A Two-Individual Evolutionary Algorithm for Cumulative Capacitated Vehicle Routing With Single and Multiple Depots

The cumulative capacitated vehicle routing problem (CCVRP) with single or multiple depots (MDCCVRP) is a variant of the popular capacitated vehicle routing problem. Instead of minimizing the total travel time, the objective here is to minimize the sum of all customers’ waiting times. This problem has a variety of real-world applications, especially in post-disaster humanitarian relief. To solve the challenging CCVRP and MDCCVRP, we propose a unified two-individual evolutionary algorithm that follows the memetic search framework. The algorithm integrates several key features: a two-individual population mechanism to accelerate convergence while maintaining population diversity, a dedicated edge assembly crossover to generate high-quality offspring, and an adaptive feasible and infeasible local search to achieve a balanced exploration between feasible and infeasible solutions. The algorithm is evaluated on 39 CCVRP instances and 78 MDCCVRP instances commonly used in the literature. Computational results show that for the CCVRP, the algorithm outperforms the leading algorithms by achieving improved best results (new upper bound) for 13 instances and matching the best results for 23 other instances. For the MDCCVRP, the algorithm achieves nine improved best results and matches the best results for the remaining instances. The critical components of the algorithm are investigated to understand their contributions.