A Performance Study of the Impact of Different Perturbation Methods on the Efficiency of GVNS for Solving TSP

Abstract

The purpose of this paper is to assess how three shaking procedures affect the performanceof a metaheuristic GVNS algorithm. The first shaking procedure is generally known in the literatureas intensified shaking method. The second is a quantum-inspired perturbation method, and thethird is a shuffle method. The GVNS schemes are evaluated using a search strategy for both Firstand Best improvement and a time limit of one and two minutes. The formed GVNS schemes wereapplied on Traveling Salesman Problem (sTSP, nTSP) benchmark instances from the well-knownTSPLib. To examine the potential advantage of any of the three metaheuristic schemes, extensivestatistical analysis was performed on the reported results. The experimental data shows that for aTSPinstances the first two methods perform roughly equivalently and, in any case, much better thanthe shuffle approach. In addition, the first method performs better than the other two when usingthe First Improvement strategy, while the second method gives results quite similar to the third.However, no significant deviations were observed when different methods of perturbation were usedfor Symmetric TSP instances (sTSP, nTSP).