An effective hybrid evolutionary algorithm for the set orienteering problem

Abstract

The Set Orienteering Problem (SOP) is a variant of the popular Orienteering Problem (OP) arising from a number of real-life applications. The aim is to find a tour across a subset of customers, while maximizing the collected profit within a given travel time limit. In SOP, vertices (customers) are partitioned into clusters, where a profit is associated to each cluster. The profit of a cluster is collected only if at least one vertex belonging to the cluster is contained in the tour. For this NP-hard problem, we present a highly effective hybrid evolutionary algorithm that integrates a cluster-based crossover operator, a randomized mutation operator to generate multiple distinct promising offspring solutions, and a two-phase local refinement procedure that explores both feasible and infeasible solutions in search of high-quality local optima. Extensive experiments on 192 large benchmark instances show that the proposed algorithm significantly outperforms all the existing approaches from the SOP literature. In particular, it reports improved best-known solutions (new lower bounds) for 54 instances, while matching the existing best-known result for 133 instances. We further investigate the contribution of the key algorithmic elements to the success of the proposed approach.