Heuristics and metaheuristics for the maximum diversity problem

Martı́, Rafael; Gallego, Micael; Duarte, Abraham; Pardo, Eduardo G.

doi:10.1007/s10732-011-9172-4

Cited by 73 publications

(39 citation statements)

References 33 publications

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“…The MEWCP is to find a clique C in G such that the sum of the weights of the edges in C is maximized and the number of vertices in C is no more than m. Like the MVWCP, the decision version of the MEWCP is NP-complete (Ausiello, Crescenzi, Gambosi, Kann, Marchetti-Spaccamela, & Protasi, 1999), as far as it reduces to the maximum clique problem. The MEWCP or its variants are also studied under other names: Maximum diversity (Martí, Gallego, Duarte, & Pardo, 2013;Palubeckis, 2007), maxisum dispersion (Kuby, 1987), MAX-AVG dispersion (Ravi, Rosenkrantz, & Tayi, 1994), remoteclique (Chandra & Halldórsson, 2001), and maximum edge-weighted subgraph (Macambira, 2003).…”

Section: Accepted Manuscriptmentioning

confidence: 99%

A review on algorithms for maximum clique problems

Hao

2015

European Journal of Operational Research

259

168

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The maximum clique problem (MCP) is to determine in a graph a clique (i.e., a complete subgraph) of maximum cardinality. The MCP is notable for its capability of modeling other combinatorial problems and real-world applications. As one of the most studied NP-hard problems, many algorithms are available in the literature and new methods are continually being proposed. Given that the two existing surveys on the MCP date back to 1994 and 1999 respectively, one primary goal of this paper is to provide an updated and comprehensive review on both exact and heuristic MCP algorithms, with a special focus on recent developments. To be informative, we identify the general framework followed by these algorithms and pinpoint the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the most relevant clique methods, this review intends to encourage future development of more powerful methods and motivate new applications of the clique approaches.

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Section: Accepted Manuscriptmentioning

confidence: 99%

A review on algorithms for maximum clique problems

Hao

2015

European Journal of Operational Research

259

168

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“…As reviewed and compared in the most recent survey [33], ITS and VNS seem to be the most powerful algorithms for the MDP among 30 heuristic algorithms. TIG and LTS-EDA are two recently proposed algorithms and thus not included in the recent review [33].…”

Section: Reference Algorithms and Experimental Protocolmentioning

confidence: 99%

“…TIG and LTS-EDA are two recently proposed algorithms and thus not included in the recent review [33]. However, experimental results show that TIG and LTS-EDA obtain better or competitive performance than VNS and ITS.…”

Section: Reference Algorithms and Experimental Protocolmentioning

confidence: 99%

“…In addition to its theoretical significance as a difficult combinatorial problem, MDP is notable for its ability to formulate a number of practical applications: location of undesirable or mutually competing facilities [11], decision analysis with multiple objectives [36], composing jury panels [28], genetic engineering [33], medical and social sciences [27], and product design [18]. During the past three decades, MDP has been studied under many different names such as maxisum dispersion [26], MAX-AVG dispersion [39], edge-weighted clique [1,31], remote-clique [9], maximum edge-weighted subgraph [30], and dense k-subgraph [8,12].…”

Section: Introductionmentioning

confidence: 99%

“…Another approach that has received considerable attention in the solution of the MDP is greedy randomized adaptive search procedure (GRASP) [2,3,10,16,[40][41][42]. Finally, a comprehensive survey and an interesting comparison of the most significant heuristic and metaheuristic methods for MDP can be found in [6,33].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A hybrid metaheuristic method for the Maximum Diversity Problem

Hao

2013

European Journal of Operational Research

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The Maximum Diversity Problem (MDP) consists in selecting a subset of m elements from a given set of n elements (n > m) in such a way that the sum of the pairwise distances between the m chosen elements is maximized. We present a hybrid metaheuristic algorithm (denoted by MAMDP) for MDP. The algorithm uses a dedicated crossover operator to generate new solutions and a constrained neighborhood tabu search procedure for local optimization. MAMDP applies also a distance-and-quality based replacement strategy to maintain population diversity. Extensive evaluations on a large set of 120 benchmark instances show that the proposed approach competes very favorably with the current state-of-art methods for MDP. In particular, it consistently and easily attains all the best known lower bounds and yields improved lower bounds for 6 large MDP instances. The key components of MAMDP are analyzed to shed light on their influence on the performance of the algorithm.

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Discrete Diversity Optimization: Models and Instances

Martínez-Gavara

2023

Springer Optimization and Its Applications

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Heuristics and metaheuristics for the maximum diversity problem

Cited by 73 publications

References 33 publications

A review on algorithms for maximum clique problems

A review on algorithms for maximum clique problems

A hybrid metaheuristic method for the Maximum Diversity Problem

Discrete Diversity Optimization: Models and Instances

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