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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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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.
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.