An adaptive memory matheuristic for the set orienteering problem

This paper proposes a novel matheuristic algorithm for the Set Orienteering Problem (SOP). The set orienteering problem generalizes the Orienteering Problem (OP) by considering customers to be divided into mutually exclusive clusters. The profit associated with each cluster is collected by visiting at least one of the customers belonging to this cluster. The problem calls for the determination of the closed route that maximizes the collected profit without violating a given maximum route duration. We propose a matheuristic algorithm based on local search. The proposed algorithm is equipped with mathematical programming components for dealing with various subproblems, as well as an adaptive memory structure for producing high-quality starting solutions. Promising and diverse solutions are collected and multiple solution reconstruction mechanisms are presented. Extensive computational experiments are conducted for parameter tuning, and for evaluating the contribution of the mathematical programming components and the adaptive memory mechanism. The proposed solution approach is compared against previously published SOP algorithms. It produces the best solutions for 98.20% of the instances of the classic SOP benchmark data set. For 102 of the total 612 instances a new best solution is obtained. In addition, a new large data set of 304 instances is introduced with instances of up to 3162 customers and 634 clusters to evaluate the scalability of the proposed algorithm, and the effectiveness of the various adaptive memory schemes. The proposed algorithm manages to outperform or match the best-known solution for 281 out of 304 instances when compared with a state-of-the-art open source SOP algorithm.