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. INDEX TERMS Ant colony system, brain storm optimization, heuristics, swarm intelligence, vehicle routing problem with time windows.

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The Dynamic Vehicle Routing Problem (DVRP) has many real-world applications and practical values. The objective of DVRP is to find the optimal routes for a fleet of vehicles to service the given customer requests, without violating the vehicle capacity constraint. In this paper, a hybrid algorithm is proposed for solving the DVRP with the objective to minimize the total distance of the vehicles. The Brain Storm Optimization in objective space (BSO-OS) is applied to guide the choice of different strategies for the periodic reoptimization of routes. In the BSO-OS procedure, Adaptive Large Neighborhood Search (ALNS) and Ant Colony System (ACS) are used to generate new solutions. The experiments on the DVRP benchmark and comparative studies are conducted, from which 12 out of 21 new best solutions are obtained by the proposed algorithm, and the other nine solutions are also very competitive. The experimental results show that the proposed algorithm is very effective and competitive.