A double traveling salesman problem with three-dimensional loading constraints for bulky item delivery

This article considers bulky item delivery problems in which multiple items are retrieved and loaded onto a vehicle from different warehouses and then delivered. This problem is described as a double traveling salesman problem with three-dimensional container loading constraints with multiple stacks. The double TSP with multiple stacks is used to determining the shortest route performing pickups and deliveries in two separated networks (one for pickups and one for deliveries) using only one container. Repacking is not allowed after loading the items into the container. An integer linear programming model is proposed to solve this problem, a standard genetic algorithm and an improved genetic algorithm is designed. In the improved genetic algorithm, a Lin-Kernighan algorithm is used to improve the delivery route, a k-means clustering algorithm, and a heuristic packing scheme improvement rules work together to improve the loading route. The results show that the improved genetic algorithm is superior to the standard genetic algorithm in large scale problems.