Differential evolution: difference vectors and movement in solution space

  • Authors:

  • James Montgomery

  • Affiliations:

  • Complex Intelligent Systems Laboratory, Faculty of Information & Communication Technologies, Swinburne University of Technology, Melbourne, Australia

  • Venue:
  • CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
  • Year:
  • 2009

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Abstract

In the commonly used DE/rand/1 variant of differential evolution the primary mechanism of generating new solutions is the perturbation of a randomly selected point by a difference vector. The newly selected point may, if good enough, then replace a solution from the current generation. As the magnitude of difference vectors diminishes as the population converges, the size of moves made also diminishes, an oft-touted and obvious benefit of the approach. Additionally, when the population splits into separate clusters difference vectors exist for both small and large moves. Given that a replaced solution is not the one perturbed to create the new, candidate solution, are the large difference vectors responsible for movement of population members between clusters? This paper examines the mechanisms of small and large moves, finding that small moves within one cluster result in solutions from another being replaced and so appearing to move a large distance. As clusters tighten this is the only mechanism for movement between them.