Tabu Search versus GRASP for the maximum diversity problem

Aringhieri, Roberto; Cordone, Roberto; Melzani, Yari

doi:10.1007/s10288-007-0033-9

Cited by 37 publications

(29 citation statements)

References 10 publications

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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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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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“…Metaheuristic algorithms have shown to be very successful in solving hard combinatorial optimization problems. Thus, recently lots of metaheuristic approaches, such as tabu search (TS) (Duarte 2007;Palubecki 2007;Aringhieri et al 2008), variable neighborhood search (VNS) (Brimberg et al 2009;Aringhieri 2011), greedy randomized adaptive search procedure (GRASP) (Silva et al 2007;Andrade et al 2005), Hopfield neural network (HNN) ), SS (Gallego et al 2009), iterated greedy (IG) algorithm (Lozano et al 2011) and memetic algorithm (MA) (Katayama 2004), have been successfully applied to the MDP. A well-documented review and comparison of current approaches for the MDP can be found in , Aringhieri (2011), and Lozano et al (2011).…”

Section: Introductionmentioning

confidence: 99%

“…Especially, many TS-based approaches (Duarte 2007;Palubecki 2007;Aringhieri et al 2008), have achieved superior performance; however, most of these approaches have no explicit learning mechanism to utilize global statistical information, which motivates us to propose a learnable TS. In this paper, a learnable TS guided by estimation of distribution algorithm (EDA), called LTS-EDA, is proposed for the MDP.…”

Section: Introductionmentioning

confidence: 99%

Learnable tabu search guided by estimation of distribution for maximum diversity problems

et al. 2011

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This paper presents a learnable tabu search (TS) guided by estimation of distribution algorithm (EDA), called LTS-EDA, for maximum diversity problem. The LTS-EDA introduces knowledge model and can extract knowledge during the search process of TS, and thus it adopts dual or cooperative evolution/search structure, consisting of probabilistic model space in clustered EDA and solution space searched by TS. The clustered EDA, as a learnable constructive method, is used to create a new starting solution, and the simple TS, as an improvement method, attempts to improve the solution created by the clustered EDA in the LTS-EDA. A distinguishing feature of the LTS-EDA is the usage of the clustered EDA with effective linkage learning to guide TS. In the clustered EDA, different clusters (models) focus on different substructures, and the combination of information from different clusters (models) effectively combines substructures. The LTS-EDA is tested on 50 large size benchmark problems with the size ranging from 2,000 to 5,000. Simulation results show that the LTS-EDA is better than the advanced algorithms proposed recently.

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“…When a swap(s u , s v ) move is performed to give a new solution, the potential associated with each element s i in N can be efficiently updated using the following formula, as shown in [4,6]:…”

Section: Algorithm 2 Constrained Neighborhood Tabu Search Procedures Fmentioning

confidence: 99%

“…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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Tabu Search versus GRASP for the maximum diversity problem

Cited by 37 publications

References 10 publications

A simple and effective algorithm for the MaxMin diversity problem

A simple and effective algorithm for the MaxMin diversity problem

Learnable tabu search guided by estimation of distribution for maximum diversity problems

A hybrid metaheuristic method for the Maximum Diversity Problem

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