Abstract
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.
Highlights
In recent years, logistics has been playing an important role in many areas, such as economy, industry and environment, etc
We address Vehicle Routing Problem with Time Windows (VRPTW), aiming to minimize the number of vehicles (NV) first, and the total distance (TD)
We further explore and implement multiple heuristics including Ant Colony System (ACS), Brain Storm Optimization (BSO), 2-opt and λ-interchange to achieve near-optimal solutions for VRPTW
Summary
Logistics has been playing an important role in many areas, such as economy, industry and environment, etc. The main differences between their work and ours are: 1) A penalty cost is added to their objective function if the constraints of the time window is violated, while we focus on VRP with hard time windows, i.e., time window constraints must be satisfied by all vehicles; 2) The algorithm proposed by us hybridized ACS instead of the classic ACO in order to balance exploration and exploitation better due to the state transition rule in the ACS [47]; 3) The global pheromone update in the ACS makes the search more directed; 4) In the BSO procedure, we applied a different clustering scheme which clusters the population according to the geographical coordinates of customers in different routes, while the IBSO-ACO clusters the population according to the cost; 5) The IBSO-ACO was performed at the solution level, i.e., it maintains a population of solutions, and generates new solution randomly, which is very time consuming and will probably lead to infeasible solutions.
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