The Clustered Orienteering Problem with Subgroups

This paper introduces an extension to the Orienteering Problem (OP), called Clustered Orienteering Problem with Subgroups (COPS). In this variant, nodes are arranged into subgroups, and the subgroups are organized into clusters. A reward is associated with each subgroup and is gained only if all of its nodes are visited; however, at most one subgroup can be visited per cluster. The objective is to maximize the total collected reward while attaining a travel budget. We show that our new formulation has the ability to model and solve two previous well-known variants, the Clustered Orienteering Problem (COP) and the Set Orienteering Problem (SOP), in addition to other scenarios introduced here. An Integer Linear Programming (ILP) formulation and a Tabu Search-based heuristic are proposed to solve the problem. Experimental results indicate that the ILP method can yield optimal solutions at the cost of time, whereas the metaheuristic produces comparable solutions within a more reasonable computational cost.