Clustered Orienteering Problem with Subgroups
This work addresses a combinatorial optimization problem for routing and scheduling applications, but it is incremental as it extends existing variants like the Clustered Orienteering Problem and Set Orienteering Problem.
The paper tackles the Clustered Orienteering Problem with Subgroups (COPS), an extension of the Orienteering Problem where nodes are grouped into subgroups and clusters, with rewards gained only if all nodes in a subgroup are visited and at most one subgroup per cluster is visited, aiming to maximize reward under a travel budget. It proposes an Integer Linear Programming (ILP) method that yields optimal solutions but is time-consuming, and a Tabu Search heuristic that provides comparable solutions more efficiently.
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.