A Hybrid Genetic Search for Selective Routing with Overlapping Clusters: A Case Study in Order Picking

We propose a hybrid genetic search heuristic tailored to the Selective Vehicle Routing Problem (SVRP), a generalization of the Capacitated VRP in which customers are grouped into overlapping clusters, and exactly one customer must be visited per cluster. This structure introduces a combinatorial challenge in both node selection and route construction, which we address through a novel three-chromosome individual representation, an adaptive local search scheme, and a selective shortest path algorithm designed to handle overlapping cluster memberships efficiently. Our method extends and generalizes established frameworks in vehicle routing heuristics by enabling flexible treatment of cluster-to-node mappings during the search process. We test the algorithm on both standard and newly generated benchmark instances, including 275 medium-to-large cases with varying levels of cluster overlap. Compared with the mixed-integer linear programming formulation solved using CPLEX, our heuristic consistently achieves near-optimal or best-known solutions in substantially shorter computation times. We further demonstrate the applicability of our approach on a logistic-inspired case study based on a real-world order-picking problem in a warehouse environment. The results highlight the strength of the proposed heuristic framework in solving large scale applications. Code available at: https://github.com/vlatorre847/HGS-SVRP.