TY - JOUR
T1 - Combining penalty‐based and Gauss–Seidel methods for solving stochastic mixed‐integer problems
AU - Oliveira, Fabricio
AU - Christiansen, Jeffrey
AU - Dandurand, Brian
AU - Eberhard, Andrew
PY - 2020/1
Y1 - 2020/1
N2 - In this paper, we propose a novel decomposition approach (named PBGS) for stochastic mixed‐integer programming (SMIP) problems, which is inspired by the combination of penalty‐based Lagrangian and block Gauss–Seidel methods. The PBGS method is developed such that the inherent decomposable structure that SMIP problems present can be exploited in a computationally efficient manner. The performance of the proposed method is compared with the progressive hedging (PH) method, which also can be viewed as a Lagrangian‐based method for obtaining solutions for SMIP problems. Numerical experiments performed using instances from the literature illustrate the efficiency of the proposed method in terms of computational performance and solution quality.
AB - In this paper, we propose a novel decomposition approach (named PBGS) for stochastic mixed‐integer programming (SMIP) problems, which is inspired by the combination of penalty‐based Lagrangian and block Gauss–Seidel methods. The PBGS method is developed such that the inherent decomposable structure that SMIP problems present can be exploited in a computationally efficient manner. The performance of the proposed method is compared with the progressive hedging (PH) method, which also can be viewed as a Lagrangian‐based method for obtaining solutions for SMIP problems. Numerical experiments performed using instances from the literature illustrate the efficiency of the proposed method in terms of computational performance and solution quality.
KW - stochastic programming
KW - decomposition methods
KW - Lagrangian duality
KW - penalty-based method
KW - Gauss-Seidel method
UR - http://www.scopus.com/inward/record.url?scp=85044281182&partnerID=8YFLogxK
U2 - 10.1111/itor.12525
DO - 10.1111/itor.12525
M3 - Article
SN - 0969-6016
VL - 27
SP - 494
EP - 524
JO - International Transactions in Operational Research
JF - International Transactions in Operational Research
IS - 1
ER -