| Summary: | The Vehicle Routing Problem with Time Windows (VRPTW) has drawn considerable attention in the last decades. The objective of VRPTW is to find the optimal set of routes for a fleet of vehicles in order to serve a given set of customers within capacity and time window constraints. As a combinatorial optimization problem, VRPTW is proved NP-hard and is best solved by heuristics. In this paper, a hybrid swarm intelligence algorithm by hybridizing Ant Colony System (ACS) and Brain Storm Optimization (BSO) algorithm is proposed, to solve VRPTW with the objective of minimizing the total distance. In the BSO procedure, both inter-route and intra-route improvement heuristics are introduced. Experiments are conducted on Solomon's 56 instances with 100 customers benchmark, the results show that 42 out of 56 optimal solutions (18 best and 24 competitive solutions) are obtained, which illustrates the effectiveness of the proposed algorithm.
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