Perturbation heuristics for the pickup and delivery traveling salesman problem

The Traveling Salesman Problem with Pickup and Delivery (PDTSP) is considered. Seven perturbation heuristics are applied to instances ranging from 51 to 443 vertices. The main point of perturbation heuristics is to help a local search process to move away from a local optimum. The seven heuristics fall into three categories: Instance Perturbation (IP), Algorithmic Perturbation (AP), and Solution Perturbation (SP). The main idea of these heuristics is to make perturbations to the problem instance, the method, or the solution, respectively. The optimal tours of the instances considered are known and the computational results are compared to these optima. The performances of most of the perturbation heuristics are fairly similar with, in the best case, an average deviation of around 16 percent from the optimum. Only the AP schemes perform considerably worse with an average deviation of around 60 percent from the optimal solution. Improvements in the performances are made by adjusting the initialization of the method, as well as by varying one of the user-controlled parameters of the process.