Asynchronous Lagrangian scenario decomposition

We present a distributed asynchronous algorithm for solving two-stage stochastic mixed-integer programs (SMIP) using scenario decomposition, aimed at industrial-scale instances of the stochastic unit commitment (SUC) problem. The algorithm is motivated by large differences in run times observed amon...

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Vydáno v:Mathematical programming computation Ročník 13; číslo 1; s. 1 - 50
Hlavní autoři: Aravena, Ignacio, Papavasiliou, Anthony
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2021
Springer Nature B.V
Témata:
Algorithms
Computer networks
Decomposition
Distributed processing
Full Length Paper
Mathematics
Mathematics and Statistics
Mathematics of Computing
Mixed integer
Operations Research/Decision Theory
Optimization
Run time (computers)
Theory of Computation
Unit commitment
68W20
90C10
High performance computing
Unit commitment
90C06
90C15
68W15
Asynchronous algorithm
Stochastic programming
ISSN:1867-2949, 1867-2957
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Shrnutí:We present a distributed asynchronous algorithm for solving two-stage stochastic mixed-integer programs (SMIP) using scenario decomposition, aimed at industrial-scale instances of the stochastic unit commitment (SUC) problem. The algorithm is motivated by large differences in run times observed among scenario subproblems of SUC instances, which can result in inefficient use of distributed computing resources by synchronous parallel algorithms. Our algorithm performs dual iterations asynchronously using a block-coordinate subgradient descent method which allows performing block-coordinate updates using delayed information, while candidate primal solutions are recovered from the solutions of scenario subproblems using heuristics. We present a high performance computing implementation of the asynchronous algorithm, detailing the operations performed by each parallel process and the communication mechanisms among them. We conduct numerical experiments using SUC instances of the Western Electricity Coordinating Council system with up to 1000 scenarios and of the Central Western European system with up to 120 scenarios. We also conduct numerical experiments on generic SMIP instances from the SIPLIB library (DCAP and SSLP). The results demonstrate the general applicability of the proposed algorithm and its ability to solve industrial-scale SUC instances within operationally acceptable time frames. Moreover, we find that an equivalent synchronous parallel algorithm would leave cores idle up to 80.4% of the time on our realistic test instances, an observation which underscores the need for designing asynchronous optimization schemes in order to fully exploit distributed computing on real world applications.
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ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-020-00185-4