String- and permutation-coded genetic algorithms for the static weapon-target assignment problem

  • Authors:
  • Bryant A. Julstrom

  • Affiliations:
  • St. Cloud State University, St. Cloud, MN, USA

  • Venue:
  • Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers
  • Year:
  • 2009

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Abstract

In the Weapon-Target Assignment Problem, m enemy targets are inbound, each with a value Vj representing the damage it may do. The defense has n weapons, and the probability that weapon i will kill target j is pij. The problem is to assign the weapons to targets so as to reduce as much as possible the total expected value of the targets. A greedy heuristic for this problem repeatedly assigns a weapon to a target to maximally degrade the target's value. Two genetic algorithms encode candidate assignments as strings of target labels indexed by weapon labels and as permutations of weapon labels decoded by a greedy algorithm, respectively. Both GAs can be seeded with the greedy heuristic's solution. In comparisons on fifteen randomly-generated problem instances, all the algorithms significantly reduced the hypothetical strikes' values, but the greedy heuristic was both effective and fast, while the seeded permutation-coded GA returned the best results. The times that all the GAs require grow quickly with problem size.