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An evolutionary approach to the traveling salesman problem

Abstract

Evolutionary optimization has been proposed as a method to generate machine learning through automated discovery. A simulation of natural evolution is conducted using the traveling salesman problem as an artificial environment. For an exact solution of a traveling salesman problem, the only known algorithms require the number of steps to grow at least exponentially with the number of elements in the problem. Three adaptive techniques are described and analyzed. Evolutionary adaptation is demonstrated to be worthwhile in a variety of contexts. Local stagnation is prevented by allowing for the probabilistic survival of the simulated organisms. In complex problems, the final routing is estimated to be better than 99.99999999999% of all possible tours, even though only a small fraction (8.58 × 10−151) of the total number of tours are examined.

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Fogel, D.B. An evolutionary approach to the traveling salesman problem. Biol. Cybern. 60, 139–144 (1988). https://doi.org/10.1007/BF00202901

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Keywords

  • Exact Solution
  • Probabilistic Survival
  • Complex Problem
  • Natural Evolution
  • Travel Salesman Problem