Bounds and Approximations for Multistage Stochastic Programs

Maggioni, Francesca; Pflug, Georg Ch.

doi:10.1137/140971889

Cited by 33 publications

(22 citation statements)

References 16 publications

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“…The concept of partitioning has been used in the context of SMIPs in a completely different manner. Instead of completely decomposing the problem so that each scenario can be treated as a separate subproblem, scenarios can be grouped together to form larger subproblems (Boland et al 2016, Maggioni and Pflug 2016, Ryan et al 2016, Sandikçi and Ozaltin 2017. This approach can potentially yield better relaxations at the cost of having more expensive subproblems.…”

Section: Related Workmentioning

confidence: 99%

Parallelizing Subgradient Methods for the Lagrangian Dual in Stochastic Mixed-Integer Programming

Lim

Linderoth

Luedtke

et al. 2021

INFORMS Journal on Optimization

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The dual decomposition of stochastic mixed-integer programs can be solved by the projected subgradient algorithm. We show how to make this algorithm more amenable to parallelization in a master-worker model by describing two approaches, which can be combined in a natural way. The first approach partitions the scenarios into batches and makes separate use of subgradient information for each batch. The second approach drops the requirement that evaluation of function and subgradient information is synchronized across the scenarios. We provide convergence analysis of both methods. We also evaluate their performance on two families of problems from SIPLIB on a single server with 32 single-core worker processes, demonstrating that when the number of workers is high relative to the number of scenarios, these two approaches (and their synthesis) can significantly reduce running time.

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Section: Related Workmentioning

confidence: 99%

Parallelizing Subgradient Methods for the Lagrangian Dual in Stochastic Mixed-Integer Programming

Lim

Linderoth

Luedtke

et al. 2021

INFORMS Journal on Optimization

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show abstract

“…Another stream of research focuses on group subproblem approach to obtain bounds for risk-neutral (Sandıkçı et al 2013;Maggioni et al 2014Sandıkçı and Özaltın 2017) and risk-averse (see Maggioni and Pflug 2016;Mahmutogulları et al 2018) mixed-integer multi-stage stochastic programming problems. The method is based on solving the problem for subsets of scenarios instead of the original set of scenarios in order to obtain bounds on the optimal value of the problem.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

An exact solution approach for risk-averse mixed-integer multi-stage stochastic programming problems

2019

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Risk-averse mixed-integer multi-stage stochastic programming problems are challenging, large scale and non-convex optimization problems. In this study, we propose an exact solution algorithm for a type of these problems with an objective of dynamic mean-CVaR risk measure and binary first stage decision variables. The proposed algorithm is based on an evaluate-andcut procedure and uses lower bounds obtained from a scenario tree decomposition method called as group subproblem approach. We also show that, under the assumption that the first stage integer variables are bounded, our algorithm solves problems with mixed-integer variables in all stages. Computational experiments on risk-averse multi-stage stochastic server location and generation expansion problems reveal that the proposed algorithm is able to solve problem instances with more than one million binary variables within a reasonable time under a modest computational setting.

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“…As the lower bound cut, we decided to use the one that we can compute with the least effort. As there have been several lower bounds proposed for stochastic programs (for DOI: 10.14736/kyb-2017- example in [3] and [11]) the question of the appropriate one for our problem will be left open for future research.…”

Section: Introductionmentioning

confidence: 99%