An Automatic Decomposition Algorithm for Solving Stochastic Mixed-Integer Programs Based on Progressive Hedging Algorithm

This study focuses on stochastic mixed-integer programming problems and proposes an automatic decomposition algorithm that is capable of detecting the problem structure and then determining the best way to separate the original problem into sub-problems. We utilize the hypergraph to capture the relationship between decision variables and constraints according to the nonzero elements in the left-hand-side matrix of the original problem. The proposed decomposition method is shown to be terminated in finite iterations. Additionally, the decomposed problem is solved using the progressive hedging algorithm, with various configurations adjusted to enhance runtime. Computational experiments use public instances of two-stage stochastic integer programs. The result shows that most linked variables are continuous as the number of decomposed sub-problems decreases. This improves the convergence of the progressive hedging algorithm, yielding optimal or near-optimal solutions even for very large-scale instances that cannot be solved by commercial solvers.