A novel hybrid column generation-metaheuristic approach for the vehicle routing problem with general soft time window

The vehicle routing problem with general soft time window involves designing a set of routes for a fleet of vehicles based at a central depot that is required to service a number of geographically dispersed customers while minimizing the total travel distance and delivery time costs. Delivery time cost function is a general piecewise linear function. In this study, we propose a mathematical model of this problem. Then an efficient hybrid column generation-metaheuristic approach is developed. In the proposed algorithm, the hybridization of column generation (CG) and the metaheuristic is performed in both integrative and collaborative modes. In the integrative phase, a quantum-inspired evolutionary algorithm is used to solve the sub-problems of column generation. In the collaborative phase, the column generation and electromagnetism algorithms are parallelized, and the information from these two algorithms is exchanged to find better solutions. Finally, the performance of the proposed approach is evaluated using a set of modified classic benchmark instances adopted from the literature.