The goal of this survey is to provide a road-map for exploring the growing area of stochastic mixed-integer programming (SMIP) models and algorithms. We provide a comprehensive overview of existing decomposition algorithms for two-stage SMIPs, including Dantzig-Wolfe decomposition, dual decomposition, Lagrangian cuts, and decomposition approaches using parametric cutting planes and scaled cuts. Moreover, we explicitly … Read more
We study a broad class of vehicle routing problems in which the cost of a route is allowed to be any nonnegative rational value computable in polynomial time in the input size. To address this class, we introduce a unifying framework that generalizes existing integer L-shaped (ILS) formulations developed for vehicle routing problems with stochastic … Read more
In the earlier paper “On solving large-scale multistage stochastic optimization problems with a new specialized interior-point approach, European Journal of Operational Research, 310 (2023), 268–285” the authors presented a novel approach based on a specialized interior-point method (IPM) for solving (risk neutral) large-scale multistage stochastic optimization problems. The method computed the Newton direction by combining … Read more
In this work, we are concerned with the study of optimization problems featuring so-called probability or chance constraints. Probability constraints measure the level of satisfaction of an underlying random inequality system and ensure that this level is high enough. Such an underlying inequality system could be expressed by an abstractly known or perhaps costly to … Read more
We show how to extract alternative solutions for optimization problems solved by Benders Decom- position. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative solutions but none appear to support such generation when using Benders Decomposition. We propose a new post-processing method that extracts multiple optimal and … Read more
We introduce new algorithms to identify the trade-off (TRO) between adopting a distributional belief and hedging against ambiguity when modeling uncertainty in a capacitated fixed charge facility location problem (CFLP). We first formulate a TRO model for the CFLP (TRO-CFLP), which determines the number of facilities to open by minimizing the fixed establishment cost and … Read more
The widespread existence of various uncertainties makes the inherently complex refinery production scheduling problem even more challenging. To address this issue, this paper proposes a viable systematic data-driven multistage scheduling optimization framework and develops a corresponding structured modeling methodology. Under this paradigm, unit-level advanced control and plant-level intelligent scheduling are coordinated to jointly deal with … Read more
The Progressive Hedging (PH) algorithm is one of the cornerstones in large-scale stochastic programming. However, its traditional development requires that all scenario subproblems are solved per iteration, and a probability distribution with finitely many outcomes. This paper introduces a stochastic dual PH algorithm (SDPH) to overcome these challenges. We introduce an adaptive sampling process and … Read more
Stochastic Dual Dynamic Programming (SDDP) is widely recognized as the predominant methodology for solving large-scale multistage stochastic linear programming (MSLP) problems. This paper aims to contribute to the extant literature by conducting a comprehensive survey of the literature on SDDP within the realm of practical applications. We systematically identify and analyze the various domains where … Read more
Climate change is increasingly impacting power system operations, not only through more frequent extreme weather events but also through shifts in routine weather patterns. Factors such as increased temperatures, droughts, changing wind patterns, and solar irradiance shifts can impact both power system production and transmission and electric load. The current power system was not designed … Read more