Stochastic Mixed‐Integer Programming Algorithms: Beyond Benders' Decomposition

Sen, Suvrajeet

doi:10.1002/9780470400531.eorms0232

Cited by 13 publications

(12 citation statements)

References 41 publications

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“…Interesting reviews on approximation of multi-stage stochastic optimization problems with mixed-integer variables can be found in [45], [46], [47]. Two-stage optimization problems with continuous and integer variables in the second stage were considered for the first time in [48] where an approach to compute modified Benders cut is proposed under the assumption that the first stage only contains binary variables.…”

Section: A Decomposition Techniquesmentioning

confidence: 99%

Planning With Multiple Transmission and Storage Investment Options Under Uncertainty: A Nested Decomposition Approach

Falugi

Konstantelos

Štrbac

2018

IEEE Trans. Power Syst.

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Abstract-Achieving the ambitious climate change mitigation objectives set by governments worldwide is bound to lead to unprecedented amounts of network investment to accommodate low-carbon sources of energy. Beyond investing in conventional transmission lines, new technologies such as energy storage can improve operational flexibility and assist with the costeffective integration of renewables. Given the long lifetime of these network assets and their substantial capital cost, it is imperative to decide on their deployment on a long-term costbenefit basis. However, such an analysis can result in large-scale Mixed Integer Linear Programming (MILP) problems which contain many thousands of continuous and binary variables. Complexity is severely exacerbated by the need to accommodate multiple candidate assets and consider a wide range of exogenous system development scenarios that may occur. In this manuscript we propose a novel, efficient and highly-generalizable framework for solving large-scale planning problems under uncertainty by using a temporal decomposition scheme based on the principles of Nested Benders. The challenges that arise due to the presence of non-sequential investment state equations and sub-problem non-convexity are highlighted and tackled. The substantial computational gains of the proposed method are demonstrated via a case study on the IEEE 118 bus test system that involve planning of multiple transmission and storage assets under longterm uncertainty. The proposed method is shown to substantially outperform the current state-of-the-art. All the parameters involved in the optimization model can be represented by the vector ρ containing B n,g Bus-to-generation incidence matrix. I n,ℓ Bus-to-line incidence matrix. S n,s Bus-to-storage incidence matrix.

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Section: A Decomposition Techniquesmentioning

confidence: 99%

Planning With Multiple Transmission and Storage Investment Options Under Uncertainty: A Nested Decomposition Approach

Falugi

Konstantelos

Štrbac

2018

IEEE Trans. Power Syst.

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“…In any event, we have chosen to summarize these two methods because of their ability to manage general integer decisions in both stages. For prior research on more special cases, we refer to [53].…”

Section: Decomposition For Two-stage Stochastic Mixed-integer Programsmentioning

confidence: 99%

“…We refer the reader to [66] and [8] for an introduction to these topics. Furthermore, the reader should note that we have omitted some SMIP ideas that have appeared in earlier surveys on this subject ( [53], [52]).…”

Section: Introductionmentioning

confidence: 99%

An Introduction to Two-Stage Stochastic Mixed-Integer Programming

Küçükyavuz

Sen

2017

The Operations Research Revolution

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This paper provides an introduction to algorithms for two-stage stochastic mixed-integer programs. Our focus is on methods which decompose the problem by scenarios representing randomness in the problem data. The design of these algorithms depend on where the uncertainty appears (right-hand-side, recourse matrix and/or technology matrix) and where the continuous and discrete decision variables are (first-stage and/or secondstage). In addition we provide computational evidence that, similar to other classes of stochastic programming problems, decomposition methods can provide desirable theoretical properties (such as finite convergence) as well as enhanced computational performance when compared to solving a deterministic equivalent formulation using an advanced commercial MIP solver.

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“…Where stochastic optimization [123] focuses on optimizing the expected objective value, robust optimization aims to find a solution that optimizes the worst case considered (to be specified below). In this contribution, we promote Assuming w.l.o.g.…”

Section: Robust Optimization and Network Designmentioning

confidence: 99%

Future research directions in design of reliable communication systems

et al. 2015

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In this position paper on reliable networks, we discuss new trends in the design of reliable communication systems. We focus on a wide range of research directions including protection against software failures as well as failures of communication systems equipment. In particular, we outline future research trends in software failure mitigation, reliability of wireless communications, robust optimization and network design, multilevel and multirealm network resilience, multiple criteria routing approaches in multilayer networks, resilience options of the fixed IP backbone network in the interplay with the optical layer survivability, reliability of cloud computing networks, and

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Stochastic Mixed‐Integer Programming Algorithms: Beyond Benders' Decomposition

Cited by 13 publications

References 41 publications

Planning With Multiple Transmission and Storage Investment Options Under Uncertainty: A Nested Decomposition Approach

Planning With Multiple Transmission and Storage Investment Options Under Uncertainty: A Nested Decomposition Approach

An Introduction to Two-Stage Stochastic Mixed-Integer Programming

Future research directions in design of reliable communication systems

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