Abstract
The traveling salesman problem has long been regarded as a challenging application for existing optimization methods as well as a benchmark application for the development of new optimization methods. As with many existing algorithms, a traditional genetic algorithm will have limited success with this problem class, particularly as the problem size increases. A rule based genetic algorithm is proposed and demonstrated on sets of traveling salesman problems of increasing size. The solution character as well as the solution efficiency is compared against a simulated annealing technique as well as a standard genetic algorithm. The rule based genetic algorithm is shown to provide superior performance for all problem sizes considered. Furthermore, a post optimal analysis provides insight into which rules were successfully applied during the solution process which allows for rule modification to further enhance performance.
Highlights
The traveling salesman problem is an example of a NP complete problem where the computational time required to generate an exact solution increases exponentially with the number of cities involved
The traveling salesman problem has long been regarded as a challenging application for existing optimization methods as well as a benchmark application for the development of new optimization methods
In order to demonstrate the robust nature of the rule based evolutionary approach, an additional 15 problems were solved. These problems were selected from the test problem set maintained by the University of Heidelberg and represent traveling salesman problems varying in the number of cities
Summary
The traveling salesman problem is an example of a NP complete problem where the computational time required to generate an exact solution increases exponentially with the number of cities involved. The goal here is to demonstrate that a rule based genetic algorithm operating with a simplistic rule set can perform as well or better than an expert, which in this case will be represented by an algorithm explicitly designed for this class of problems, the method of simulated annealing. None of the algorithms tested are claimed to be overly efficient, but the results represent the general trend which would be expected in the application of a generic implementation of the particular algorithm class The results from this comparative study show the initial promise of the rule based approach. Rules generated from previous hybrid methods have been combined with new strategies to form an efficient solution algorithm This algorithm is tested on a wide variety of problems to demonstrate the ability of the approach in generating the global optimum for problems. This can lead to an automated rule update which would allow for an aspect of learning occurring
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