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We consider linear combinatorial optimization problems under uncertain disruptions that increase the cost coefficients of the objective function. A decision maker, or planner, can invest resources to probe the components (i.e., the coefficients) in order to learn their disruption status. In the proposed probing optimization problem, the planner, knowing just the disruptions’ probabilities, selects which components to probe subject to a probing budget in a first decision stage. Then, the uncertainty realizes, and the planner observes the disruption status of the probed components, after which the planner solves the combinatorial problem in the second stage. In contrast to standard two-stage stochastic optimization, the planner does not have access to the full uncertainty realization in the second stage. Consequently, the planner cannot directly optimize the second-stage objective function, which is given by the actual cost after disruptions, and the decisions have to be made based on an estimate of the cost. By assuming that the estimate is given by the conditional expected cost given the information revealed by probing, we reformulate the probing optimization problem as a bilevel problem with multiple followers and propose an exact algorithm based on a value function reformulation and three heuristic algorithms. We derive theoretical results that bound the value of information and the price of not having full information and a bound on the required probing budget that attains the same performance as full information. Our extensive computational experiments suggest that probing a fraction of the components is sufficient to yield large improvements in the optimal value, that our exact algorithm is competitive for small- to medium-scale instances, and that the proposed heuristics find high-quality solutions in large-scale instances. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Air Force Office of Scientific Research [Grant FA9550-22-1-0236] and the Division of Civil, Mechanical and Manufacturing Innovation [Grant CMMI 2145553]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0629 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0629 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
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ROC++: Robust Optimization in C++
Over the last two decades, robust optimization has emerged as a popular means to address decision-making problems affected by uncertainty. This includes single-stage and multi-stage problems involving real-valued and/or binary decisions and affected by exogenous (decision-independent) and/or endogenous (decision-dependent) uncertain parameters. Robust optimization techniques rely on duality theory potentially augmented with approximations to transform a (semi-)infinite optimization problem to a finite program, the robust counterpart. Whereas writing down the model for a robust optimization problem is usually a simple task, obtaining the robust counterpart requires expertise. To date, very few solutions are available that can facilitate the modeling and solution of such problems. This has been a major impediment to their being put to practical use. In this paper, we propose ROC++, an open-source C++ based platform for automatic robust optimization, applicable to a wide array of single-stage and multi-stage robust problems with both exogenous and endogenous uncertain parameters, that is easy to both use and extend. It also applies to certain classes of stochastic programs involving continuously distributed uncertain parameters and endogenous uncertainty. Our platform naturally extends existing off-the-shelf deterministic optimization platforms and offers ROPy, a Python interface in the form of a callable library, and the ROB file format for storing and sharing robust problems. We showcase the modeling power of ROC++ on several decision-making problems of practical interest. Our platform can help streamline the modeling and solution of stochastic and robust optimization problems for both researchers and practitioners. It comes with detailed documentation to facilitate its use and expansion. The latest version of ROC++ can be downloaded from https://sites.google.com/usc.edu/robust-opt-cpp/ . Summary of Contribution: The paper “ROC++: Robust Optimization in C++” proposes a new open-source C++ based platform for modeling, automatically reformulating, and solving robust optimization problems. ROC++ can address both single-stage and multi-stage problems involving exogenous and/or endogenous uncertain parameters and real- and/or binary-valued adaptive variables. The ROC++ modeling language is similar to the one provided for the deterministic case by state-of-the-art deterministic optimization solvers. ROC++ comes with detailed documentation to facilitate its use and expansion. It also offers ROPy, a Python interface in the form of a callable library. The latest version of ROC++ can be downloaded from https://sites.google.com/usc.edu/robust-opt-cpp/ . History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: This material is based upon work supported by the National Science Foundation under Grant No. 1763108. This support is gratefully acknowledged. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1209 ) or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at ( https://dx.doi.org/10.5281/zenodo.6360996 ).
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- Award ID(s):
- 1763108
- PAR ID:
- 10433804
- Date Published:
- Journal Name:
- INFORMS Journal on Computing
- Volume:
- 34
- Issue:
- 6
- ISSN:
- 1091-9856
- Page Range / eLocation ID:
- 2873 to 2888
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/ijoc.2022.1209
