Abstract:The vehicle routing problem (VRP) exists extensively in the modern logistics industry, which is an NP-hard problem in combinatorial optimization. Affected by factors such as diverse customer demand and road traffic restrictions, VRP becomes more complex, and it can hardly be solved by the traditional combinatorial optimization methods and operations research methods. In this study, a common VRP with time windows is studied. The waiting time of vehicles is reduced by the adjustment to the priority of customers according to the parameters of time windows. On this basis, several common heuristic algorithms are improved, and 56 common VRPs are tested. The experimental results reveal that the improved savings algorithm can produce good results for capacitated VRPs, and the improved insertion method has superior performance in VRPs with time windows. In addition, the improved heuristic algorithms can make the total distance better than the known optimal value when using more vehicles on the four test cases.