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.
Highlights
The Traveling Salesman Problem (TSP) is easy to qualify and describe but difficult and very hard to be solved
Genetic algorithm and local search algorithm to solve the travelling salesman problem implement in two forms, namely: 1) Individual form: Genetic algorithm works in single form without any local improvement local mechanism, and for comparing some of Crossover mechanism from previous studies are implemented
This paper Suggested new Crossover mechanism to solve travelling salesman problem using genetic algorithms, has proposed anew local improve algorithm to naming search for neighbor solutions algorithm entered on genetic algorithms to improve its performance and get better results and less and an increase of up to (10%) of the time implementation required to obtain the final result compared with other algorithms that have been comparison
Summary
The Traveling Salesman Problem (TSP) is easy to qualify and describe but difficult and very hard to be solved. 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 researches increased in this problem by the increased development in computers in terms of processing speed and storage capacity and memory, And has this problem drew the attention of many mathematicians and computer experts (Michalewicz, 1995) [15] for several reasons including: 1) Easy description, but its solution is very difficult because it belongs to a class of optimization problems called NP-complete which mean that there are no known algorithm that can find the ideal time of the result can be represented by multiple dimensions equation (Johnson polynomial). 3) We have a lot of information available and the standard questions about this problem, which it considered the mother problem (Michalewicz, 1995) [15] for many of the problems, so you can make many experiments on this problem and present the solution methods to other problems
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