Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed‐Integer Nonlinear Programs

This paper considers deterministic global optimization of scenario‐based, two‐stage stochastic mixed‐integer nonlinear programs (MINLPs) in which the participating functions are nonconvex and separable in integer and continuous variables. A novel decomposition method based on generalized Benders decomposition, named nonconvex generalized Benders decomposition (NGBD), is developed to obtain ϵ‐optimal solutions of the stochastic MINLPs of interest in finite time. The dramatic computational advantage of NGBD over state‐of‐the‐art global optimizers is demonstrated through the computational study of several engineering problems, where a problem with almost 150,000 variables is solved by NGBD within 80 minutes of solver time.