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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 123 (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.
Evolutionary Computation in Constraint Satisfaction and Machine Learning
 Faculty of Natural Sciences, Mathematics, and Computer Science
, 2001
"... Introduction At rst sight the two problem areas constraint satisfaction and machine learning do not appear to be similar. The rst has a clear denition of its problem domain and a crisp denition of solutions. The second is a much broader dened problem domain, which leads to many objectives to be sol ..."
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Cited by 33 (4 self)
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Introduction At rst sight the two problem areas constraint satisfaction and machine learning do not appear to be similar. The rst has a clear denition of its problem domain and a crisp denition of solutions. The second is a much broader dened problem domain, which leads to many objectives to be solved. Many research areas have focused there attention on constraint satisfaction, operating research, ant colonies, evolutionary computation and, most notable, constraint programming. Although the problems that are being studied share the same goal, which is to satisfy a set of constraints, their precise denition varies. Among these problems we nd numerous well known ones such as, kgraph colouring, 3sat and nqueens. For any of these problems we can transform them to a binary constraint satisfaction problem without loss of generality. This holds for any nite constraint satisfaction problem, and it means that we can solve a probl
A Survey of Constraint Handling Techniques used with Evolutionary Algorithms
 Laboratorio Nacional de Informática Avanzada
, 1999
"... Despite the extended applicability of evolutionary algorithms to a wide range of domains, the fact that these algorithms are unconstrained optimization techniques leaves open the issue regarding how to incorporate constraints of any kind (linear, nonlinear, equality and inequality) into the fitness ..."
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Cited by 29 (0 self)
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Despite the extended applicability of evolutionary algorithms to a wide range of domains, the fact that these algorithms are unconstrained optimization techniques leaves open the issue regarding how to incorporate constraints of any kind (linear, nonlinear, equality and inequality) into the fitness function as to search efficiently. The main goal of this paper is to provide a detailed and comprehensive survey of the many constraint handling approaches that have been proposed for evolutionary algorithms, analyzing in each case their advantages and disadvantages, and concluding with some of the most promising paths of research.
An application of Iterated Local Search to Graph Coloring Problem
 PROCEEDINGS OF THE COMPUTATIONAL SYMPOSIUM ON GRAPH COLORING AND ITS GENERALIZATIONS
, 2002
"... Graph coloring is a well known problem from graph theory that, when solving it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors k, one has to find a feasible coloring; once such a coloring is found, the number of colo ..."
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Cited by 27 (2 self)
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Graph coloring is a well known problem from graph theory that, when solving it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors k, one has to find a feasible coloring; once such a coloring is found, the number of colors is decreased and the local search starts again. Here we explore the application of Iterated Local Search to the graph coloring problem. Iterated Local Search is a simple and powerful metaheuristic that has shown very good results for a variety of optimization problems. In our research we investigate different perturbation schemes and present computational results on some hard instances from the DIMACS benchmark suite.
A Superior Evolutionary Algorithm for 3SAT
 Proceedings of the 7th Annual Conference on Evolutionary Programming, number 1477 in LNCS
, 1998
"... . We investigate three approaches to Boolean satisfiability problems. We study and compare the best heuristic algorithm WGSAT and two evolutionary algorithms, an evolution strategy and an evolutionary algorithm adapting its own fitness function while running. The results show that the adaptive EA ou ..."
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Cited by 23 (0 self)
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. We investigate three approaches to Boolean satisfiability problems. We study and compare the best heuristic algorithm WGSAT and two evolutionary algorithms, an evolution strategy and an evolutionary algorithm adapting its own fitness function while running. The results show that the adaptive EA outperforms the other two approaches. The power of this EA originates from the adaptive mechanism, which is completely problem independent and generally applicable to any constraint satisfaction problem. This suggests that the adaptive EA is not only a good solver for satisfiability problems, but for constraint satisfaction problems in general. 1 Introduction Handling NPcomplete problems with evolutionary algorithms (EAs) is a great challenge. In particular, the presence of constraints makes finding solutions difficult for an EA. In this paper, we investigate solving constraint satisfaction problems (CSPs), in particular the 3SAT problem, and try three different approaches for solving it: O...
A Comparison of Genetic Programming Variants for Data Classification
, 1999
"... In this paper we report the results of a comparative study on different variations of genetic programming applied on binary data classification problems. The first genetic programming variant is weighting data records for calculating the classification error and modifying the weights during the run. ..."
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Cited by 22 (1 self)
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In this paper we report the results of a comparative study on different variations of genetic programming applied on binary data classification problems. The first genetic programming variant is weighting data records for calculating the classification error and modifying the weights during the run. Hereby the algorithm is defining its own fitness function in an online fashion giving higher weights to `hard' records. Another novel feature we study is the atomic representation, where `Booleanization' of data is not performed at the root, but at the leafs of the trees and only Boolean functions are used in the trees' body. As a third aspect we look at generational and steadystate models in combination of both features.
Solving Constraint Satisfaction Problems with Heuristicbased Evolutionary Algorithms
 In Proceedings of the 2000 Congress on Evolutionary Computation
, 1999
"... Evolutionary algorithms (EAs) for solving constraint satisfaction problems (CSPs) can be roughly divided into two classes: EAs using adaptive fitness functions and EAs using heuristics. In [5] the most effective EAs of the first class have been compared experimentally using a large set of benchma ..."
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Cited by 21 (4 self)
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Evolutionary algorithms (EAs) for solving constraint satisfaction problems (CSPs) can be roughly divided into two classes: EAs using adaptive fitness functions and EAs using heuristics. In [5] the most effective EAs of the first class have been compared experimentally using a large set of benchmark instances consisting of randomly generated binary CSPs. In this paper we complete this comparison by studying the most effective EAs that use heuristics.
SAWing EAs: adapting the fitness function for solving constrained problems
, 1999
"... In this chapter we describe a problem independent method for treating constraints in an evolutionary algorithm. Technically, this method amounts to changing the definition of the fitness function during a run of an EA, based on feedback from the search process. Obviously, redefining the fitness func ..."
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Cited by 15 (3 self)
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In this chapter we describe a problem independent method for treating constraints in an evolutionary algorithm. Technically, this method amounts to changing the definition of the fitness function during a run of an EA, based on feedback from the search process. Obviously, redefining the fitness function means rede ning the problem to be solved. On the short term this deceives the algorithm making the fitness values deteriorate, but as experiments clearly indicate, on the long run it is beneficial. We illustrate the power of the method on different constraint satisfaction problems and point out other application areas of this technique.
A NEW VERTEX COLORING ALGORITHM BASED ON VARIABLE ACTIONSET LEARNING AUTOMATA
"... Abstract. In this paper, we propose a learning automatabased iterative algorithm for approximating a near optimal solution to the vertex coloring problem. Vertex coloring is a wellknown NPhard optimization problem in graph theory in which each vertex is assigned a color so that no two adjacent ve ..."
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Cited by 14 (6 self)
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Abstract. In this paper, we propose a learning automatabased iterative algorithm for approximating a near optimal solution to the vertex coloring problem. Vertex coloring is a wellknown NPhard optimization problem in graph theory in which each vertex is assigned a color so that no two adjacent vertices have the same color. Each iteration of the proposed algorithm is subdivided into several stages, and at each stage a subset of the uncolored non adjacent vertices are randomly selected and assigned the same color. This process continues until no more vertices remain uncolored. As the proposed algorithm proceeds, taking advantage of the learning automata the number of stages per iteration and so the required number of colors tends to the chromatic number of the graph since the number of vertices which are colored at each stage is maximized. To show the performance of the proposed algorithm we compare it with several existing vertex coloring algorithms in terms of the time and the number of colors required for coloring the graphs. The obtained results show the superiority of the proposed algorithm over the others.
Evolutionary algorithms and constraint satisfaction: Definitions, survey, methodology, and research directions
 Theoretical Aspects of Evolutionary Computing
"... Abstract. In this tutorial we consider the issue of constraint handling by evolutionary algorithms (EA). We start this study with a categorization of constrained problems and observe that constraint handling is not straightforward in an EA. Namely, the search operators mutation and recombination a ..."
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Cited by 10 (1 self)
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Abstract. In this tutorial we consider the issue of constraint handling by evolutionary algorithms (EA). We start this study with a categorization of constrained problems and observe that constraint handling is not straightforward in an EA. Namely, the search operators mutation and recombination are `blind ' to constraints. Hence, there is no guarantee that if the parents satisfy some constraints the offspring will satisfy them as well. This suggests that the presence of constraints in a problem makes EAs intrinsically unsuited to solve this problem. This should especially hold if there are no objectives only constraints in the original problem specication the category of constraint satisfaction problems. A survey of related literature, however, discloses that there are quite a few successful attempts to evolutionary constraint satisfaction. Based on this survey we identify a number of common features in these approaches and arrive to the conclusion that the presence of constraints is not harmful, but rather helpful in that it provides extra information that EAs can utilize. The tutorial is concluded by considering a number of key questions on research methodology and some promising future research directions.