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A method combining genetic algorithm with simultaneous perturbation stochastic approximation for linearly constrained stochastic optimization problems

Author

Listed:
  • Zhang Huajun

    (Huazhong University of Science and Technology)

  • Zhao Jin

    (Huazhong University of Science and Technology)

  • Luo Hui

    (Huazhong University of Science and Technology)

Abstract

This paper considers the optimization of linearly constrained stochastic problem which only noisy measurements of the loss function are available. We propose a method which combines genetic algorithm (GA) with simultaneous perturbation stochastic approximation (SPSA) to solve linearly constrained stochastic problems. The hybrid method uses GA to search for optimum over the whole feasible region, and SPSA to search for optimum at local region. During the GA and SPSA search process, the hybrid method generates new solutions according to gradient projection direction, which is calculated based on active constraints. Because the gradient projection method projects the search direction into the subspace at a tangent to the active constraints, it ensures new solutions satisfy all constraints strictly. This paper applies the hybrid method to nine typical constrained optimization problems and the results coincide with the ideal solutions cited in the references. The numerical results reveal that the hybrid method is suitable for multimodal constrained stochastic optimization problem. Moreover, each solution generated by the hybrid method satisfies all linear constraints strictly.

Suggested Citation

  • Zhang Huajun & Zhao Jin & Luo Hui, 2016. "A method combining genetic algorithm with simultaneous perturbation stochastic approximation for linearly constrained stochastic optimization problems," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 979-995, April.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:3:d:10.1007_s10878-014-9803-4
    DOI: 10.1007/s10878-014-9803-4
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    References listed on IDEAS

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    1. Rashika Gupta & Manju Agarwal, 2006. "Penalty guided genetic search for redundancy optimization in multi-state series-parallel power system," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 257-277, November.
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