Solving travelling salesman problem (TSP) by hybrid genetic algorithm (HGA)

Abstract

The Traveling Salesman Problem (TSP) is easy to qualify and describe but difficult and very hard to be solved. There is known algorithm that can solve it and find the ideal outcome in polynomial time, so it is NP-Complete problem. The Traveling Salesman Problem (TSP) is related to many others problems because the techniques used to solve it can be easily used to solve other hard Optimization problems, which allows of circulating it results on many other optimization problems. Many techniques were proposed and developed to solve such problems, including Genetic Algorithms. The aim of the paper is to improve and enhance the performance of genetic algorithms to solve the Traveling Salesman Problem (TSP) by proposing and developing a new Crossover mechanism and a local search algorithm called the Search for Neighboring Solution Algorithm, with the goal of producing a better solution in a shorter period of time and fewer generations. The results of this study for a number of different size standard benchmarks of TSP show that the proposed algorithms that use Crossover proposed mechanism can find the optimum solution for many of these TSP benchmarks by (100%), and within the rate (96%-99%) of the optimal solution to some for others. The comparison between the proposed Crossover mechanism and other known Crossover mechanisms show that it improves the quality of the solutions. The proposed Local Search algorithm and Crossover mechanism produce superior results compared to previously propose local search algorithms and Crossover mechanisms. They produce near optimum solutions in less time and fewer generations.