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On a Feasible-Infeasible Two-Population (FI-2Pop) genetic algorithm for constrained optimization: Distance tracing and no free lunch

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  • Kimbrough, Steven Orla
  • Koehler, Gary J.
  • Lu, Ming
  • Wood, David Harlan

Abstract

We explore data-driven methods for gaining insight into the dynamics of a two-population genetic algorithm (GA), which has been effective in tests on constrained optimization problems. We track and compare one population of feasible solutions and another population of infeasible solutions. Feasible solutions are selected and bred to improve their objective function values. Infeasible solutions are selected and bred to reduce their constraint violations. Interbreeding between populations is completely indirect, that is, only through their offspring that happen to migrate to the other population. We introduce an empirical measure of distance, and apply it between individuals and between population centroids to monitor the progress of evolution. We find that the centroids of the two populations approach each other and stabilize. This is a valuable characterization of convergence. We find the infeasible population influences, and sometimes dominates, the genetic material of the optimum solution. Since the infeasible population is not evaluated by the objective function, it is free to explore boundary regions, where the optimum is likely to be found. Roughly speaking, the No Free Lunch theorems for optimization show that all blackbox algorithms (such as Genetic Algorithms) have the same average performance over the set of all problems. As such, our algorithm would, on average, be no better than random search or any other blackbox search method. However, we provide two general theorems that give conditions that render null the No Free Lunch results for the constrained optimization problem class we study. The approach taken here thereby escapes the No Free Lunch implications, per se.

Suggested Citation

  • Kimbrough, Steven Orla & Koehler, Gary J. & Lu, Ming & Wood, David Harlan, 2008. "On a Feasible-Infeasible Two-Population (FI-2Pop) genetic algorithm for constrained optimization: Distance tracing and no free lunch," European Journal of Operational Research, Elsevier, vol. 190(2), pages 310-327, October.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:2:p:310-327
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    References listed on IDEAS

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    1. David H. Wolpert & William G. Macready, 1995. "No Free Lunch Theorems for Search," Working Papers 95-02-010, Santa Fe Institute.
    2. Gary J. Koehler, 2007. "Conditions that Obviate the No-Free-Lunch Theorems for Optimization," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 273-279, May.
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    1. Felipe, Angel & Teresa Ortuño, M. & Tirado, Gregorio, 2011. "Using intermediate infeasible solutions to approach vehicle routing problems with precedence and loading constraints," European Journal of Operational Research, Elsevier, vol. 211(1), pages 66-75, May.
    2. Barkat Ullah, Abu S.S.M. & Sarker, Ruhul & Lokan, Chris, 2012. "Handling equality constraints in evolutionary optimization," European Journal of Operational Research, Elsevier, vol. 221(3), pages 480-490.

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