Tabu search algorithm for the distance-constrained vehicle routing problem with split deliveries by order

The vehicle routing problem (VRP) has a wide range of applications in the field of logistics distribution. In order to reduce the cost of logistics distribution, the distance-constrained and capacitated VRP with split deliveries by order (DCVRPSDO) was studied. We show that the customer demand, which can't be split in the classical VRP model, can only be discrete split deliveries by order. A model of double objective programming is constructed by taking the minimum number of vehicles used and minimum vehicle traveling cost as the first and the second objective, respectively. This approach contains a series of constraints, such as single depot, single vehicle type, distance-constrained and load capacity limit, split delivery by order, etc. DCVRPSDO is a new type of VRP. A new tabu search algorithm is designed to solve the problem and the examples testing show the efficiency of the proposed algorithm. This paper focuses on constructing a double objective mathematical programming model for DCVRPSDO and designing an adaptive tabu search algorithm (ATSA) with good performance to solving the problem. The performance of the ATSA is improved by adding some strategies into the search process, including: (a) a strategy of discrete split deliveries by order is used to split the customer demand; (b) a multi-neighborhood structure is designed to enhance the ability of global optimization; (c) two levels of evaluation objectives are set to select the current solution and the best solution; (d) a discriminating strategy of that the best solution must be feasible and the current solution can accept some infeasible solution, helps to balance the performance of the solution and the diversity of the neighborhood solution; (e) an adaptive penalty mechanism will help the candidate solution be closer to the neighborhood of feasible solution; (f) a strategy of tabu releasing is used to transfer the current solution into a new neighborhood of the better solution.