A Hybrid Water Flow-Like Algorithm and Variable Neighbourhood Search for Traveling Salesman Problem

Abstract

Various metaheuristic methods have been proposed earlier and applied for solving the Travelling Salesman Problem (TSP). Water Flow Algorithm (WFA) is one of the recent population-based metaheuristic optimization techniques used for solving this problem. Past research has shown that improving WFA local search strategy has a significant impact on the algorithm performance. Therefore, this paper aims to solve TSP by enhancing WFA searching strategy based on a Variable Neighbourhood Search (VNS) known as hybrid WFA-VNS. It is a mixture of the exploration of WFA and the exploitation capability of VNS. This study is conducted in two stages: Pre-experiment and initial experiment. The objective of doing pre-experiment is to select four neighborhood structures to be used for the initial experiment. At the first stage, three instances are used, and there are five neighborhood structures involved. Those neighborhood structures are two opt, three opt, four opt, swapping, and insertion move. Because of pre-experiment, it discovers four best neighborhood structures, which are two opt, three opt, exchanging and insertion move. These neighborhood structures will be used in the initial experiment, which an improvement approach is employed. In an initial experiment, the performance of the proposed hybrid WFA-VNS is further studied and tested on 26 established benchmarked symmetric TSP datasets using four neighborhood structures selected in pre-experiment earlier. The TSP datasets involved are categorized into three types: small datasets, medium datasets, and large datasets. Selected neighborhood structures obtained in pre-experiment are applied and generated randomly to intensify the initial solution achieved at an earlier stage of hybrid WFA-VNS. The results of the comparison show that this hybrid approach represents an improvement and able to produce competitive results.

Improvement of the Bees Algorithm for Solving the Traveling Salesman Problems

“…If attention is paid to the table, it seems that better values were found for KroB100 and KroD100 than the best known value. However, these values were found to be reached by other researchers [32,33]. For problems with 150 cities, values with a deviation of 0.8-1.25% from the best known value were found.…”

Partial Leader Optimizer

“…This model is optimized using the variable neighborhood search (VNS) and iterated greedy algorithm [2]. Othman et al [3] proposed a new method by hybridizing the water flow algorithm and VNS to solve the classic traveling salesman problem. Fathollahi-Fard et al [4] proposed an optimization model in the home healthcare system to optimize the total cost and unemployment time and maintain continuity.…”