Adaptive GRASP for the maximum diversity problem

Abstract

The problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem. GRASP is a multi-start method that consists of two phases: a solution construction phase, which randomly constructs a greedy solution, and an improvement phase, which uses that solution as an initial starting point. In the last few years, the GRASP methodology has arisen as a prospective metaheuristic approach to find high-quality solutions for this difficult problem in reasonable computational times. With the aim of providing additional results and insights along this line of research, this paper proposes a new GRASP model with two innovative components: a customized iterated greedy metaheuristic that acts as an improvement method and an adaptive construction phase that creates new solutions, incorporating pieces of the best solution found so far (the number of elements forming these pieces increases as time goes by), in this way balancing the diversification and intensification kept by GRASP. The benefits of the proposal in comparison to other metaheuristic proposed in the literature to deal with the problem are experimentally shown.