Solving the team orienteering problem with nonidentical agents: A Lagrangian approach

Abstract

The team orienteering problem (TOP) requires a team of time-constrained agents to maximize the total collected profit by serving a subset of given customers. The exact solution approaches for TOP in the literature have considered only the case of identical agents, even though the heterogeneity of the agents is of essence in many applications. The heuristic approaches, on the other hand, although providing good feasible solutions, do not offer any measure of solution quality, such as an optimality gap. In this study, we consider an extension of the conventional TOP in which the agents are allowed to be identical as well as completely nonidentical. We explore a Lagrangian relaxation based approach that simultaneously obtains tight upper and lower bounds on the optimal solution of the problem and, therefore, provides a measure of solution quality by way of duality gap. Our algorithm achieves an average gap of less than 2% within an average time of around 120 s across 135 randomly generated instances with up to 100 customers and five nonidentical agents. We also introduce a new set of valid symmetry breaking constraints that significantly improves the effectiveness of our formulation and Lagrangian implementation for the case of identical agents. For the three most difficult sets of benchmark instances for TOP with identical agents, our approach achieves upper bounds that are, on average, 1.08% above the best-known solutions, and feasible solutions that are 0.35% below the best-known solutions. The average time taken to solve these problems was about 115 s.

A Hierarchical Approach to Intelligent Mission Planning for Heterogeneous Fleets of Autonomous Underwater Vehicles

“…The latter includes energy-saving and collision avoidance, along with the necessity for all vehicles to return to the rendezvous location by the end of the shift. Thus, the routing problem itself here is related in many ways to the team orienteering problem with non-identical agents, which can be treated by a variety of approaches [27]. Finally, low-level controllers provide a proper and safe implementation of the planned actions on the individual level.…”