Journal of Optimization Theory and Applications

, Volume 147, Issue 2, pp 395–410

Annealing a Genetic Algorithm for Constrained Optimization

Article

DOI: 10.1007/s10957-010-9716-z

Cite this article as:
Mendivil, F. & Shonkwiler, R. J Optim Theory Appl (2010) 147: 395. doi:10.1007/s10957-010-9716-z

Abstract

In this paper, we adapt a genetic algorithm for constrained optimization problems. We use a dynamic penalty approach along with some form of annealing, thus forcing the search to concentrate on feasible solutions as the algorithm progresses. We suggest two different general-purpose methods for guaranteeing convergence to a globally optimal (feasible) solution, neither of which makes any assumptions on the structure of the optimization problem. The former involves modifying the GA evolution operators to yield a Boltzmann-type distribution on populations. The latter incorporates a dynamic penalty along with a slow annealing of acceptance probabilities. We prove that, with probability one, both of these methods will converge to a globally optimal feasible state.

Keywords

Genetic algorithms Constrained optimization Simulated annealing Markov chain Convergence proofs 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsAcadia UniversityWolfvilleCanada
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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