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GRASP AND PATH RELINKING FOR THE MAXMIN DIVERSITY PROBLEM
"... Abstract. The MaxMin Diversity Problem (MMDP) consists in selecting a subset of elements from a given set in such a way that the diversity among the selected elements is maximized. The problem is NPhard and can be formulated as an integer linear program. Since the 1980s, several solution methods f ..."
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Cited by 22 (11 self)
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Abstract. The MaxMin Diversity Problem (MMDP) consists in selecting a subset of elements from a given set in such a way that the diversity among the selected elements is maximized. The problem is NPhard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in the social and biological sciences. We propose a heuristic method – based on the GRASP and path relinking methodologies – for finding approximate solutions to this optimization problem. We explore different ways to hybridize GRASP and path relinking, including the recently proposed variant known as GRASP with evolutionary path relinking. Empirical results indicate that the proposed hybrid implementations compare favorably to previous metaheuristics, such as tabu search and simulated annealing. 1.
Heuristics and metaheuristics for the Maximum Diversity Problem
 ACCEPTED TO JOURNAL OF HEURISTICS
, 2011
"... This paper presents extensive computational experiments to compare 10 heuristics and 20 metaheuristics for the maximum diversity problem (MDP). This problem consists of selecting a subset of maximum diversity from a given set of elements. It arises in a wide range of realworld settings and we can f ..."
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Cited by 3 (1 self)
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This paper presents extensive computational experiments to compare 10 heuristics and 20 metaheuristics for the maximum diversity problem (MDP). This problem consists of selecting a subset of maximum diversity from a given set of elements. It arises in a wide range of realworld settings and we can find a large number of studies, in which heuristic and metaheuristic methods are proposed. However, probably due to the fact that this problem has been referenced under different names, we have only found limited comparisons with a few methods on some sets of instances. This paper reviews all the heuristics and metaheuristics for finding nearoptimal solutions for the MDP. We present the new benchmark library MDPLIB, which includes most instances previously used for this problem, as well as new ones, giving a total of 315. We also present an exhaustive computational comparison of the 30 methods on the MDPLIB. Nonparametric statistical tests are reported in our study to draw significant conclusions.
Tabu search vs. GRASP for the Maximum Diversity Problem
, 2005
"... The Maximum Diversity Problem (MDP) consists in determining a subset M of given cardinality from a set of elements N, in such a way that the sum of the pairwise distances between the elements of M is maximum. This problem, introduced by Glover [6], has been deeply studied using GRASP methodologies [ ..."
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Cited by 3 (1 self)
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The Maximum Diversity Problem (MDP) consists in determining a subset M of given cardinality from a set of elements N, in such a way that the sum of the pairwise distances between the elements of M is maximum. This problem, introduced by Glover [6], has been deeply studied using GRASP methodologies [5, 1, 13, 2]. GRASP is often characterized by a strong design effort dedicated to build high quality randomized starting solutions, while the subsequent improvement phase is usually performed by a standard local search technique. The purpose of this paper is to explore a somewhat opposite approach, that is to refine the local search phase, by adopting Tabu Search methodologies, while keeping a very simple initialization procedure. Extensive computational results show that Tabu Search achieves both better results and much shorter computational times with respect to those reported for GRASP.
A Hybrid Metaheuristic Method for the Maximum Diversity Problem
"... 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 algor ..."
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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 distanceandquality 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 stateofart 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.
Semidefinite Bounds for the Maximum Diversity Problem
, 2006
"... The Maximum Diversity Problem consists in extracting a subset of given cardinality from a larger set in such a way that the sum of their pairwise distances is maximum. In this paper we propose a set of bounds for this problem based on semidefinite programming techniques. An extensive computational c ..."
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The Maximum Diversity Problem consists in extracting a subset of given cardinality from a larger set in such a way that the sum of their pairwise distances is maximum. In this paper we propose a set of bounds for this problem based on semidefinite programming techniques. An extensive computational campaign shows the tightness of the bounds computed with respect to the best known results in literature and to bounds obtained by a linearized integer programming formulation. 1
GRASP WITH EXTERIOR PATH RELINKING FOR DIFFERENTIAL DISPERSION MINIMIZATION
"... Abstract. We propose several new hybrid heuristics for the differential dispersion problem are proposed, the best of which consists of a GRASP with sampled greedy construction with variable neighborhood search for local improvement. The heuristic maintains an elite set of highquality solutions t ..."
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Abstract. We propose several new hybrid heuristics for the differential dispersion problem are proposed, the best of which consists of a GRASP with sampled greedy construction with variable neighborhood search for local improvement. The heuristic maintains an elite set of highquality solutions throughout the search. After a fixed number of GRASP iterations, exterior path relinking is applied between all pairs of elite set solutions and the best solution found is returned. Exterior path relinking, or path separation, a variant of the more common interior path relinking, is first applied in this paper. In interior path relinking, paths in the neighborhood solution space connecting good solutions are explored between these solutions in the search for improvements. Exterior path relinking, as opposed to exploring paths between pairs of solutions, explores paths beyond those solutions. This is accomplished by considering an initiating solution and a guiding solution and introducing in the initiating solution attributes not present in the guiding solution. To complete the process, the roles of initiating and guiding solutions are exchanged. Extensive computational experiments on 190 instances from the literature demonstrate the competitiveness of this algorithm. 1.
The scatter search methodology
"... Scatter search (SS) is an evolutionary approach for optimization. It has been applied to problems with continuous and discrete variables and with a single or multiple objectives. The success of scatter search as an optimization technique is well documented in a constantly growing number of journal a ..."
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Scatter search (SS) is an evolutionary approach for optimization. It has been applied to problems with continuous and discrete variables and with a single or multiple objectives. The success of scatter search as an optimization technique is well documented in a constantly growing number of journal articles and book chapters. This chapter first focuses on the basic scatter search framework, which is responsible for most of the outcomes reported in the literature, and then covers advanced elements that have been introduced in a few selected papers, such as the hybridization with tabu search, a wellknown memorybased metaheuristic. We consider the maximum diversity problem to illustrate the search elements, methods and strategies described here. The scatter search methodology