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arXiv · 2406.05052

Column generation for multistage stochastic mixed-integer nonlinear programs with discrete state variables

Tushar Rathi·Benjamin P. Riley·Angela Flores-Quiroz·Qi Zhang
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Abstract

Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the presence of discrete decisions and nonlinearities. In this work, we consider multistage stochastic mixed-integer nonlinear programs (MINLPs) with discrete state variables, which exhibit a decomposable structure that allows its solution using a column generation approach. Following a Dantzig-Wolfe reformulation, we apply column generation such that each pricing subproblem is an MINLP of much smaller size, making it more amenable to global MINLP solvers. We further propose a method for generating additional columns that satisfy the nonanticipativity constraints, leading to significantly improved convergence and optimal or near-optimal solutions for many large-scale instances in a reasonable computation time. The effectiveness of the tailored column generation algorithm is demonstrated via computational case studies on a multistage blending problem and a problem involving the routing of mobile generators in a power distribution network.

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Tushar Rathi, Benjamin P. Riley, Angela Flores-Quiroz, Qi Zhang. 2024-06-07. Column generation for multistage stochastic mixed-integer nonlinear programs with discrete state variables. https://arxiv.org/abs/2406.05052

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