Algorithmic innovations and software for the dual decomposition method applied to stochastic mixed-integer programs

Kim, Ki-Baek; Zavala, Ví­ctor M.

doi:10.1007/s12532-017-0128-z

Cited by 37 publications

(33 citation statements)

References 41 publications

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“…Papavasiliou et al [21] proposed a dual scenario decomposition scheme where the dual is solved using the subgradient method, and where the dual function is evaluated in parallel. Kim and Zavala [22] also used a dual scenario decomposition scheme, but solved the dual problem using a bundle method. Cheung et al [23] present a parallel implementation of the progressive hedging algorithm of Rockafellar and Wets [24].…”

Section: Scenario Decomposition Of the Suc Problemmentioning

confidence: 99%

A Distributed Computing Architecture for the Large-Scale Integration of Renewable Energy and Distributed Resources in Smart Grids

Aravena¹,

Papavasiliou²,

Papalexopoulos³

2017

Recent Progress in Parallel and Distributed Computing

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We present a distributed computing architecture for smart grid management, composed of two applications at two different levels of the grid. At the high voltage level, we optimize operations using a stochastic unit commitment (SUC) model with hybrid time resolution. The SUC problem is solved with an asynchronous distributed subgradient method, for which we propose stepsize scaling and fast initialization techniques. The asynchronous algorithm is implemented in a high-performance computing cluster and benchmarked against a deterministic unit commitment model with exogenous reserve targets in an industrial scale test case of the Central Western European system (679 buses, 1037 lines, and 656 generators). At the distribution network level, we manage demand response from small clients through distributed stochastic control, which enables harnessing residential demand response while respecting the desire of consumers for control, privacy, and simplicity. The distributed stochastic control scheme is successfully tested on a test case with 10,000 controllable devices. Both applications demonstrate the potential for efficiently managing flexible resources in smart grids and for systematically coping with the uncertainty and variability introduced by renewable energy.

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Section: Scenario Decomposition Of the Suc Problemmentioning

confidence: 99%

A Distributed Computing Architecture for the Large-Scale Integration of Renewable Energy and Distributed Resources in Smart Grids

Aravena¹,

Papavasiliou²,

Papalexopoulos³

2017

Recent Progress in Parallel and Distributed Computing

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“…To address the computation challenges, we propose exploiting problem structure and using massively parallel optimization solvers such as 43,44 for the subproblems (P2) and (P3). 9,39-42 Yet modeling multiscale effects (minutes to decades) and uncertainty often result in extremely large optimization problems.…”

Section: Discussionmentioning

confidence: 99%

“…9,[39][40][41][42] Yet modeling multiscale effects (minutes to decades) and uncertainty often result in extremely large optimization problems. To address the computation challenges, we propose exploiting problem structure and using massively parallel optimization solvers such as 43,44 for the subproblems (P2) and (P3). We also plan to apply this decomposition algorithm to other chemical processes and thermal energy storage systems.…”

Section: Discussionmentioning

confidence: 99%

A decomposition algorithm for simultaneous scheduling and control of CSP systems

2018

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We present a decomposition algorithm to perform simultaneous scheduling and control decisions in concentrated solar power (CSP) systems. Our algorithm is motivated by the need to determine optimal market participation strategies at multiple timescales. The decomposition scheme uses physical insights to create surrogate linear models that are embedded within a mixed‐integer linear scheduling layer to perform discrete (operational mode) decisions. The schedules are then validated for physical feasibility in a dynamic optimization layer that uses a continuous full‐resolution CSP model. The dynamic optimization layer updates the physical variables of the surrogate models to refine schedules. We demonstrate that performing this procedure recursively provides high‐quality solutions of the simultaneous scheduling and control problem. We exploit these capabilities to analyze different market participation strategies and to explore the influence of key design variables on revenue. Our results also indicate that using scheduling algorithms that neglect detailed dynamics significantly decreases market revenues. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2408–2417, 2018

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“…open-source software package DSP [14] and numerical experiments. In Section 5, we summarize the paper and discuss possible directions for future research.…”

Section: Section 3 Presents An Asynchronous Variant Of the Methods Andmentioning

confidence: 99%

“…DD methods for SMIP problems have been widely studied in the literature (e.g., [5,1,14]). These methods offer the ability to address integer recourse variables (i.e., integer variables in the second stage and beyond) and the opportunity to evaluate the dual function by solving parallel subproblems.…”

mentioning

confidence: 99%

An Asynchronous Bundle-Trust-Region Method for Dual Decomposition of Stochastic Mixed-Integer Programming

Kim¹,

Petra²,

Zavala³

2019

SIAM J. Optim.

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We present an asynchronous bundle-trust-region algorithm within the context of Lagrangian dual decomposition for stochastic mixed-integer programs. The approach solves the Lagrangian master problem by using a bundle method with a trust-region constraint. This scheme enables asynchronous computations and can thus help mitigate severe load imbalance issues (associated with the solution of scenario subproblems) and improve parallel efficiency. We provide a convergence analysis and an implementation of the proposed scheme. We also present extensive numerical results on eighty instances of a large-scale stochastic unit commitment problem, and demonstrate that the proposed approach provides significant reductions in solution time and achieves strong scaling.

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Algorithmic innovations and software for the dual decomposition method applied to stochastic mixed-integer programs

Cited by 37 publications

References 41 publications

A Distributed Computing Architecture for the Large-Scale Integration of Renewable Energy and Distributed Resources in Smart Grids

A Distributed Computing Architecture for the Large-Scale Integration of Renewable Energy and Distributed Resources in Smart Grids

A decomposition algorithm for simultaneous scheduling and control of CSP systems

An Asynchronous Bundle-Trust-Region Method for Dual Decomposition of Stochastic Mixed-Integer Programming

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