Variable Neighborhood Search for the Set Orienteering Problem and its application to other Orienteering Problem variants

Abstract

This paper addresses the recently proposed generalization of the Orienteering Problem (OP), referred to as the Set Orienteering Problem (SOP). The OP stands to find a tour over a subset of customers, each with an associated profit, such that the profit collected from the visited customers is maximized and the tour length is within the given limited budget. In the SOP, the customers are grouped in clusters, and the profit associated with each cluster is collected by visiting at least one of the customers in the respective cluster. Similarly to the OP, the SOP limits the tour cost by a given budget constraint, and therefore, only a subset of clusters can usually be served. We propose to employ the Variable Neighborhood Search (VNS) metaheuristic for solving the SOP. In addition, a novel Integer Linear Programming (ILP) formulation of the SOP is proposed to find the optimal solution for small and medium-sized problems. Furthermore, we show other OP variants that can be addressed as the SOP, i.e., the Orienteering Problem with Neighborhoods (OPN) and the Dubins Orienteering Problem (DOP). While the OPN extends the OP by collecting a profit within the neighborhood radius of each customer, the DOP uses airplane-like smooth trajectories to connect individual customers. The presented computational results indicate the feasibility of the proposed VNS algorithm and ILP formulation, by improving the solutions of several existing SOP benchmark instances and requiring significantly lower computational time than the existing approaches.