Hybrid heuristics for the maximum diversity problem

Gallego, Micael; Duarte, Abraham; Laguna, Manuel; Martı́, Rafael

doi:10.1007/s10589-007-9161-6

Cited by 40 publications

(29 citation statements)

References 10 publications

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“…Many different methods have been proposed to search for solutions to the MDP. Recently, Silva et al (2004) presented two GRASP approaches, Duarte and Martí (2007) introduced a tabu search and Gallego et al (2008) a scatter search method. We will use the latter method in our comparison since it has been shown to outperform previous approaches.…”

Section: Optimization Problems Used For Testingmentioning

confidence: 99%

“…We are only using them as a baseline for comparison. Specifically, for the Max-cut instances, we consider the SS method by Martí et al (2009), for the MDP instances we use the SS method by Gallego et al (2008), and for the Knapsack instances we use Expknap by Pisinger (1995). In this experiment, we add the MDMKP instances and the Almha procedure by Arntzen et al (2006).…”

Section: Problemmentioning

confidence: 99%

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Black box scatter search for general classes of binary optimization problems

Gortázar

Duarte

Laguna

et al. 2010

Computers & Operations Research

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The purpose of this paper is to apply the scatter search methodology to general classes of binary problems. We focus on optimization problems for which the solutions are represented as binary vectors and that may or may not include constraints. Binary problems arise in a variety of settings, including engineering design and statistical mechanics (e.g., the spin glass problem). A distinction is made between two sets of general constraint types that are handled directly by the solver and other constraints that are addressed via penalty functions. In both cases, however, the heuristic treats the objective function evaluation as a black box. We perform computational experiments with four well-known binary optimization problems to study the efficiency (speed) and effectiveness (solution quality) of the proposed method. Comparisons are made against both commercial software and specialized procedures on a set of 376 instances. We chose commercial software that is similar in nature to the proposed procedure, namely, it treats the objective function as a black box and the search is based on evolutionary optimization techniques.

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Section: Optimization Problems Used For Testingmentioning

confidence: 99%

Section: Problemmentioning

confidence: 99%

Black box scatter search for general classes of binary optimization problems

Gortázar

Duarte

Laguna

et al. 2010

Computers & Operations Research

Self Cite

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“…A number of computational studies of MDP have been performed, including those of Kuo et al (1993), Ghosh (1996), Glover et al (1998), Silva et al (2004), Andrade et al (2005), Duarte and Marti (2007), Gallego et al (2009), Palubeckis (2007), Aringhieri et al (2008), Santos et al (2008), Wang et al (2009) and Aringhieri and Cordone (2011). As observed in Kuo et al (1993) the maximum diversity problem has applications in plant breeding, social problems, ecological preservation, pollution control, product design, capital investment, workforce management, curriculum design and genetic engineering.…”

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 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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“…This includes tabu search [1,4,6,10,30,44], iterated tabu search [36], simulated annealing [25], iterated greedy algorithm [28], estimation of distribution algorithms [43], genetic algorithms [13], variable neighborhood search [6,8], scatter search [15,21], path-relinking method [2,3] and memetic search [24]. 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].…”

Section: Introductionmentioning

confidence: 99%

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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Hybrid heuristics for the maximum diversity problem

Cited by 40 publications

References 10 publications

Black box scatter search for general classes of binary optimization problems

Black box scatter search for general classes of binary optimization problems

A simple and effective algorithm for the MaxMin diversity problem

A hybrid metaheuristic method for the Maximum Diversity Problem

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