The VRP is a well-known combinatorial optimization problem in transport and logistics distribution. Customers require simultaneous pickup of goods from their location and the delivery of goods to their place in some cases. The cargo loading problem plays an essential role in physical distribution. The weight and volume of the vehicle are effectively used so that freight is reasonably loaded with as many goods as possible. A reasonable loading plan can improve the load and space utilization ratio of cars, reduce the logistics cost of distribution enterprises, and increase their competitive capacity. Therefore, the vehicle routing problem and cargo loading have gotten the great attention of logistics scholars and enterprises, and both belong to NP-hard problems. This paper presents a mathematical formulation and genetic algorithm method for solving a vehicle routing problem with simultaneous pickup and delivery and cargo loading (VRPSPD-CL), was analyzed the theory of logistics distribution optimization problem as a case study. The calculation example data was selected to analyze the actual problem of VRPSPD with cargo loading. The paper selected the genetic algorithm to solve the problem and improved GA and the basic genetic algorithm to get the optimal solution for the simulation experiment. Then, the paper concretely designs every step in the algorithm to make the algorithm compact, efficient, and fit, to solve the VRPSPD with cargo loading optimization and mathematical model was established. At the same time, MATLAB software is adopted to solve a related practical problem. Finally, the results obtained show the optimal objective function iteration value of the simulation experiment was satisfactory by the improved GA compare with the basic of GA for the VRPSPD cargo loading with the simulation.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.