Abstract
This paper presents a novel genetic algorithm to solve the traveling salesman problem. The proposed method combines the Newton-Raphson numerical method with an inversion genetic algorithm; the method is called inversion with embedded Newton-Raphson Search. Different benchmark problems, including 10-, 30-, 50-, 75-, 105-, and 318-city topologies, are used to evaluate the approach. The best-known solutions have been produced by this hybrid genetic algorithm. In this paper we also report other results, such as the average tour distance, distribution of the results, and average number of generations. The proposed approach has been shown to outperform other genetic operators. An analysis based on the survival rate of the o-schemata and Holland's fundamental theory is included.
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