<i>K</i>-Adaptability in Two-Stage Robust Binary Programming

Hanasusanto, Grani A.; Kühn, Daniel; Wiesemann, Wolfram

doi:10.1287/opre.2015.1392

Cited by 128 publications

(125 citation statements)

References 55 publications

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“…It is illustrative to consider the size of the adaptable formulation at each iteration for the methods proposed in this paper versus the approach in Hanasusanto et al (2014). Their approach uses O (KN ) binary variables and O (2 K KN ) continuous variables where K is the number of partitions (selected a priori), with fractionality-inducing "big-M" constraints.…”

Section: Capital Budgetingmentioning

confidence: 99%

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Multistage Robust Mixed-Integer Optimization with Adaptive Partitions

Bertsimas

Dunning

2016

Operations Research

101

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We present a new method for multistage adaptive mixed integer optimization (AMIO) problems that extends previous work on finite adaptability. The approach analyzes the optimal solution to a non-adaptive version of an AMIO problem to gain insight into which regions of the uncertainty set are restricting the objective function value. We use this information to construct partitions in the uncertainty set, leading to a finitely adaptable formulation of the AMIO problem. We repeat this process iteratively to further improve the objective until appropriate termination criteria are reached. We provide theoretical motivation for this method, and fully detail how to apply finite adaptability to multistage AMIO problems in a way that respects the natural nonanticipativity constraints. We provide lower and upper bounds on the solution quality that have implications for computational tractability. Finally we demonstrate in computational experiments that the method can provide substantial improvements over a non-adaptive solution and existing methods. In particular, we find that our method delivers high-quality solutions even as the problem scales in both number of time stages and in the number of decision variables.

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Section: Capital Budgetingmentioning

confidence: 99%

“…To compare our results with Hanasusanto et al (2014) we measured performance our method by the same metric: the improvement in objective relative to the solution with no adaptability, We add a new metric, gap, which estimates how far we are from the fully adaptive solution using the bound presented in Section 4.1,…”

Section: Capital Budgetingmentioning

confidence: 99%

Multistage Robust Mixed-Integer Optimization with Adaptive Partitions

Bertsimas

Dunning

2016

Operations Research

101

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“…For classical two-stage robust binary programs, it has been shown that the approximation provided by the Kadaptability formulation is tight whenever K exceeds the affine dimension of either the uncertainty set or the second-stage feasible region, see [6,Theorem 1]. We now show that this favorable approximation behavior generalizes to distributionally robust two-stage binary programs.…”

Section: The K-adaptability Problem With Objective Uncertaintymentioning

confidence: 55%

“…The assertion now follows if we replace the sets Ξ( ) with their inner approximations Ξ ( ), ∈ L, and reformulate the constraints as in [6,Theorem 5].…”

Section: B Omitted Proofsmentioning

confidence: 99%

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K-adaptability in two-stage distributionally robust binary programming

Hanasusanto

Kühn

Wiesemann

2016

Operations Research Letters

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We propose to approximate two-stage distributionally robust programs with binary recourse decisions by their associated K-adaptability problems, which pre-select K candidate secondstage policies here-and-now and implement the best of these policies once the uncertain parameters have been observed. We analyze the approximation quality and the computational complexity of the K-adaptability problem, and we derive explicit mixed-integer linear programming reformulations. We also provide efficient procedures for bounding the probabilities with which each of the K second-stage policies is selected.

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On the relation between flexibility analysis and robust optimization for linear systems

2016

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Flexibility analysis and robust optimization are two approaches to solving optimization problems under uncertainty that share some fundamental concepts, such as the use of polyhedral uncertainty sets and the worst-case approach to guarantee feasibility. The connection between these two approaches has not been sufficiently acknowledged and examined in the literature. In this context, the contributions of this work are fourfold: (1) a comparison between flexibility analysis and robust optimization from a historical perspective is presented; (2) for linear systems, new formulations for the three classical flexibility analysis problems-flexibility test, flexibility index, and design under uncertainty-based on duality theory and the affinely adjustable robust optimization (AARO) approach are proposed; (3) the AARO approach is shown to be generally more restrictive such that it may lead to overly conservative solutions; (4) numerical examples show the improved computational performance from the proposed formulations compared to the traditional flexibility analysis models.

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K-Adaptability in Two-Stage Robust Binary Programming

Cited by 128 publications

References 55 publications

Multistage Robust Mixed-Integer Optimization with Adaptive Partitions

Multistage Robust Mixed-Integer Optimization with Adaptive Partitions

K-adaptability in two-stage distributionally robust binary programming

On the relation between flexibility analysis and robust optimization for linear systems

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