GRASP and path relinking for the max–min diversity problem

Resende, Maurício G. C.; Martı́, Rafael; Gallego, Micael; Duarte, Abraham

doi:10.1016/j.cor.2008.05.011

Cited by 175 publications

(72 citation statements)

References 19 publications

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“…A comprehensive survey of previous work can be found in Resende et al (2010). In terms of practical results for MMDP, there are two very recent studies that achieved very high performances, thus providing a solid comparison base for benchmarking new algorithms.…”

Section: Xy∈x D(x Y) : X ∈ Z(k)mentioning

confidence: 99%

“…In terms of practical results for MMDP, there are two very recent studies that achieved very high performances, thus providing a solid comparison base for benchmarking new algorithms. Resende et al (2010) presented a refined GRASP (with Path Relinking) approach, as well as extensive comparisons with previous algorithms (e.g. Erkut 1990;Kincaid 1992;Ghosh 1996).…”

Section: Xy∈x D(x Y) : X ∈ Z(k)mentioning

confidence: 99%

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A simple and effective algorithm for the MaxMin diversity problem

2011

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The challenge of maximizing the diversity of a collection of points arises in a variety of settings, including the setting of search methods for hard optimization problems. One version of this problem, called the Maximum Diversity Problem (MDP), produces a quadratic binary optimization problem subject to a cardinality constraint, and has been the subject of numerous studies. This study is focused on the Maximum Minimum Diversity Problem (MMDP) but we also introduce a new formulation using MDP as a secondary objective. We propose a fast local search based on separate add and drop operations and on simple tabu mechanisms. Compared to previous local search approaches, the complexity of searching for the best move at each iteration is reduced from quadratic to linear; only certain streamlining calculations might (rarely) require quadratic time per iteration. Furthermore, the strong tabu rules of the drop strategy ensure a powerful diversification capacity. Despite its simplicity, the approach proves superior to most of the more advanced methods from the literature, yielding optimally-proved solutions for many problems in a matter of seconds and even attaining a new lower bound.

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Section: Xy∈x D(x Y) : X ∈ Z(k)mentioning

confidence: 99%

Section: Xy∈x D(x Y) : X ∈ Z(k)mentioning

confidence: 99%

A simple and effective algorithm for the MaxMin diversity problem

2011

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“…The proposed work helps to deal with binary optimization problems [78]. Another work include of Resende et al (2010) proposed several variants of a hybrid algorithm which is a combination of GRASP and path relinking. The hybridization is carried for maximum minimum diversity problem [82].…”

Section: Hybrid Metaheuristicsmentioning

confidence: 99%

“…Another work include of Resende et al (2010) proposed several variants of a hybrid algorithm which is a combination of GRASP and path relinking. The hybridization is carried for maximum minimum diversity problem [82]. Another work proposed by Hanafi et al is a Variable neighborhood decomposition approach (2010) which hybridizes VNS with general purpose CPLEX MIP solver.…”

Section: Hybrid Metaheuristicsmentioning

confidence: 99%

Survey of Metaheuristic Algorithms for Combinatorial Optimization

Baghel¹,

Agrawal²,

Silakari³

2012

IJCA

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This paper is intended to give a review of metaheuristic and their application to combinatorial optimization problems. This paper comprises a snapshot of the rapid evolution of metaheuristic concepts, their convergence towards a unified framework and the richness of potential application in combinatorial optimization problems. Over the years, combinatorial optimization problems are gaining awareness of the researchers both in scientific as well as industrial world. This paper aims to present a brief survey of different metaheuristic algorithms for solving the combinatorial optimization problems. Basically we have divided the metaheuristic into three broad categories namely trajectory methods, population based methods and hybrid methods. Trajectory methods are those that deal with a single solution. These include simulated annealing, tabu search, variable neighborhood search and greedy randomized adaptive search procedure. Population based methods deal with a set of solutions. These include genetic algorithm, ant colony optimization and particle swarm optimization. Hybrid methods deal with the hybridization of single point search methods and population based methods. These are further categorized into five different types. Finally we conclude the paper by giving some issues which are needed to develop a well performed metaheuristic algorithm.

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“…Representative examples include location routing (Marinakis & Magdalene, 2008), vehicle routing (Rahimi-Vahed et al, 2012), max-min diversity (Resende et al, 2010), permutation flowshop (Vallada & Rubén, 2010), warehouse layout (Zhang & Lai, 2006), unconstrained quadratic programming , and quadratic assignment (Yagiura et al, 2006). Often, local search/constructive heuristics such as tabu search (Carrasco et al, 2015;Yagiura et al, 2006; and GRASP (Resende et al, 2010) are combined with the path relinking method. Fundamentally, EPR operates with a population of (elite) solutions and employs path relinking procedures to generate (many) intermediate solutions (Glover et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

An evolutionary path relinking approach for the quadratic multiple knapsack problem

Chen

Hao

Glover

2016

Knowledge-Based Systems

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The quadratic multiple knapsack problem (QMKP) is a challenging combinatorial optimization problem with numerous applications. In this paper, we propose the first evolutionary path relinking approach (EPR) for solving the QMKP approximately. This approach combines advanced features both from the path relinking (PR) method and the responsive threshold search algorithm. Thanks to the tunneling property which allows a controlled exploration of infeasible regions, the proposed EPR algorithm is able to identify very high quality solutions. Experimental studies on the set of 60 well-known benchmarks and a new set of 30 large-sized instances show that EPR outperforms several state-ofthe-art algorithms. In particular, it discovers 10 improved results (new lower bounds) and matches the best known result for the remaining 50 cases. More significantly, EPR demonstrates remarkable efficacy on the 30 new larger instances by easily dominating the current best performing algorithms across the whole instance set. Key components of the algorithm are analyzed to shed lights on their impact on the proposed approach.

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GRASP and path relinking for the max–min diversity problem

Cited by 175 publications

References 19 publications

A simple and effective algorithm for the MaxMin diversity problem

A simple and effective algorithm for the MaxMin diversity problem

Survey of Metaheuristic Algorithms for Combinatorial Optimization

An evolutionary path relinking approach for the quadratic multiple knapsack problem

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