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Theoretical and Numerical ConstraintHandling Techniques used with Evolutionary Algorithms: A Survey of the State of the Art
, 2002
"... This paper provides a comprehensive survey of the most popular constrainthandling techniques currently used with evolutionary algorithms. We review approaches that go from simple variations of a penalty function, to others, more sophisticated, that are biologically inspired on emulations of the imm ..."
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Cited by 178 (26 self)
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This paper provides a comprehensive survey of the most popular constrainthandling techniques currently used with evolutionary algorithms. We review approaches that go from simple variations of a penalty function, to others, more sophisticated, that are biologically inspired on emulations of the immune system, culture or ant colonies. Besides describing briefly each of these approaches (or groups of techniques), we provide some criticism regarding their highlights and drawbacks. A small comparative study is also conducted, in order to assess the performance of several penaltybased approaches with respect to a dominancebased technique proposed by the author, and with respect to some mathematical programming approaches. Finally, we provide some guidelines regarding how to select the most appropriate constrainthandling technique for a certain application, ad we conclude with some of the the most promising paths of future research in this area.
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 150 (22 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.
An Updated Survey of GABased Multiobjective Optimization Techniques
 ACM COMPUTING SURVEYS
, 1998
"... ... this paper is to summarize and organize the information on these current approaches, emphasizing the importance of analyzing the Operations Research techniques in which most of them are based, in an attempt to motivate researchers to look into these mathematical programming approaches for new wa ..."
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Cited by 124 (0 self)
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... this paper is to summarize and organize the information on these current approaches, emphasizing the importance of analyzing the Operations Research techniques in which most of them are based, in an attempt to motivate researchers to look into these mathematical programming approaches for new ways of exploiting the search capabilities of evolutionary algorithms. Furthermore, a summary of the main algorithms behind these approaches is provided, together with a brief criticism that includes their advantages and disadvantages, their degree of applicability and some of their known applications. Finally, the future trends in this area and some possible paths of further research are also addressed.
Scalable MultiObjective Optimization Test Problems
 in Congress on Evolutionary Computation (CECâ€™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 112 (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.
The Advantages of Generative Grammatical Encodings for Physical Design
 In Congress on Evolutionary Computation
, 2001
"... One of the applications of evolutionary algorithms is the automatic creation of designs. For evolutionary techniques to scale to the complexities necessary for actual engineering problems, it has been argued that generative systems, where the genotype is an algorithm for constructing the final desig ..."
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Cited by 106 (15 self)
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One of the applications of evolutionary algorithms is the automatic creation of designs. For evolutionary techniques to scale to the complexities necessary for actual engineering problems, it has been argued that generative systems, where the genotype is an algorithm for constructing the final design, should be used as the encoding. We describe a system for creating generative specifications by combining Lindenmayer systems with evolutionary algorithms and apply it to the problem of generating table designs. Designs evolved by our system reach an order of magnitude more parts than previous generative systems. Comparing it against a nongenerative encoding we find that the generative system produces designs with higher fitness and is faster than the nongenerative system. Finally, we demonstrate the ability of our system to go from design to manufacture by constructing evolved table designs using rapid prototyping equipment. 1 Introduction Evolutionary algorithms (EAs) have been succe...
On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers
, 1996
"... Abstract. This work proposes a quantitative, nonparametric interpretation of statistical performance of stochastic multiobjective optimizers, including, but not limited to, genetic algorithms. It is shown that, according to this interpretation, typical performance can be defined in terms analogous ..."
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Cited by 103 (7 self)
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Abstract. This work proposes a quantitative, nonparametric interpretation of statistical performance of stochastic multiobjective optimizers, including, but not limited to, genetic algorithms. It is shown that, according to this interpretation, typical performance can be defined in terms analogous to the notion of median for ordinal data, as can other measures analogous to other quantiles. Nonparametric statistical test procedures are then shown to be useful in deciding the relative performance of different multiobjective optimizers on a given problem. Illustrative experimental results are provided to support the discussion. 1
The Pareto Envelopebased Selection Algorithm for Multiobjective Optimization
 Proceedings of the Parallel Problem Solving from Nature VI Conference
, 2000
"... . We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelopebased Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hypergrid based scheme. PESA's selection method is relatively unusual in comparison with current ..."
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Cited by 94 (2 self)
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. We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelopebased Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hypergrid based scheme. PESA's selection method is relatively unusual in comparison with current well known multiobjective evolutionary algorithms, which tend to use counts based on the degree to which solutions dominate others in the population. The diversity maintenance method is similar to that used by certain other methods. The main attraction of PESA is the integration of selection and diversity maintenance, whereby essentially the same technique is used for both tasks. The resulting algorithm is simple to describe, with full pseudocode provided here and real code available from the authors. We compare PESA with two recent strongperforming MOEAs on some multiobjective test problems recently proposed by Deb. We find that PESA emerges as the best method overall on these problems...
Multiobjective Optimization Using Dynamic Neighborhood Particle Swarm Optimization
, 2002
"... This paper presents a Particle Swarm Optimization (PSO) algorithm for multiobjective optimization problems. PSO is modified by using a dynamic neighborhood strategy, new particle memory updating, and onedimension optimization to deal with multiple objectives. Several benchmark cases were tested and ..."
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Cited by 84 (2 self)
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This paper presents a Particle Swarm Optimization (PSO) algorithm for multiobjective optimization problems. PSO is modified by using a dynamic neighborhood strategy, new particle memory updating, and onedimension optimization to deal with multiple objectives. Several benchmark cases were tested and showed that PSO could efficiently find multiple Pareto optimal solutions.
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 78 (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.
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 77 (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...