Markov Chain-based Policies for Multi-stage Stochastic Integer Linear Programming with an Application to Disaster Relief Logistics

We introduce a novel aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state variables by leveraging the information of the underlying stochastic process, which is modeled as a Markov chain (MC). We present a novel branch-and-cut algorithm integrated … Read more

Modeling uncertainty processes for multi-stage optimization of strategic energy planning: An auto-regressive and Markov chain formulation

This paper deals with the modeling of stochastic processes in long-term multistage energy planning problems when little information is available on the degree of uncertainty of such processes. Starting from simple estimates of variation intervals for uncertain parameters, such as energy demands and costs, we model the temporal correlation of these parameters through autoregressive (AR) … Read more

Stochastic Dual Dynamic Programming for Optimal Power Flow Problems under Uncertainty

We propose the first computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in alternating current (AC) power systems. To this end, we use recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian … Read more

Stochastic Dual Dynamic Programming And Its Variants

We provide a tutorial-type review on stochastic dual dynamic programming (SDDP), as one of the state-of-the-art solution methods for multistage stochastic programs. Since introduced about 30 years ago for solving large-scale multistage stochastic linear programming problems in a hydrothermal context, SDDP has been applied to practical problems from several fields and is enriched by various … Read more

Distributionally Robust Stochastic Dual Dynamic Programming

We consider a multi-stage stochastic linear program that lends itself to solution by stochastic dual dynamic programming (SDDP). In this context, we consider a distributionally robust variant of the model with a finite number of realizations at each stage. Distributional robustness is with respect to the probability mass function governing these realizations. We describe a … Read more

Assessing the Cost of the Hazard-Decision Simplification in Multistage Stochastic Hydrothermal Scheduling

Hydropower is one of the world’s primary renewable energy sources whose usage has profound economic, environmental, and social impacts. We focus on the dispatch of generating units and the storage policy of hydro resources. In this context, an accurate assessment of the water opportunity-cost is cru- cial for driving the sustainable use of this scarce … Read more

Envelope Theorems for Multi-Stage Linear Stochastic Optimization

We propose a method to compute derivatives of multi-stage linear stochastic optimization problems with respect to parameters that influence the problem’s data. Our results are based on classical envelope theorems, and can be used in problems directly solved via their deterministic equivalents as well as in stochastic dual dynamic programming for which the derivatives of … Read more

High-dimensional risk-constrained dynamic asset allocation via Markov stochastic dual dynamic programming

Dynamic portfolio optimization has a vast literature exploring different simplifications by virtue of computational tractability of the problem. Previous works provide solution methods considering unrealistic assumptions, such as no transactional costs, small number of assets, specific choices of utility functions and oversimplified price dynamics. Other more realistic strategies use heuristic solution approaches to obtain suitable … Read more

Regularized Stochastic Dual Dynamic Programming for convex nonlinear optimization problems

We define a regularized variant of the Dual Dynamic Programming algorithm called REDDP (REgularized Dual Dynamic Programming) to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called SDDP-REG, can be seen as an extension of a regularization of the Stochastic Dual Dynamic Programming (SDDP) … Read more

A two-level SDDP Solving Strategy with Risk-Averse multivariate reservoir Storage Levels for Long Term power Generation Planning

Power generation planning in large-scale hydrothermal systems is a complex optimization task, specially due to the high uncertainty in the inflows to hydro plants. Since it is impossible to traverse the huge scenario tree of the multi-stage problem, stochastic dual dynamic programming (SDDP) is the leading optimization technique to solve it, originally from an expected-cost … Read more