Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal scheduling

Homem-de-Mello, Tito; Matos, Vitor Luiz de; Finardi, Erlon Cristian

doi:10.1007/s12667-011-0024-y

Cited by 113 publications

(41 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A computational assessment of conditional sampling, antithetic sampling, control variates and importance sampling appeared in Higle (1998). QMC and Latin Hypercube Sampling (LHS) were compared in Homem-de Mello et al (2011). The effect of sampling on the solution quality of stochastic programming problems was discussed in Linderoth et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach

Parpas

Ustun

Webster

et al. 2015

INFORMS Journal on Computing

View full text Add to dashboard Cite

Stochastic programming models are large-scale optimization problems that are used to facilitate decisionmaking under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integral whose integrand is an optimization problem. In turn, the recourse function has to be estimated using techniques such as scenario trees or Monte Carlo methods, both of which require numerous functional evaluations to produce accurate results for large-scale problems with multiple periods and high-dimensional uncertainty. In this work, we introduce an importance sampling framework for stochastic programming that can produce accurate estimates of the recourse function using a small number of samples. Our framework combines Markov Chain Monte Carlo methods with Kernel Density Estimation algorithms to build a non-parametric importance sampling distribution, which can then be used to produce a lower-variance estimate of the recourse function. We demonstrate the increased accuracy and efficiency of our approach using variants of well-known multistage stochastic programming problems. Our numerical results show that our framework produces more accurate estimates of the optimal value of stochastic programming models, especially for problems with moderate variance, multimodal or rare-event distributions.

show abstract

Section: Introductionmentioning

confidence: 99%

Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach

Parpas

Ustun

Webster

et al. 2015

INFORMS Journal on Computing

View full text Add to dashboard Cite

show abstract

“…Our description above also admits algorithms that select x 1 t ; x 2 t ; : : : ; x Jt t by other means (e.g. the quasi-Monte Carlo method described in [7]). …”

mentioning

confidence: 99%

On Solving Multistage Stochastic Programs with Coherent Risk Measures

Philpott

Matos²,

Finardi

2013

Operations Research

103

View full text Add to dashboard Cite

We consider a class of multistage stochastic linear programs in which at each stage a coherent risk measure of future costs is to be minimized. A general computational approach based on dynamic programming is derived that can be shown to converge to an optimal policy. By computing an inner approximation to future cost functions, we can evaluate an upper bound on the cost of an optimal policy, and an outer approximation delivers a lower bound. The approach we describe is particularly useful in sampling-based algorithms, and a numerical example is provided to show the e¢ cacy of the methodology when used in conjunction with stochastic dual dynamic programming.

show abstract

“…This has proved to be more reliable than the standard test for the problems we are solving (see [3], [6] for a discussion of the drawbacks of the standard convergence criterion).…”

Section: Stochastic Dual Dynamic Programmingmentioning

confidence: 99%

“…This allows cuts to be shared between di¤erent states, e¤ectively collapsing the scenario tree. Although it was developed over twenty years ago, and has been cited over the years in many applied papers, SDDP has received some recent attention in the mathematical programming literature ( [2], [3], [4], [5], [6], [7]) that explores the mathematical properties of this method, in some cases extending it to deal with risk-averse objective functions. This paper is concerned with some of the implementation details of SDDP algorithms.…”

Section: Introductionmentioning

confidence: 99%

Improving the performance of Stochastic Dual Dynamic Programming

Matos

Philpott

Finardi

2015

Journal of Computational and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

This paper is concerned with tuning the Stochastic Dual Dynamic Programming algorithm to make it more computationally e¢ cient. We report the results of some computational experiments on a large-scale hydrothermal scheduling model developed for Brazil. We …nd that the best improvements in computation time are obtained from an implementation that increases the number of scenarios in the forward pass with each iteration and selects cuts to be included in the stage problems in each iteration. This gives an order of magnitude decrease in computation time with little change in solution quality.

show abstract

Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal scheduling

Cited by 113 publications

References 36 publications

Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach

Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach

On Solving Multistage Stochastic Programs with Coherent Risk Measures

Improving the performance of Stochastic Dual Dynamic Programming

Contact Info

Product

Resources

About