A Hybrid PSO-GA Algorithm for Traveling Salesman Problems in Different Environments

Abstract

In this study particle swarm optimization (PSO) is modified and hybridised with genetic algorithm (GA) using one’s output as the other's input to solve Traveling Salesman Problem(TSP). Here multiple velocity update rules are introduced to modify the PSO and at the time of the movement of a solution, one rule is selected depending on its performances using roulette wheel selection process. Each velocity update rule and the corresponding solution update rule are defined using swap sequence (SS) and swap operation (SO). K-Opt operation is applied in a regular interval of iterations for the movement of any stagnant solution. GA is applied on the final output swarm of the PSO to search the optimal path of the large size TSPs. Roulette wheel selection process, multi-point cyclic crossover and the K-opt operation for the mutation are used in the GA phase. The algorithm is tested in crisp environment using different size benchmark test problems available in the TSPLIB. In the crisp environment the algorithm gives approximately 100% success rate for the test problems up to considerably large sizes. Efficiency of the algorithm is tested with some other existing algorithms in the literature using Friedman test. Some approaches are incorporated with this algorithm for finding solutions of the TSPs in imprecise (fuzzy/rough) environment. Imprecise problems are generated from the crisp problems randomly, solved and obtained results are discussed. It is observed that the performance of the proposed algorithm is better compared to the some other algorithms in the existing literature with respect to the accuracy and the consistency for the symmetric TSPs as well as the Asymmetric TSPs.

Hybrid Algorithm Based on Ant Colony Optimization and Simulated Annealing Applied to the Dynamic Traveling Salesman Problem

“…The improved Lin–Kernigham algorithm called LKH was introduced by Helsgaun [ 18 ]; this algorithm provided the best solution reported thus far for the World TSP instance containing 1,904,711 vertices [ 19 ]. Different metaheuristic methods for the TSP also emerged using various principles such as ant colony optimization (ACO) [ 20 ], particle swarm optimization (PSO) [ 21 ], simulated annealing [ 22 ], genetic algorithms [ 23 ], and others [ 24 ], as well as their combinations [ 25 , 26 , 27 ].…”

A Hybrid Particle Swarm Optimization Algorithm Enhanced with Nonlinear Inertial Weight and Gaussian Mutation for Job Shop Scheduling Problems

“…Researchers can derive inspiration from the behavior of biological populations in nature or the laws of biological evolution to design algorithms [46]. As one of many swarm intelligence algorithms, PSO has been proven effective in various optimization fields [47][48][49][50][51][52].…”

Multi-Subdomain Grouping-Based Particle Swarm Optimization for the Traveling Salesman Problem

“…It optimized the PSO by using five velocity update rules. Meanwhile, it also introduced roulette wheel selection, multi-point cyclic crossover and 3opt to the GA phase [1]. To reduce computational time, VTPSO applied the swap operators of the considered velocity swap sequence one after another, and chose the best solution as a new tour [46].…”

“…The traveling salesman problem (TSP) is a typical nondeterministic polynomial (NP) hard combinatorial optimization problem. The problem can be stated as a procedure to find the shortest or minimum-cost cyclic route for a salesman who travels to all target cities and returns to the departure city without repetition [1]. This is always a classical model for various fields of household, civil and military, such as vehicle route planning [2][3][4], scheduling, threading of scan cells, computer wiring, automatic drilling of printed circuit boards and circuits, and X-ray crystallography [5].…”

“…Khan et al applied the GA at the final stage of PSO to further improve the solutions of the output swarm. This method attained a success rate of approximately 100% for large TSPs in a crisp environment [1]. To optimize the parameters for underactuated autonomous underwater vehicle control, the PSO and artificial fish school algorithm were executed simultaneously, providing an admirable control effect in both simulation tests and field trials [20].…”