  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.
