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**1 - 3**of**3**### 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 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.

### GRASP WITH EXTERIOR PATH RELINKING FOR DIFFERENTIAL DISPERSION MINIMIZATION

"... Abstract. We propose several new hybrid heuristics for the differential dis-persion problem are proposed, the best of which consists of a GRASP with sam-pled greedy construction with variable neighborhood search for local improve-ment. The heuristic maintains an elite set of high-quality solutions t ..."

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Abstract. We propose several new hybrid heuristics for the differential dis-persion problem are proposed, the best of which consists of a GRASP with sam-pled greedy construction with variable neighborhood search for local improve-ment. The heuristic maintains an elite set of high-quality 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. Exte-rior 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 initiat-ing 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.

### www.iord.in www.iord.in Page 24

"... Abstract — The problem of forming groups from among a given set of people or entities arises in numerous settings and situations. In all these cases, there are preferences that exist among the people or entities involved, to work together or be together in the same group. It is beneficial to assign ..."

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Abstract — The problem of forming groups from among a given set of people or entities arises in numerous settings and situations. In all these cases, there are preferences that exist among the people or entities involved, to work together or be together in the same group. It is beneficial to assign persons to the same group who prefer each other than to someone else, for the overall better outcomes of the work done by the groups. However, this boils down to a balancing act, since trying to satisfy the preferences of members in a group might result in forcing members to be in the same group as others who are much lower in their preference lists. The combinatorial explosion of the solution space makes obtaining the optimal solution intractable. Central to finding solutions to the grouping problem is the preference matrix. This paper presents the properties of the preference matrix leading to interesting implications on the groupings.