handling problems having more than two objectives. In this paper, we have suggested three di#erent approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of exact shape and location of the resulting Paretooptimal front, and introduction of controlled di#culties in both converging to the true Paretooptimal front and maintaining a widely distributed set of solutions are the main features of the suggested test problems. Because of the above features, they should be found useful in various research activities on MOEAs, such as testing the performance of a new MOEA, comparing di#erent MOEAs, and better understanding of the working principles of MOEAs.
Scalable MultiObjective Optimization Test Problems
 in Congress on Evolutionary Computation (CEC’2002
, 2002
"... After adequately demonstrating the ability to solve different twoobjective optimization problems, multiobjective evolutionary algorithms (MOEAs) must now show their efficacy in handling problems having more than two objectives. In this paper, we suggest three different approaches for systematicall ..."
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Cited by 106 (8 self)
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After adequately demonstrating the ability to solve different twoobjective optimization problems, multiobjective evolutionary algorithms (MOEAs) must now show their efficacy in handling problems having more than two objectives. In this paper, we suggest three different approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of exact shape and location of the resulting Paretooptimal front, and ability to control difficulties in both converging to the true Paretooptimal front and maintaining a widely distributed set of solutions are the main features of the suggested test problems. Because of these features, they should be found useful in various research activities on MOEAs, such as testing the performance of a new MOEA, comparing different MOEAs, and having a better understanding of the working principles of MOEAs.
On a MultiObjective Evolutionary Algorithm and Its Convergence to the Pareto Set
 IN PROCEEDINGS OF THE 5TH IEEE CONFERENCE ON EVOLUTIONARY COMPUTATION
, 1998
"... Although there are many versions of evolutionary algorithms that are tailored to multicriteria optimization, theoretical results are apparently not yet available. Here, it is shown that results known from the theory of evolutionary algorithms in case of single criterion optimization do not carry ov ..."
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Cited by 60 (7 self)
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Although there are many versions of evolutionary algorithms that are tailored to multicriteria optimization, theoretical results are apparently not yet available. Here, it is shown that results known from the theory of evolutionary algorithms in case of single criterion optimization do not carry over to the multicriterion case. At first, three different step size rules are investigated numerically for a selected problem with two conflicting objectives. The empirical results obtained by these experiments lead to the observation that only one of these step size rules may have the property to ensure convergence to the Pareto set. A theoretical analysis finally shows that a special version of an evolutionary algorithm with this step size rule converges with probability one to the Pareto set for the test problem under consideration.
P.: A Spatial PredatorPrey Approach to MultiObjective Optimization: A Preliminary Study
 Proceedings of the Parallel Problem Solving From Nature – PPSN V
, 1998
"... Abstract. This paper presents a novel evolutionary approach of approximating the shape of the Paretooptimal set of multiobjective optimization problems. The evolutionary algorithm (EA) uses the predatorprey model from ecology. The prey are the usual individuals of an EA that represent possible so ..."
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Cited by 40 (5 self)
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Abstract. This paper presents a novel evolutionary approach of approximating the shape of the Paretooptimal set of multiobjective optimization problems. The evolutionary algorithm (EA) uses the predatorprey model from ecology. The prey are the usual individuals of an EA that represent possible solutions to the optimization task. They are placed at vertices of a graph, remain stationary, reproduce, and are chased by predators that traverse the graph. The predators chase the prey only within its current neighborhood and according to one of the optimization criteria. Because there are several predators with different selection criteria, those prey individuals, which perform best with respect to all objectives, are able to produce more descendants than inferior ones. As soon as a vertex for the prey becomes free, it is refilled by descendants from alive parents in the usual way of EA, i.e., by inheriting slightly altered attributes. After a while, the prey concentrate at Paretooptimal positions. The main objective of this preliminary study is the answer to the question whether the predatorprey approach to multiobjective optimization works at all. The performance of this evolutionary algorithm is examined under several stepsize adaptation rules. 1
Evolutionary Search for Minimal Elements in Partially Ordered Finite Sets
 EVOLUTIONARY PROGRAMMING VII, PROCEEDINGS OF THE 7TH ANNUAL CONFERENCE ON EVOLUTIONARY PROGRAMMING
, 1998
"... The task of finding minimal elements of a partially ordered set is a generalization of the task of finding the global minimum of a realvalued function or of finding paretooptimal points of a multicriteria optimization problem. It is shown that evolutionary algorithms are able to converge to t ..."
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Cited by 33 (8 self)
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The task of finding minimal elements of a partially ordered set is a generalization of the task of finding the global minimum of a realvalued function or of finding paretooptimal points of a multicriteria optimization problem. It is shown that evolutionary algorithms are able to converge to the set of minimal elements in finite time with probability one, provided that the search space is finite, the timeinvariant variation operator is associated with a positive transition probability function and that the selection operator obeys the socalled `elite preservation strategy.'
A Survey of Multiobjective Optimization in Engineering Design Johan
, 2000
"... Real world engineering design problems are usually characterized by the presence of many conflicting objectives. Therefore, it is natural to look at the engineering design problem as a multiobjective optimization problem. This report summarizes a survey of techniques to conduct multiobjective optimi ..."
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Cited by 27 (0 self)
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Real world engineering design problems are usually characterized by the presence of many conflicting objectives. Therefore, it is natural to look at the engineering design problem as a multiobjective optimization problem. This report summarizes a survey of techniques to conduct multiobjective optimization in an engineering design context.
The nature of niching: genetic algorithms and the evolution of optimal, cooperative populations
, 1997
"... ..."
Multidimensional Exploration of Software Implementations for DSP Algorithms
 JOURNAL OF VLSI SIGNAL PROCESSING SYSTEMS
, 1999
"... When implementing software for programmable digital signal processors (PDSPs), the design space is defined by a complex range of constraints and optimization objectives. Three implementation metrics that are crucial in many PDSP applications are the program memory requirement (code size), data mem ..."
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Cited by 13 (11 self)
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When implementing software for programmable digital signal processors (PDSPs), the design space is defined by a complex range of constraints and optimization objectives. Three implementation metrics that are crucial in many PDSP applications are the program memory requirement (code size), data memory requirement, and execution time. This paper addresses the problem of exploring the 3dimensional space of tradeoffs that is defined by these crucial metrics. Given a software library for a target PDSP, and a dataflowbased block diagram specification of a DSP application in terms of this library, our objective in this paper is to compute a full range of Paretooptimal solutions. For solving this multiobjective optimization problem, an evolutionary algorithm based approach is applied. We illustrate our techniques by analyzing the tradeoff fronts of a practical application for a number of wellknown, commercial PDSPs.