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Discrete optimization via gradient-based adaptive stochastic search methods

Author

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  • Xi Chen
  • Enlu Zhou
  • Jiaqiao Hu

Abstract

Gradient-based Adaptive Stochastic Search (GASS) is a new stochastic search optimization algorithm that has recently been proposed. It iteratively searches promising candidate solutions through a population of samples generated from a parameterized probabilistic model on the solution space, and updates the parameter of the probabilistic model based on a direct gradient method. Under the framework of GASS, we propose two discrete optimization algorithms: discrete Gradient-based Adaptive Stochastic Search (discrete-GASS) and annealing Gradient-based Adaptive Stochastic Search (annealing-GASS). In discrete-GASS, we transform the discrete optimization problem into a continuous optimization problem on the parameter space of a family of independent discrete distributions, and apply a gradient-based method to find the optimal parameter, such that the corresponding distribution has the best capability to generate optimal solution(s) to the original discrete problem. In annealing-GASS, we use a Boltzmann distribution as the parameterized probabilistic model, and propose a gradient-based temperature schedule that changes adaptively with respect to the current performance of the algorithm. We show convergence of both discrete-GASS and annealing-GASS under appropriate conditions. Numerical results on several benchmark optimization problems and the traveling salesman problem indicate that both algorithms perform competitively against a number of other algorithms, including model reference adaptive search, the cross-entropy method, and multi-start simulated annealing with different temperature schedules.

Suggested Citation

  • Xi Chen & Enlu Zhou & Jiaqiao Hu, 2018. "Discrete optimization via gradient-based adaptive stochastic search methods," IISE Transactions, Taylor & Francis Journals, vol. 50(9), pages 789-805, September.
  • Handle: RePEc:taf:uiiexx:v:50:y:2018:i:9:p:789-805
    DOI: 10.1080/24725854.2018.1448489
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