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Genetic algorithms for the traveling salesman problem based on a heuristic crossover operation

Abstract

We apply strategies inspired by natural evolution to a classical example of discrete optimization problems, the traveling salesman problem. Our algorithms are based on a new knowledge-augmented crossover operation. Even if we use only this operation in the reproduction process, we get quite good results. The most obvious faults of the solutions can be eliminated and the results can further be improved by allowing for a simple form of mutation. If each crossover is followed by an affordable local optimization, we get the optimum solution for a 318-town problem, probably the optimum solutions for several different 100-town problems, and very nearly optimum solutions for 350-town and 1000-town problems. A new strategy for the choice of parents considerably speeds up the convergence of the latter method.

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Pál, K.F. Genetic algorithms for the traveling salesman problem based on a heuristic crossover operation. Biol. Cybern. 69, 539–546 (1993). https://doi.org/10.1007/BF00199453

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Keywords

  • Genetic Algorithm
  • Simple Form
  • Local Optimization
  • Natural Evolution
  • Travel Salesman Problem