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41
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 45 (15 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.
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.
A Global Repair Operator for Capacitated Arc Routing Problem
"... Abstract—Capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NPhard and exact methods are only applicable for small instances, heuristics and metaheuristic methods are widely adopted when solving CARP ..."
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Cited by 17 (10 self)
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Abstract—Capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NPhard and exact methods are only applicable for small instances, heuristics and metaheuristic methods are widely adopted when solving CARP. This paper demonstrates one major disadvantage encountered by traditional search algorithms and proposes a novel operator named global repair operator (GRO) to address it. We further embed GRO in a recently proposed tabu search algorithm (TSA) and apply the resultant repairbased tabu search (RTS) algorithm to five wellknown benchmark test sets. Empirical results suggest that RTS not only outperforms TSA in terms of quality of solutions but also converges to the solutions faster. Moreover, RTS is also competitive with a number of stateoftheart approaches for CARP. The efficacy of GRO is thereby justified. More importantly, since GRO is not specifically designed for the referred TSA, it might be a potential tool for improving any existing method that adopts the same solution representation. Index Terms—Capacitated arc routing problem (CARP), global repair operator (GRO), heuristic search, tabu search. I.
An introduction and survey of estimation of distribution algorithms
 SWARM AND EVOLUTIONARY COMPUTATION
, 2011
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MultiStart Tabu Search and Diversification Strategies for the Quadratic Assignment Problem
, 2006
"... The quadratic assignment problem (QAP) is a well known combinatorial optimization problem most commonly used to model the facilitylocation problem. The widely acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this study, we introduce several mul ..."
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Cited by 15 (1 self)
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The quadratic assignment problem (QAP) is a well known combinatorial optimization problem most commonly used to model the facilitylocation problem. The widely acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this study, we introduce several multistart tabu search variants and show the benefit of utilizing strategic diversification within the tabu search framework for the QAP. Computational results for a set of problems obtained from QAPLIB demonstrate the ability of our TS multistart variants to improve on the classic tabu search approach that is one of the principal and most widely used methods for the QAP. We also show that our new procedures are highly competitive with the best recently introduced methods from the literature, including more complex hybrid approaches that incorporate a classic tabu search method as a subroutine.
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 Multilevel Memetic Approach for Improving Graph Kpartitions
, 2011
"... Graph partitioning is one of the most studied NPcomplete problems. Given a graph G = (V, E), the task is to partition the vertex set V into k disjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this work, we present a highly ef ..."
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Cited by 13 (5 self)
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Graph partitioning is one of the most studied NPcomplete problems. Given a graph G = (V, E), the task is to partition the vertex set V into k disjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this work, we present a highly effective multilevel memetic algorithm, which integrates a new multiparent crossover operator and a powerful perturbationbased tabu search algorithm. The proposed crossover operator tends to preserve the backbone with respect to a certain number of parent individuals, i.e. the grouping of vertices which is common to all parent individuals. Extensive experimental studies on numerous benchmark instances from the Graph Partitioning Archive show that the proposed approach, within a time limit ranging from several minutes to several hours, performs far better than any of the existing graph partitioning algorithm in terms of solution quality.
A modelbased evolutionary algorithm for biobjective optimization
 in Proceedings of the Congress on Evolutionary Computation (CEC
, 2005
"... Abstract The Pareto optimal solutions to a multiobjective optimization problem often distribute very regularly in both the decision space and the objective space. Most existing evolutionary algorithms do not explicitly take advantage of such a regularity. This paper proposed a modelbased evolution ..."
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Cited by 10 (3 self)
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Abstract The Pareto optimal solutions to a multiobjective optimization problem often distribute very regularly in both the decision space and the objective space. Most existing evolutionary algorithms do not explicitly take advantage of such a regularity. This paper proposed a modelbased evolutionary algorithm (MMOEA) for biobjective optimization problems. Inspired by the ideas from estimation of distribution algorithms, MMOEA uses a probability model to capture the regularity of the distribution of the Pareto optimal solutions. The Local PCA and the leastsquares method are employed for building the model. New solutions are sampled from the model thus built. At alternate generations, MMOEA uses crossover and mutation to produce new solutions. The selection in MMOEA is the same as in NSGAII. Therefore, MOEA can be regarded as a combination of EDA and NSGAII. The preliminary experimental results show that MMOEA performs better than NSGAII. 1
Multiobjective Evolutionary Algorithms for Electric Power Dispatch Problem
 IEEE Transaction On Evolutionary Computation, Vol.10, No
, 2006
"... A Wireless Sensor Network (WSN) design often requires the decision of optimal locations (deployment) and transmit power levels (power assignment) of the sensors to be deployed in an area of interest. Few attempts have been made on optimizing both decision variables for maximizing the network coverag ..."
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Cited by 9 (0 self)
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A Wireless Sensor Network (WSN) design often requires the decision of optimal locations (deployment) and transmit power levels (power assignment) of the sensors to be deployed in an area of interest. Few attempts have been made on optimizing both decision variables for maximizing the network coverage and lifetime objectives, even though, most of the latter studies consider the two objectives individually. This paper defines the multiobjective Deployment and Power Assignment Problem (DPAP). Using the MultiObjective Evolutionary Algorithm based on Decomposition (MOEA/D), the DPAP is decomposed into a set of scalar subproblems that are classified based on their objective preference and tackled in parallel by using neighborhood information and problemspecific evolutionary operators, in a single run. The proposed operators adapt to the requirements and objective preferences of each subproblem dynamically during the evolution, resulting in significant improvements on the overall performance of MOEA/D. Simulation results have shown the superiority of the problemspecific MOEA/D against the NSGAII in several network instances, providing a diverse set of high quality network designs to facilitate the decision maker’s choice. Key words: deployment, power assignment, sensor networks, multiobjective optimization, evolutionary algorithms 1. Introduction and
Breakout local search for maximum clique problems
 Computers & Operations Research
"... The maximum clique problem (MCP) is one of the most popular combinatorial optimization problems with various practical applications. An important generalization of MCP is the maximum weight clique problem (MWCP) where a positive weight is associate to each vertex. In this paper, we present Breakout ..."
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Cited by 9 (6 self)
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The maximum clique problem (MCP) is one of the most popular combinatorial optimization problems with various practical applications. An important generalization of MCP is the maximum weight clique problem (MWCP) where a positive weight is associate to each vertex. In this paper, we present Breakout Local Search (BLS) which can be applied to both MC and MWC problems without any particular adaptation. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Extensive experimental evaluations using the DIMACS and BOSHLIB benchmarks show that the proposed approach competes favourably with the current stateofart heuristic methods for MCP. Moreover, it is able to provide some new improved results for a number of MWCP instances. This paper also reports for the first time a detailed landscape analysis, which has been missing in the literature. This analysis not only explains the difficulty of several benchmark instances, but also justifies to some extent the behaviour of the proposed approach and the used parameter settings.