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

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

The Traveling Salesman Problem: An Analysis and Comparison of Metaheuristics and Algorithms

One of the most investigated topics in operations research is the Traveling Salesman Problem (TSP) and the algorithms that can be used to solve it. Despite its relatively simple formulation, its computational difficulty keeps it and potential solution methods at the forefront of current research. This paper defines and analyzes numerous proposed solutions to the TSP in order to facilitate understanding of the problem. Additionally, the efficiencies of different heuristics are studied and compared to the aforementioned algorithms’ accuracy, as a quick algorithm is often formulated at the expense of an exact solution

Spatial Transformation of Equality – Generalized Travelling Salesman Problem to Travelling Salesman Problem

The Equality-Generalized Travelling Salesman Problem (E-GTSP), which is an extension of the Travelling Salesman Problem (TSP), is stated as follows: given groups of points within a city, like banks, supermarkets, etc., find a minimum cost Hamiltonian cycle that visits each group exactly once. It can model many real-life combinatorial optimization scenarios more efficiently than TSP. This study presents five spatially driven search-algorithms for possible transformation of E-GTSP to TSP by considering the spatial spread of points in a given urban city. Presented algorithms are tested over 15 different cities, classified by their street-network’s fractal-dimension. Obtained results denote that the R-Search algorithm, which selects the points from each group based on their radial separation with respect to the start–end point, is the best search criterion for any E-GTSP to TSP conversion modelled for a city street network. An 8.8% length error has been reported for this algorithm