Distribution Path Optimization by an Improved Genetic Algorithm Combined with a Divide-and-Conquer Strategy

The multivehicle routing problem (MVRP) is a variation of the classical vehicle routing problem (VRP). The MVRP is to find a set of routes by multiple vehicles that serve multiple customers at a minimal total cost while the travelling-time delay due to traffic congestion is tolerated. It is an NP problem and is conventionally solved by metaheuristics such as evolutionary algorithms. For the MVRP in a distribution network, we propose an optimal distribution path optimization method that is composed of a distribution sequence search stage and a distribution path search stage that exploits a divide-and-conquer strategy, inspired by the idea of dynamic programming. Several optimization objectives subject to constraints are defined. The search for the optimal solution of the number of distribution vehicles, distribution sequence, and path is implemented by using an improved genetic algorithm (GA), which is characterized by an operation for preprocessing infeasible solutions, an elitist’s strategy, a sequence-related two-point crossover operator, and a reversion mutation operator. The improved GA outperforms the simple GA in terms of total cost, route topology, and route feasibility. The proposed method can help to reduce costs and increase efficiency for logistics and transportation enterprises and can also be used for flow-shop scheduling by manufacturing enterprises.