The Impact of perturbation mechanisms on the operation of the swap heuristic

In this study, an attempt was made to assess the impact of the most popular perturbation movements (i.e. Multiple-Swap(2-2), Multiple-Shift(2-2) and Multiple-K-Shift(1)), as well as the number of their calls on the quality of solutions and the time in which Swap(2-1) heuristics returns them. For this purpose, the iterative local search algorithm (ILS) was triggered, in which Swap(2-1) heuristics has cooperated with a single perturbation mechanism. The number of perturbations was changed in the range from 1 to 30. Each time the time and the difference between the percentage improvement of the objective function value of the solution obtained utilizing the Swap(2-1) algorithm cooperating with the perturbation mechanism and this algorithm working alone was checked. Based on the results obtained, it was found that the overall level of improvement in the quality of the returned solution is similar when using all of the considered perturbation mechanisms (is in the range of 2.49% to 4.02%). It has been observed that increasing the number of initiated perturbations does not guarantee an improvement in the quality of the returned solution. Perturbation movements similar to the motion initiated by the local search algorithm do not significantly improve the solution (they only entail extending the duration of action). The structure of the study has the following form. The Introduction chapter provides information on the Vehicle Routing Problem. The chapter Research methods contain a description of ILS and Swap(2-1) approaches and perturbation mechanisms considered. The last two chapters include the results of tests and conclusions.