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Combining Penalty-based and Gauss-Seidel Methods for solving Stochastic Mixed-Integer Problems

Fabricio Oliveira(fabricio.oliveira***at***rmit.edu.au)
Christiansen Jeffrey(s3507717***at***student.rmit.edu.au)
Dandurand Brian(brian.dandurand***at***rmit.edu.au)
Eberhard Andrew(andrew.eberhard***at***rmit.edu.au)

Abstract: In this paper, we propose a novel decomposition approach for mixed-integer stochastic programming (SMIP) problems that is inspired by the combination of penalty-based Lagrangian and block Gauss-Seidel methods (PBGS). In this sense, PBGS is developed such that the inherent decomposable structure that SMIPs present can be exploited in a computationally efficient manner. The performance of the proposed method is compared with the Progressive Hedging method (PH), which also can be viewed as a Lagrangian- based method for obtaining solutions for SMIP. Numerical experiments performed using instances from the literature illustrate the efficiency of the proposed method in terms of computational performance and solution quality.

Keywords: Stochastic programming, Decomposition methods, Lagrangian duality, Penalty-based method, Gauss-Seidel method

Category 1: Stochastic Programming

Citation: Mathematical Sciences, School of Science, RMIT University (2016)

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Entry Submitted: 10/27/2016
Entry Accepted: 10/27/2016
Entry Last Modified: 10/27/2016

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