An Ant Colony Optimization approach to the Maximum Diversity Problem Roberto Aringhieri Roberto Cordone Yari Melzani DTI, University of Milan - via Bramante 65 I-26013 Crema aringhieri@dti.unimi.it cordone@dti.unimi.it ymelzani@crema.unimi.it October 31, 2007 Abstract The purpose of the Maximum Diversity Problem (MDP ) is to ex- tract from a set of elements N a subset M of given cardinality, such that the sum of the pairwise distances between the elements of M is maximum. It models several practical problems in fields such as hu- man resource management, data mining, project financing, and so on. In the literature, it has been attacked both by metaheuristics focusing on refined constructive phases (GRASP ) and on refined improvement phases (Tabu Search). In this paper, we describe the combination of the two approaches into an Ant Colony Optimization algorithm, which achieves a graceful interaction between diversification features (pro- vided by the Ant Colony Optimization) and intensification features (mainly provided by Tabu Search). The resulting algorithm outper- forms the construction-based algorithms and proves more robust than the improvement-based ones. 1 Introduction Let N be a set of n elements, m an integer (with m<n) and d ij a diversity measure between unordered pairs of elements i and j in N : d ij = 0 when i = j , d ij = d ji > 0 otherwise. The Maximum Diversity Problem (MDP ) consists in extracting from N a subset M ⊂ N of cardinality m, such that the sum of the pairwise distances between the elements of M is maximum. 1