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mixed-integer linear optimization for cardinality-constrained random forests

optimization LETTERS 2025年 1-19页

作者： Burgard, Jan Pablo Pinheiro, Maria Eduarda Schmidt, Martin Trier Univ Dept Econ & Social Stat Univ Sring 15 D-54296 Trier Germany Trier Univ Dept Math Univ Ring 15 D-54296 Trier Germany

Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classify a new given point. In some scenarios, however, labels are only accessible for a proper subset of the given points. Moreover, this subset can be non-representative, e.g., due to collection bias. Semi-supervised learning considers the setting of labeled and unlabeled data and often improves the reliability of the results. In addition, it can be possible to obtain additional information about class sizes from undisclosed sources. We propose a mixed-integer linear optimization model for computing a semi-supervised random forest that covers the setting of labeled and unlabeled data points as well as the overall number of points in each class for a binary classification. Since the solution time rapidly grows as the number of variables increases, we present some problem-tailored preprocessing techniques and an intuitive branching rule. Our numerical results show that our approach leads to better accuracy and a better Matthews correlation coefficient for biased samples compared to random forests by majority vote, even if only a few labeled points are available.

关键词： Random forests Semi-supervised learning mixed-integer linear optimization Preprocessing Cardinality constraints

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Discovery of biomarker combinations that predict periodontal health or disease with high accuracy from GCF samples based on high-throughput proteomic analysis and mixed-integer linear optimization

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JOURNAL OF CLINICAL PERIODONTOLOGY 2013年第2期40卷 131-139页

作者： Baliban, Richard C. Sakellari, Dimitra Li, Zukui Guzman, Yannis A. Garcia, Benjamin A. Floudas, Christodoulos A. Princeton Univ Dept Chem & Biol Engn Princeton NJ 08544 USA Aristotle Univ Thessaloniki Dept Prevent Dent Periodontol & Implant Biol GR-54006 Thessaloniki Greece Princeton Univ Dept Mol Biol Princeton NJ 08544 USA

Aim To identify optimal combination(s) of proteomic based biomarkers in gingival crevicular fluid (GCF) samples from chronic periodontitis (CP) and periodontally healthy individuals and validate the predictions through known and blind test sets. Materials and Methods GCF samples were collected from 96 CP and periodontally healthy subjects and analysed using high-performance liquid chromatography, tandem mass spectrometry and the PILOT_PROTEIN algorithm. A mixed-integer linear optimization (MILP) model was then developed to identify the optimal combination of biomarkers which could clearly distinguish a blind subject sample as healthy or diseased. Results A thorough cross-validation of the MILP model capability was performed on a training set of 55 samples and greater than 99% accuracy was consistently achieved when annotating the testing set samples as healthy or diseased. The model was then trained on all 55 samples and tested on two different blind test sets, and using an optimal combination of 7 human proteins and 3 bacterial proteins, the model was able to correctly predict 40 out of 41 healthy and diseased samples. Conclusions The proposed large-scale proteomic analysis and MILP model led to the identification of novel combinations of biomarkers for consistent diagnosis of periodontal status with greater than 95% predictive accuracy.

关键词： biomarkers gingival crevicular fluid mixed-integer linear optimization periodontitis tandem mass spectrometry

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Design of closed-loop manufacturing-remanufacturing system network considering uncertain defect and waste rate: Scenario-based chance-constrained programming

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 259卷

作者： Wang, Gaolong Wang, Yue Li, Xinchao Lu, Shan Liaoning Petrochem Univ Sch Informat & Control Engn Fushun 113001 Peoples R China Shenzhen Polytech Univ Inst Intelligence Sci & Engn Shenzhen 518055 Peoples R China

To facilitate sustainability by extending the life-cycle and residual value of production materials, a collaborate scheduling scheme for closed-loop manufacturing system with disturbance uncertainty is studied. Based on the features of the closed-loop manufacturing system under multi-product and multi-period scenarios, a mixedinteger linear optimization model is developed, where manufacturing and remanufacturing units are coordinated by recycling the production materials from work-in-process and final products. Based on this, a novel closed-loop manufacturing-remanufacturing scheduling framework is proposed. Additionally, in response to variations in product quality and processing capabilities, a scenario-based chance-constrained programming is introduced to address potential sources of uncertainty. Subsequently, a sequential optimization method is devised to reduce computational complexity. Finally, an industrial case from the electronic factory is investigated to demonstrate its applicability by implementing the proposed approach with comparison to several other strategies.

关键词： Closed-loop manufacturing-remanufacturing system mixed-integer linear optimization Scenario-based chance-constrained programming

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On the relation between affinely adjustable robust linear complementarity and mixed-integer linear feasibility problems

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optimization LETTERS 2024年第5期18卷 1303-1311页

作者： Biefel, Christian Schmidt, Martin Trier Univ Dept Math Univ Ring 15 D-54296 Trier Germany

We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (SIAM J Optim 32:152-172, 2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an adjustable robust solution of a given linear complementarity problem is equivalent to solving a properly chosen mixed-integer linear feasibility problem.

关键词： linear complementarity problems Adjustable robustness Robust optimization mixed-integer linear optimization

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Robust stabilization of polytopic systems via fast and reliable neural network-based approximations

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INTERNATIONAL JOURNAL OF ROBUST AND NONlinear CONTROL 2024年第9期34卷 6180-6201页

作者： Fabiani, Filippo Goulart, Paul J. IMT Sch Adv Studies Lucca Lucca Italy Univ Oxford Dept Engn Sci Oxford England IMT Sch Adv Studies Lucca Piazza S Francesco 19 I-55100 Lucca Italy

We consider the design of fast and reliable neural network-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a (minimal) selection policy. Building upon recent approaches for the design of reliable control surrogates with guaranteed structural properties, we develop a systematic procedure to certify the closed-loop stability and performance of a linear uncertain system when a trained rectified linear unit (ReLU)-based approximation replaces such traditional controllers. First, we provide a sufficient condition, which involves the worst-case approximation error between ReLU-based and traditional controller-based state-to-input mappings, ensuring that the system is ultimately bounded within a set with adjustable size and convergence rate. Then, we develop an offline, mixed-integer optimization-based method that allows us to compute that quantity exactly.

关键词： mixed-integer linear optimization neural networks robust control uncertain systems

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Minimizing delays of patient transports with incomplete information: A modeling approach based on the vehicle routing problem

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OR SPECTRUM 2024年 1-40页

作者： Adelhuette, Dennis Braun, Kristin Liers, Frauke Tschuppik, Sebastian Friedrich Alexander Univ Erlangen Nurnberg Dept Data Sci Cauerstr 11 D-91058 Erlangen Germany Fraunhofer Inst Integrated Circuits IIS Nordostpk 84 D-90411 Nurnberg Germany

We investigate a challenging task in ambulatory care, the minimizing of delays of patient transports. In practice, a limited number of vehicles is available for non-rescue transports. Furthermore, the dispatcher rarely has access to complete information when establishing a transport plan for dispatching the vehicles. If additional transport is requested on demand then schedules need to be updated, which can lead to long delays. We model the scheduling of patient transports as a vehicle routing problem with general time windows and solve it as a mixed-integer linear problem that is modified whenever additional transport information becomes available. We propose a modeling approach that is designed to determine fair and stable plans. Furthermore, we show that the model can easily be modified when transports need to satisfy additional requirements, e.g., during pandemics, exemplarily the Covid-19 pandemic. To show the applicability and efficiency of our modeling approach, we conduct a numerical study using historical data from the region of Middle Franconia. The results reveal and show that, by applying mathematical optimization-or, to be more precise by solving mixed-integer linear problem formulations-one can significantly decrease delays and have considerable potential for optimized patient transports.

关键词： OR in health services Vehicle routing Heuristics mixed-integer linear optimization Patient transport

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Optimizing design and dispatch of a renewable energy system with combined heat and power

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optimization AND ENGINEERING 2022年第3期23卷 1-31页

作者： Hirwa, Jusse Ogunmodede, Oluwaseun Zolan, Alexander Newman, Alexandra M. Colorado Sch Mines 1500 Illinois St Golden CO 80401 USA Natl Renewable Energy Lab Thermal Energy Syst Grp 15013 Denver West Pkwy Golden CO 80401 USA

We embellish a mixed-integer program that prescribes a set of renewable energy, conventional generation, and storage technologies to procure, along with a corresponding dispatch strategy. Specifically, we add combined heat and power to this set. The model minimizes fixed and operational costs less incentives for the use of various technologies, subject to a series of component interoperability and system-wide constraints. The resulting mixed-integer linear program contains hundreds of thousands of variables and constraints. We demonstrate how to efficiently formulate and solve the corresponding instances such that we produce near-optimal solutions in minutes. A previous rendition of the model required hours of solution time for the same instances.

关键词： mixed-integer linear optimization Renewable energy Combined heat and power systems Efficient formulations

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Pseudo-optimal five-level DCC modulation based on machine learning

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年 158卷

作者： Montero-Robina, Pablo Gordillo, Francisco Gomez-Estern, Fabio Cuesta, Federico Autel Iberia SL Barcelona Spain Univ Seville Escuela Tecn Super Ingn Seville Spain Univ Loyola Andalucia Escuela Tecn Super Ingn Seville Spain

This paper presents a method for the control design of five-level DCC converters based on mixed-integer optimization and machine learning. The resulting controller is computationally simple and can be easily implemented on low-resource control hardware using simple nested "if-else"statements. The optimization problem is recalled from previous work by modifying the cost function to further enhance the dynamic performance. Additionally, and in contrast to previous works, the online implementation accomplished in this paper allows the system to cover a wider range of operating points. For this, the optimization problem is solved offline for several operating conditions, and the results are gathered into a dataset to train classification and regression trees (CARTs), which are later used online. Due to the generalization capability of the CARTs, a more flexible and less resource-intensive implementation is achieved which is capable of operating at points outside the ones considered in the training dataset. The resulting control strategy is compared in simulation and experiments with several alternative approaches found in the literature. This approach can be extended to other power converter topologies, allowing the implementation of optimized modulations.

关键词： Classification and regression trees Diode-clamped converter mixed-integer linear optimization Multilevel converter

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Mathematical optimization in classification and regression trees

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TOP 2021年第1期29卷 5-33页

作者： Carrizosa, Emilio Molero-Rio, Cristina Romero Morales, Dolores Univ Seville Inst Matemat Seville Spain Copenhagen Business Sch Dept Econ Frederiksberg Denmark

Classification and regression trees, as well as their variants, are off-the-shelf methods in Machine Learning. In this paper, we review recent contributions within the Continuous optimization and the mixed-integer linear optimization paradigms to develop novel formulations in this research area. We compare those in terms of the nature of the decision variables and the constraints required, as well as the optimization algorithms proposed. We illustrate how these powerful formulations enhance the flexibility of tree models, being better suited to incorporate desirable properties such as cost-sensitivity, explainability, and fairness, and to deal with complex data, such as functional data.

关键词： Classification and regression trees Tree ensembles mixed-integer linear optimization Continuous nonlinear optimization Sparsity Explainability

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Scheduling of a Constellation of Satellites: Creating a mixed-integer linear Model

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JOURNAL OF optimization THEORY AND APPLICATIONS 2021年第2-3期191卷 846-873页

作者： Monmousseau, Philippe Univ Toulouse ENAC F-31055 Toulouse France

The purpose of this paper is to provide a new scheduling model of a large constellation of imaging satellites that does not use a heuristic solving method. The objective is to create a mixed-integer linear model that would be competitive in speed and in its closeness to reality against a current model using simulated annealing, while trying to improve both models. Each satellite has the choice between a number of possible events, each event having a utility and a cost, and the chosen schedule must take into account numerous time-related constraints. The main difficulties appeared in modeling realistically a battery level and in handling infeasible configurations due to inaccurate parameters. The obtained linear model has enabled a better understanding of the performance of the simulated annealing solver, and could also be adapted to different real-world scheduling problems.

关键词： Scheduling Constellation of satellites mixed-integer linear optimization Simulated annealing linear battery propagation model

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