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A Genetic Algorithm for the Traveling Salesman Problem using an Ant Colony Optimisation inspired selection operator, and Partially Mapped Crossover

Typical representations of the Travelling Salesman Problem (TSP), as a specialised instance of a combinatorial optimisation problem, suffer a handicap in comparison to other artificial intelligence techniques when encoded in a Genetic Algorithm (GA). The handicap is such that encoding genes as a permutation constrained string restricts use of the GA’s core operators, crossover and mutation. Classical GA operators are typically constraint agnostic, or deal specifically with the constraints relating to the value, range, and encoding of individual chromosomes rather than the ’gene’ as a whole such as TSPs require. Therefore, alternative operators that consider the constraints of the problem at hand are required in order to use a GA for the purposes of solving a TSP.

This paper sets forth a solution that makes use of Partially-Mapped Crossover as proposed and implemented by Goldberg, Lingle et al. (1985), and a new operator for parent selection that takes inspiration from the way in which Ant Colony Optimisation algorithms build a candidate solution by way of iterative traversal.

This algorithm processes data in TSPLib format (Reinelt, 1991). The main examples of which can be found at the official homepage: http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/

Useage

The executable can be invoked with the following command-line flags

  -crossover
        whether or not the algorithm should use crossover operators (default false)
  -generations int
        the number of generations to run for (default 50)
  -input string
        the path to a TSPLib input file ".tsp" containing cities to find a solution for (default "data/berlin52.tsp")
  -mutate
        whether or not the algorithm should use mutation operators (default false)
  -mutateMethod string
        mutation method to use, one of 'inversion' or 'swap'  (default "inversion")
  -optimal string
        the path to a TSPLib optimal route file ".opt.tour" containing an optimal solution to compare against (default: automatically determined from input file)
  -selectionMethod string
        selection method to use, one of 'aco', 'tournament', 'roulette' (default "aco")
  -size int
        the number of candidates to have in the pool (default 50)
  -terminateEarly
        whether or not the algorithm should terminate early if stagnation is detected (default false)
  -terminatePercentage int
        percentage of the specified no. of generations, should the algorithm terminate if change has not been detected in that time (default 25)
  -xoMethod string
        crossover method to use, one of 'ox' (ordered), 'pmx' (partially-mapped)  (default "ox")