Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse

Bodur, Merve; Dash, Sanjeeb; Günlük, Oktay; Luedtke, James

doi:10.1287/ijoc.2016.0717

Cited by 57 publications

(57 citation statements)

References 26 publications

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“…Various methods and techniques have been developed to solve a stochastic programming problem. For a two-stage stochastic linear program, Benders decomposition [39][40][41] and progressive hedging algorithm (PHA) [42][43][44] are two major decomposition methods. Benders decomposition is a vertical decomposition approach that decomposes the problem into a master problem that consists of the first-stage decisions and the subproblems that consist of second-stage decisions of all scenarios.…”

Section: Stochastic Programmingmentioning

confidence: 99%

Condition-based maintenance for multi-component systems: Modeling, structural properties, and algorithms

Zhu

Xiang

2020

IISE Transactions

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Condition-based maintenance (CBM) is an effective maintenance strategy to improve system performance while lowering operating and maintenance costs. However, most research on CBM focuses on single-component systems. Limited research has considered CBM for multi-component systems. Multi-component condition-based maintenance, which joins the components' stochastic degradation processes and the combinatorial maintenance grouping problem, remains an open issue in the literature. In this paper, we study the CBM optimization problem for multi-component systems. We first develop a multi-stage stochastic integer model with the objective of minimizing the total maintenance cost over a finite planning horizon. We then investigate the structural properties of a two-stage model. Based on the structural properties, two efficient algorithms are designed to solve the two-stage model. Algorithm 1 solves the problem to its optimality and Algorithm 2 heuristically searches for high-quality solutions based on Algorithm 1. Our computational studies show that Algorithm 1 obtains optimal solutions to the majority of test cases in a reasonable amount of time and Algorithm 2 can find high-quality solutions quickly.The multi-stage problem is solved using a rolling horizon approach based on the algorithms for the two-stage problem. KEYWORDS Condition-based maintenance, multi-component systems, multi-stage stochastic integer programming, endogenous uncertainty arXiv:1907.01031v1 [math.OC] 1 Jul 2019

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Section: Stochastic Programmingmentioning

confidence: 99%

Condition-based maintenance for multi-component systems: Modeling, structural properties, and algorithms

Zhu

Xiang

2020

IISE Transactions

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“…We tested its efficacy on three distinct classes of problems from literature, namely the capacitated facility location problem (CAP) from Bodur et al. (), the dynamic capacity allocation problem (DCAP) available in Ahmed and Garcia (), and the server location under uncertainty problem (SSLP) first introduced in Ntaimo and Sen (). To provide a more solid base of comparison, 50 random instances of two problems from each class were generated.…”

Section: Experimental Settingmentioning

confidence: 99%

“…We selected problems coded as 101 and 111 in Bodur et al. (), considering random samples of 100 scenarios from a list of 5000 scenarios available to generate instances.…”

Section: Experimental Settingmentioning

confidence: 99%

Combining penalty‐based and Gauss–Seidel methods for solving stochastic mixed‐integer problems

Oliveira

Christiansen

Dandurand

et al. 2018

Int Trans Operational Res

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In this paper, we propose a novel decomposition approach (named PBGS) for stochastic mixed‐integer programming (SMIP) problems, which is inspired by the combination of penalty‐based Lagrangian and block Gauss–Seidel methods. The PBGS method is developed such that the inherent decomposable structure that SMIP problems present can be exploited in a computationally efficient manner. The performance of the proposed method is compared with the progressive hedging (PH) method, which also can be viewed as a Lagrangian‐based method for obtaining solutions for SMIP problems. Numerical experiments performed using instances from the literature illustrate the efficiency of the proposed method in terms of computational performance and solution quality.

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“…As mentioned earlier, such implementation has successfully been used instead of the old-fashioned cutting plane implementation of Benders decomposition for some instances of two-stage stochastic integer programs in some works such as in [21]. In a classic implementation of Benders decomposition for two-stage stochastic mixed integer programs with continuous recourse, at each iteration the relaxed master problem which is a mixed-integer program is solved to optimality.…”

Section: Branch-and-cut Algorithmmentioning

confidence: 99%

“…We propose a Benders decomposition method implemented within a branch-and-cut (B&C) framework to solve this problem. Promising results of implementation of strengthened Benders cuts within a B&C framework for two-stage stochastic programs with continuous recourse have recently been reported in [21]. In this paper, we show our computationally comprehensive numerical experiments and implementation details on different IEEE test cases.…”

Section: Introductionmentioning

confidence: 99%

Large-scale stochastic power grid islanding operations by line switching and controlled load shedding

2016

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Recently, there has been an increasing concern regarding the security and reliability of power systems due to the onerous consequences of cascading failures. Among many emergency control operations, controlled power grid islanding is a last resort yet powerful method to prevent large-scale blackouts. Islanding operations split the power grid into self-sufficient operational subnetworks and avoid cascading failures by isolating the failed elements of the power system into a non-operational island. In this paper, we consider a two-stage stochastic mixed-integer program to seek the optimal islanding operations under severe contingency states. Line switching and controlled load shedding are the main tools for the islanding operations and load shedding is considered as a measurement to gauge system's inability to respond to disruption. The number of possible extreme contingencies grows exponentially as the size of the grid increases, and this results in a large-scale mixed-integer program, which is a computationally challenging problem to solve. We present an efficient decomposition method to solve this problem for large-scale power systems.

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Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse

Cited by 57 publications

References 26 publications

Condition-based maintenance for multi-component systems: Modeling, structural properties, and algorithms

Condition-based maintenance for multi-component systems: Modeling, structural properties, and algorithms

Combining penalty‐based and Gauss–Seidel methods for solving stochastic mixed‐integer problems

Large-scale stochastic power grid islanding operations by line switching and controlled load shedding

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