An efficient hybrid adaptive large neighborhood search method for the capacitated team orienteering problem

Abstract

This paper focuses on a NP-Hard vehicle routing problem with profits, and presents a hybrid heuristic solution approach for the Capacitated Team Orienteering Problem (CTOP), which is a variant of the well-known team orienteering problem. In the CTOP, given a set of homogeneous fleet and a set of clients to each is associated a deterministic profit and volume demand, one maximizes the collected profits for serving customers by operating a set of routes while respecting vehicles’ limited time and volume capacities. Our proposed method to solve the CTOP is a Hybrid Adaptive Large Neighborhood Search (HALNS) heuristic. Several removal and insertions operators with different node selection strategies and local search procedures are developed to generate solutions in the first step. In the second step, solutions’ routes are passed to a set packing problem which is solved using an exact branch-and-cut procedure in order to obtain the best solution. Compared to all the state-of-the-art methods, extensive computational experiments show that our method outperforms in terms of solution quality and/or computational times when tested on the small and large-scale benchmark CTOP instances respectively proposed by Archetti et al. (2009) and Tarantilis et al. (2023). Furthermore, our hybrid method improves 10 of the best known solutions for large-scale benchmark instances.