Stochastic dual dynamic programming for multistage stochastic mixed-integer nonlinear optimization

Multistage Stochastic Unit Commitment Using Stochastic Dual Dynamic Integer Programming

Unit commitment (UC) is a key operational problem in power systems used to determine an optimal daily or weekly generation commitment schedule. Incorporating uncertainty in this already difficult mixed-integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for ...

Stochastic Dual Dynamic Integer Programming

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, suc...

Mixed integer programming approaches for nonlinear and stochastic programming

Algorithms for Stochastic Mixed-Integer Programming Models

In this chapter, we will study algorithms for both two-stage as well as multi-stage stochastic mixed-integer programs. We present stagewise (resourcedirective) decomposition methods for two-stage models, and scenario (pricedirective) decomposition methods for multi-stage models. The manner in which these models are decomposed relies not only on the specific data elements that are random, but al...

Fenchel decomposition for stochastic mixed-integer programming

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an FD algorithm for SMIP and establi...