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37
The exploration/exploitation tradeoff in dynamic cellular genetic algorithms
 IEEE Transactions on Evolutionary Computation
, 2005
"... Abstract—This paper studies static and dynamic decentralized versions of the search model known as cellular genetic algorithm (cGA), in which individuals are located in a specific topology and interact only with their neighbors. Making changes in the shape of such topology or in the neighborhood may ..."
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Cited by 47 (8 self)
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Abstract—This paper studies static and dynamic decentralized versions of the search model known as cellular genetic algorithm (cGA), in which individuals are located in a specific topology and interact only with their neighbors. Making changes in the shape of such topology or in the neighborhood may give birth to a high number of algorithmic variants. We perform these changes in a methodological way by tuning the concept of ratio. Since the relationship (ratio) between the topology and the neighborhood shape defines the search selection pressure, we propose to analyze in depth the influence of this ratio on the exploration/exploitation tradeoff. As we will see, it is difficult to decide which ratio is best suited for a given problem. Therefore, we introduce a preprogrammed change of this ratio during the evolution as a possible additional improvement that removes the need of specifying a single ratio. A later refinement will lead us to the first adaptive dynamic kind of cellular models to our knowledge. We conclude that these dynamic cGAs have the most desirable behavior among all the evaluated ones in terms of efficiency and accuracy; we validate our results on a set of seven different problems of considerable complexity in order to better sustain our conclusions. Index Terms—Cellular genetic algorithm (cGA), evolutionary algorithm (EA), dynamic adaptation, neighborhoodtopopulation ratio. I.
RMMEDA: a regularity modelbased multiobjective estimation of distribution algorithm
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 2007
"... Under mild conditions, it can be induced from the Karush–Kuhn–Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is a piecewise continuous @ IAD manifold, where is the number of objectives. Based on this regularity property, we propose ..."
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Cited by 18 (3 self)
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Under mild conditions, it can be induced from the Karush–Kuhn–Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is a piecewise continuous @ IAD manifold, where is the number of objectives. Based on this regularity property, we propose a regularity modelbased multiobjective estimation of distribution algorithm (RMMEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a @ IAD piecewise continuous manifold. The local principal component analysis algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A nondominated sortingbased selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RMMEDA outperforms three other stateoftheart algorithms, namely, GDE3, PCXNSGAII, and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RMMEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RMMEDA have also been identified and discussed in this paper.
On Stability of Fixed Points of Limit Models of Univariate Marginal Distribution Algorithm and Factorized Distribution Algorithm
 IEEE Trans. on Evolutionary Computation, Accepted
, 2003
"... Abstract—This paper aims to study the advantages of using higher order statistics in estimation distribution of algorithms (EDAs). We study two EDAs with twotournament selection for discrete optimization problems. One is the univariate marginal distribution algorithm (UMDA) using only firstorder s ..."
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Cited by 18 (7 self)
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Abstract—This paper aims to study the advantages of using higher order statistics in estimation distribution of algorithms (EDAs). We study two EDAs with twotournament selection for discrete optimization problems. One is the univariate marginal distribution algorithm (UMDA) using only firstorder statistics and the other is the factorized distribution algorithm (FDA) using higher order statistics. We introduce the heuristic functions and the limit models of these two algorithms and analyze stability of these limit models. It is shown that the limit model of UMDA can be trapped at any local optimal solution for some initial probability models. However, degenerate probability density functions (pdfs) at some local optimal solutions are unstable in the limit model of FDA. In particular, the degenerate pdf at the global optimal solution is the unique asymptotically stable point in the limit model of FDA for the optimization of an additively decomposable function. Our results suggest that using higher order statistics could improve the chance of finding the global optimal solution. Index Terms—Estimation of distribution algorithms (EDAs), factorized distribution algorithm (FDA), heuristic function, stability, univariate marginal distribution algorithm (UMDA). I.
An introduction and survey of estimation of distribution algorithms
 SWARM AND EVOLUTIONARY COMPUTATION
, 2011
"... ..."
Efficient Search for Robust Solutions by Means of Evolutionary Algorithm and Fitness Approximation
 IEEE Transactions on Evolutionary Computation
, 2006
"... Abstract—For many realworld optimization problems, the robustness of a solution is of great importance in addition to the solution’s quality. By robustness, we mean that small deviations from the original design, e.g., due to manufacturing tolerances, should be tolerated without a severe loss of qu ..."
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Cited by 17 (2 self)
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Abstract—For many realworld optimization problems, the robustness of a solution is of great importance in addition to the solution’s quality. By robustness, we mean that small deviations from the original design, e.g., due to manufacturing tolerances, should be tolerated without a severe loss of quality. One way to achieve that goal is to evaluate each solution under a number of different scenarios and use the average solution quality as fitness. However, this approach is often impractical, because the cost for evaluating each individual several times is unacceptable. In this paper, we present a new and efficient approach to estimating a solution’s expected quality and variance. We propose to construct local approximate models of the fitness function and then use these approximate models to estimate expected fitness and variance. Based on a variety of test functions, we demonstrate empirically that our approach significantly outperforms the implicit averaging approach, as well as the explicit averaging approaches using existing estimation techniques reported in the literature. Index Terms—Evolutionary optimization, fitness approximation, robustness, uncertainty. I.
RMMEDA: A Regularity Model Based Multiobjective Estimation of Distribution Algorithm
, 2008
"... Under mild conditions, it can be induced from the KarushKuhnTucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is (m − 1)D piecewise continuous, where m is the number of objectives. Based on this regularity property, we propose a Regul ..."
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Cited by 14 (8 self)
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Under mild conditions, it can be induced from the KarushKuhnTucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is (m − 1)D piecewise continuous, where m is the number of objectives. Based on this regularity property, we propose a Regularity Model based Multiobjective Estimation of Distribution Algorithm (RMMEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a (m−1)D piecewise continuous manifold. The Local Principal Component Analysis algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A nondominated sorting based selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RMMEDA outperforms three other stateoftheart algorithms, namely, GDE3, PCXNSGAII and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RMMEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RMMEDA have also been identified and discussed in this paper.
A generalpurpose tunable landscape generator
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 2006
"... The research literature on metaheuristic and evolutionary computation has proposed a large number of algorithms for the solution of challenging realworld optimization problems. It is often not possible to study theoretically the performance of these algorithms unless significant assumptions are ma ..."
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Cited by 13 (3 self)
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The research literature on metaheuristic and evolutionary computation has proposed a large number of algorithms for the solution of challenging realworld optimization problems. It is often not possible to study theoretically the performance of these algorithms unless significant assumptions are made on either the algorithm itself or the problems to which it is applied, or both. As a consequence, metaheuristics are typically evaluated empirically using a set of test problems. Unfortunately, relatively little attention has been given to the development of methodologies and tools for the largescale empirical evaluation and/or comparison of metaheuristics. In this paper, we propose a landscape (testproblem) generator that can be used to generate optimization problem instances for continuous, boundconstrained optimization problems. The landscape generator is parameterized by a small number of parameters, and the values of these parameters have a direct and intuitive interpretation in terms of the geometric features of the landscapes that they produce. An experimental space is defined over algorithms and problems, via a tuple of parameters for any specified algorithm and problem class (here determined by the landscape generator). An experiment is then clearly specified as a point in this space, in a way that is analogous to other areas of experimental algorithmics, and more generally in experimental design. Experimental results are presented, demonstrating the use of the landscape generator. In particular, we analyze some simple, continuous estimation of distribution algorithms, and gain new insights into the behavior of these algorithms using the landscape generator.
Analysis of Computational Time of Simple Estimation of Distribution Algorithms
, 2010
"... Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well ED ..."
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Cited by 11 (5 self)
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Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well EDAs (with a finite population size larger than two) will scale up when the dimension of the optimization problem (problem size) goes up. This paper studies the computational time complexity of a simple EDA, i.e., the univariate marginal distribution algorithm (UMDA), in order to gain more insight into EDAs complexity. First, we discuss how to measure the computational time complexity of EDAs. A classification of problem hardness based on our discussions is then given. Second, we prove a theorem related to problem hardness and the probability conditions of
A mathematical modelling technique for the analysis of the dynamics of a simple continuous EDA
 in IEEE Congress on Evolutionary Computation, CEC 2006
, 2006
"... Abstract — This paper presents some initial attempts to mathematically model the dynamics of a continuous Estimation of Distribution Algorithm (EDA) based on Gaussian distributions. Case studies are conducted on both unimodal and multimodal problems to highlight the effectiveness of the proposed tec ..."
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Cited by 11 (5 self)
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Abstract — This paper presents some initial attempts to mathematically model the dynamics of a continuous Estimation of Distribution Algorithm (EDA) based on Gaussian distributions. Case studies are conducted on both unimodal and multimodal problems to highlight the effectiveness of the proposed technique and explore some fundamental issues of the EDA. With some general assumptions, we can show that, for onedimensional unimodal problems and with the (µ, λ) scheme: (1). The convergence behaviour of the EDA is independent of the test function except its general shape; (2). When starting far away from the global optimum, the EDA may get stuck; (3). Given a certain selection pressure, there is a unique parameter value that could help the EDA achieve desirable performance; for onedimensional multimodal problems: (1). The EDA could get stuck with the (µ, λ) scheme; (2). The EDA will never get stuck with the (µ+λ) scheme. I.
Evolutionary algorithms refining a heuristic: Hyperheuristic for sharedpath protections in WDM networks under SRLG constraints
 IEEE Transactions on Systems, Man and Cybernetics, Part B
, 2007
"... Abstract—An evolutionary algorithm (EA) can be used to tune the control parameters of a construction heuristic to an optimization problem and generate a nearly optimal solution. This approach is in the spirit of indirect encoding EAs. Its performance relies on both the heuristic and the EA. This pap ..."
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Cited by 7 (4 self)
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Abstract—An evolutionary algorithm (EA) can be used to tune the control parameters of a construction heuristic to an optimization problem and generate a nearly optimal solution. This approach is in the spirit of indirect encoding EAs. Its performance relies on both the heuristic and the EA. This paper proposes a threephase parameterized construction heuristic for the sharedpath protection problem in wavelength division multiplexing networks with sharedrisk link group constraints and applies an EA for optimizing the control parameters of the proposed heuristics. The experimental results show that the proposed approach is effective on all the tested network instances. It was also demonstrated that an EA with guided mutation performs better than a conventional genetic algorithm for tuning the control parameters, which indicates that a combination of global statistical information extracted from the previous search and location information of the best solutions found so far could improve the performance of an algorithm. Index Terms—Estimation of distribution algorithms (EDAs), evolutionary algorithm (EA), guided mutation, hyperheuristics, memetic algorithm (MA), network protection, sharedrisk link group (SRLG). I.