2-stage robust MILP with continuous recourse variables

Billionnet, Alain; Costa, Marie-Christine; Poirion, Pierre‐Louis

doi:10.1016/j.dam.2014.01.017

Cited by 30 publications

(24 citation statements)

References 13 publications

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“…Another popular approach for optimization under uncertainty is two-stage ARO, which hedges against the worst-case uncertainty realization within an uncertainty set. A general twostage ARO problem in its compact form is given as follows [59].…”

Section: Stochastic Robust Optimizationmentioning

confidence: 99%

Data-driven stochastic robust optimization: General computational framework and algorithm leveraging machine learning for optimization under uncertainty in the big data era

Ning

You

2018

Computers & Chemical Engineering

114

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A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various conditions, which are encoded by class labels.Machine learning methods including Dirichlet process mixture model and maximum likelihood estimation are employed for uncertainty modeling. A DDSRO framework is further proposed based on the data-driven uncertainty model through a bi-level optimization structure. The outer optimization problem follows a two-stage stochastic programming approach to optimize the expected objective across different data classes; adaptive robust optimization is nested as the inner problem to ensure the robustness of the solution while maintaining computational tractability. A decomposition-based algorithm is further developed to solve the resulting multi-level optimization problem efficiently. Case studies on process network design and planning are presented to demonstrate the applicability of the proposed framework and algorithm.

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Section: Stochastic Robust Optimizationmentioning

confidence: 99%

Data-driven stochastic robust optimization: General computational framework and algorithm leveraging machine learning for optimization under uncertainty in the big data era

Ning

You

2018

Computers & Chemical Engineering

114

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“…Constraints (22) and (23) ensure that the stock levels are within their limits at the end of each visit. Constrains (24) impose a lower bound on the inventory level at time T for consumption ports, while constrains (25) impose an upper bound on the inventory level at time T for production ports.…”

Section: Inventory Constraintsmentioning

confidence: 99%

“…The model introduced here is an adjustable robust program [22,14,30,49] which features two levels of decisions: rst-stage variables must be xed before the uncertainty is revealed, while adjustable variables can react to account for the uncertainty. Such a concept has also been known as recoverable robustness [38].…”

Section: Mathematical Model For the Robust Formulationmentioning

confidence: 99%

Robust Optimization for a Maritime Inventory Routing Problem

Agra

Christiansen

Hvattum

et al. 2018

Transportation Science

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We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous eet and multiple production and consumption ports with limited storage capacity.Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely inuenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set.In the recourse model, the routing, the order of port visits, and the quantities to load and unload are xed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances.

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“…From the above motivating example, it can be observed that the data‐driven uncertainty set tends to be tighter than other uncertainty sets when uncertainty data are corrupted. Therefore, the DDANRO approach would generates a less conservative robust solution compared with ARO with Gamma‐uncertainty …”

Section: Data‐driven Adaptive Nested Robust Optimization For High‐dimmentioning

confidence: 99%

“…For the above problem, the optimal value m 6j ð Þ has been proven to be a binary variable. 58 Therefore, we can use Glover's linearization to tackle the bilinear term m 6j ð Þ u t by the substitution g…”

Section: The Tailored Column-and-constraint Generation Algorithmmentioning

confidence: 99%

Data‐driven adaptive nested robust optimization: General modeling framework and efficient computational algorithm for decision making under uncertainty

2017

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A novel data‐driven adaptive robust optimization framework that leverages big data in process industries is proposed. A Bayesian nonparametric model—the Dirichlet process mixture model—is adopted and combined with a variational inference algorithm to extract the information embedded within uncertainty data. Further a data‐driven approach for defining uncertainty set is proposed. This machine‐learning model is seamlessly integrated with adaptive robust optimization approach through a novel four‐level optimization framework. This framework explicitly accounts for the correlation, asymmetry and multimode of uncertainty data, so it generates less conservative solutions. Additionally, the proposed framework is robust not only to parameter variations, but also to anomalous measurements. Because the resulting multilevel optimization problem cannot be solved directly by any off‐the‐shelf solvers, an efficient column‐and‐constraint generation algorithm is proposed to address the computational challenge. Two industrial applications on batch process scheduling and on process network planning are presented to demonstrate the advantages of the proposed modeling framework and effectiveness of the solution algorithm. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3790–3817, 2017

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2-stage robust MILP with continuous recourse variables

Cited by 30 publications

References 13 publications

Data-driven stochastic robust optimization: General computational framework and algorithm leveraging machine learning for optimization under uncertainty in the big data era

Data-driven stochastic robust optimization: General computational framework and algorithm leveraging machine learning for optimization under uncertainty in the big data era

Robust Optimization for a Maritime Inventory Routing Problem

Data‐driven adaptive nested robust optimization: General modeling framework and efficient computational algorithm for decision making under uncertainty

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