A revised Variable Neighborhood Search for the Discrete Ordered Median Problem

The paper presents a revised Variable Neighborhood Search (VNS) heuristic method for the Discrete Ordered Median Problem (DOMP). This method introduces a regularization concept that intensifies the searching process for problems with a not strictly monotonic objective function. This allows better quality solutions to be reached, and is especially helpful for the n-center problem. At the same time, the redesigned interchange algorithm is used to boost the computational performance. This serves as the local search and limits the searching process in non-promising directions. It determines new solutions gradually, rejecting those that cannot be better than the current one. In addition, less calculation is required to determine and evaluate new solutions, due to exploiting information from the current solution. Instead of sorting the whole cost vector at each objective function evaluation, the method sorts only the cost components that are actually changing, and updates the ordered cost vector of the current solution. To evaluate the performance, the proposed method is compared with the original VNS for DOMP, along with other existing methods for DOMP from the literature. Exhaustive computational experiments were carried out, utilizing a widely-used set of problem instances from OR-library. The comparison shows that the proposed revised VNS outperforms the other methods, both in computing time and in solution quality.