A Water Flow-Like Algorithm for the Travelling Salesman Problem

Abstract

The water flow-like algorithm (WFA) is a relatively new metaheuristic that performs well on the object grouping problem encountered in combinatorial optimization. This paper presents a WFA for solving the travelling salesman problem (TSP) as a graph-based problem. The performance of the WFA on the TSP is evaluated using 23 TSP benchmark datasets and by comparing it with previous algorithms. The experimental results show that the proposed WFA found better solutions in terms of the average solution and the percentage deviation of the average solution from the best-known solution.

Solving the Traveling Salesman Problem Using Hydrological Cycle Algorithm

“…The propagation operator mutated the tours with a probability equal to the wavelength. Therefore, a bad The water flow-like algorithm (WFA) is also used to solve the TSP [8]. Initially, a set of solutions to the water-flow is generated using a nearest-neighbor heuristic.…”

“…The second factor of the transition rule is the inverse of depth, which is calculated based on Equation (8).…”

“…Depth i j = (8) Depth (i, j) is the depth between two nodes i and j, and calculated by dividing the length of the path by the amount of soil. The depth of the path needs to be updated when the amount of soil existing on the path changes.…”

“…Figure 3 demonstrates the operation of 2-Opt. In this example, the algorithm selects edges (2, 7) and (3,8), and consecutively creates new edges (2, 3) and (7,8). The order of the nodes between the two edges must also be reversed.…”

“…The WWO results (column 9) were taken from [7]. The WFA and RFD results (columns 10 and 11) were borrowed from [8] and from [9], respectively. The best results are marked in bold font.…”