Bilevel Memetic Search Approach to the Soft-Clustered Vehicle Routing Problem

This work addresses a soft-clustered vehicle routing problem that extends the classical capacitated vehicle routing problem with one additional constraint, that is, customers are partitioned into clusters and all customers of the same cluster must be served by the same vehicle. Its potential applications include parcel delivery in courier companies and freight transportation. Due to its NP-hard nature, solving it is computationally challenging. This paper presents an efficient bilevel memetic search method to do so, which explores search space at both cluster and customer levels. It integrates three distinct modules: a group matching-based crossover (to generate promising offspring solutions), a bilevel hybrid neighborhood search (to perform local optimization), and a tabu-driven population reconstruction strategy (to help the search escape from local optima). Extensive experiments on three sets of 390 widely used public benchmark instances are conducted. The results convincingly demonstrate that the proposed method achieves much better overall performance than state-of-the-art algorithms in terms of both solution quality and computation time. In particular, it is able to find 20 new upper bounds for large-scale instances while matching the best-known upper bounds for all but four of the remaining instances. Ablation studies on three key algorithm modules are also performed to demonstrate the novelty and effectiveness of the proposed ideas and strategies.