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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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A mixed-integer linear optimization Model for Local Energy System Planning Based on Simplex and Branch-and-Bound Algorithms

A Mixed-Integer Linear Optimization Model for Local Energy S...

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International Conference on Life System Modeling and Simulation / International Conference on Intelligent Computing for Sustainable Energy and Environment (LSMS-ICSEE)

作者： Ren, Hongbo Zhou, Weisheng Gao, Weijun Wu, Qiong Ritsumeikan Univ Ritsumeikan Global Innovat Res Org Kyoto 6038577 Japan Ritsumeikan Univ Coll Policy Sci Kyoto 6038577 Japan Univ Kitakyushu Fac Environm Engn Kitakyushu Fukuoka 8080135 Japan

ISBN: (纸本)9783642156205

A mixed-integer linear optimization model is developed to support the decision making for the sustainable use of energy in the local area. It details exploitation of primary energy sources, electrical and thermal generation, end-use sectors and emissions. The model covers both the energy demand and energy supply sides, and can provide valuable information both on the technical options, and on the possible policy measures. By aiming to realize a low-carbon energy system, the proposed optimization process provides feasible generation settlements between utility grid and distributed generations, as well as optimal diffusion of energy efficiency technologies. Moreover, the mathematical methods for solving the developed model are discussed. The focus is paid on the general solution method for mixed-integer linear optimization model including simplex algorithm and branch-and-bound algorithm. By using the suggested solution methods, the local energy system optimization problem is expected to be resolved in a reasonable time with enough precision.

关键词： mixed-integer linear optimization local energy system low-carbon society simplex algorithm branch-and-bound algorithm

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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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Maximum savings approach for location and sizing of capacitors in distribution systems

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ELECTRIC POWER SYSTEMS RESEARCH 2008年第7期78卷 1192-1203页

作者： Khodr, H. M. Olsina, F. G. De Oliveira-De Jesus, P. M. Yusta, J. M. Univ Zaragoza Dept Elect Engn E-50018 Zaragoza Spain Univ Simon Bolivar Dept Energy Convers & Delivery INESC Porto Caracas Venezuela Univ Porto Fac Engn Dept Elect & Comp Engn Oporto Portugal

This paper proposes a computationally efficient methodology for the optimal location and sizing of static and switched shunt capacitors in radial distribution systems. The problem is formulated as the maximization of the savings produced by the reduction in energy losses and the avoided costs due to investment deferral in the expansion of the network. The proposed method selects the nodes to be compensated, as well as the optimal capacitor ratings and their operational characteristics, i.e. fixed or switched. After an appropriate linearization, the optimization problem was formulated as a mixed-integer linear problem, suitable for being solved by means of a widespread commercial package. Results of the proposed optimizing method are compared with another recent methodology reported in the literature using two test cases: a 15-bus and a 33-bus distribution network. For the both case's tested, the proposed methodology delivers better solutions indicated by higher loss savings, which are achieved with lower amounts of capacitive compensation. To calculate the energy savings and the deferral investment cost exactly, a load flow for radial distribution network is executed before and after the compensation. The proposed method has also been applied for compensating to an actual radial distribution network served by AES-Venezuela in the metropolitan area of Caracas. A convergence time of about 4 s after 22,298 iterations demonstrates the ability of the proposed methodology for efficiently handling compensation problems. (c) 2007 Elsevier B.V. All rights reserved.

关键词： capacitors distribution systems mixed-integer linear optimization

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Robust optimization of Dose-Volume Metrics for Prostate HDR-Brachytherapy Incorporating Target and OAR Volume Delineation Uncertainties

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INFORMS JOURNAL ON COMPUTING 2019年第1期31卷 100-114页

作者： Balvert, Marleen den Hertog, Dick Hoffmann, Aswin L. Tilburg Univ Ctr Econ Res CentER Dept Econometr & Operat Res NL-5000 LE Tilburg Netherlands Ctr Wiskunde Informat NL-1098 XG Amsterdam Netherlands Univ Utrecht Theoret Biol & Bioinformat NL-3508 TC Utrecht Netherlands Helmholtz Zentrum Dresden Rossendorf Inst Radiooncol Dresden Germany Tech Univ Dresden Univ Hosp Carl Gustav Carus Dept Radiotherapy & Radiooncol Dresden Germany Maastricht Univ Med Ctr Dept Radiat Oncol MAASTRO GROW Sch Oncol & Dev Biol Maastricht Netherlands

In radiation therapy planning, uncertainties in the definition of the target volume yield a risk of underdosing the tumor. The traditional corrective action in the context of external beam radiotherapy (EBRT) expands the clinical target volume (CTV) with an isotropic margin to obtain the planning target volume (PTV). However, the EBRT-based PTV concept is not directly applicable to brachytherapy (BT) since it can lead to undesirable dose escalation. Here, we present a treatment plan optimization model that uses worst-case robust optimization to account for delineation uncertainties in interstitial high-dose-rate BT of the prostate. A scenario-based method was developed that handles uncertainties in index sets. Heuristics were included to reduce the calculation times to acceptable proportions. The approach was extended to account for delineation uncertainties of an organ at risk (OAR) as well. The method was applied on data from prostate cancer patients and evaluated in terms of commonly used dosimetric performance criteria for the CTV and relevant OARs. The robust optimization approach was compared against the classical PTV margin concept and against a scenario-based CTV margin approach. The results show that the scenario-based margin and the robust optimization method are capable of reducing the risk of underdosage to the tumor. As expected, the scenario-based CTV margin approach leads to dose escalation within the target, whereas this can be prevented with the robust model. For cases where rectum sparing was a binding restriction, including uncertainties in rectum delineation in the planning model led to a reduced risk of a rectum overdose, and in some cases, to reduced target coverage.

关键词： brachytherapy delineation uncertainties mixed-integer linear optimization robust optimization tratment planning

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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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Energy supply modelling of a low-CO₂ emitting energy system: Case study of a Danish municipality

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APPLIED ENERGY 2017年 195卷 922-941页

作者： Sveinbjornsson, Dadi Ben Amer-Allam, Sara Hansen, Anders Bavnhoj Algren, Loui Pedersen, Allan Schroder Tech Univ Denmark Dept Energy Convers & Storage Frederiksborgvej 399 DK-4000 Roskilde Denmark Tech Univ Denmark Dept Management Engn Prod TorvetBldg 426 DK-2800 Lyngby Denmark Energinet Dk Tonne Kjaersvej 65 DK-7000 Fredericia Denmark

Municipal activities play an important role in national and global CO2-emission reduction efforts, with Nordic countries at the forefront thanks to their energy planning tradition and high penetration of renewable energy sources. In this work, we present a case study of the Danish municipality of Sonderborg, whose aim is to reach zero net CO2 emissions by 2029. Sonderborg has an official strategic plan towards 2029, which we compared with four alternative scenarios to investigate how the municipality could approach its target in the most energy-efficient and cost-effective way while simultaneously keeping biomass and waste consumption close to the limits of the locally available residual resources. We modelled all sectors of the energy system on the municipal scale, applying a broad range of energy conversion technologies, including advanced biomass conversion technologies and reversible electrolysis. We constructed five scenarios, each representing a different energy mix for Sonderborg's energy system in 2029. We modelled these scenarios using the mixed-integer linear optimization tool Sifre. We compared the results for the five scenarios using four indicators: annual total system cost, total energy system efficiency, annual net system CO2 emissions and total annual biomass consumption. The results show that scenarios with a high degree of electrification perform better on the selected indicators than scenarios with a high degree of biomass utilization. Moreover, the incorporation of advanced conversion technologies such as electrolysis, fuel cells and methanol production further reduces both the total system cost and net CO2 of the highly electrified energy system. Our sensitivity analysis demonstrates that scenarios with a low biomass consumption and a high degree of electrification are less dependent on changes in energy prices. We conclude that in order to achieve their CO2 emission goals in the most energy-efficient, cost-effective and sustainable way, municip

关键词： Energy system modelling Urban energy scenarios Renewable energy mixed-integer linear optimization Energy conversion Electrolysis

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MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems

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COMPUTATIONAL optimization AND APPLICATIONS 2018年第1期70卷 267-294页

作者： Gugat, Martin Leugering, Gunter Martin, Alexander Schmidt, Martin Sirvent, Mathias Wintergerst, David Friedrich Alexander Univ Erlangen Nurnberg FAU Lehrstuhl Angew Math 2 Cauerstr 11 D-91058 Erlangen Germany Friedrich Alexander Univ Erlangen Nurnberg FAU Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany

We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.

关键词： mixed-integer optimal control Instantaneous control Partial differential equations on graphs Gas networks mixed-integer linear optimization

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PENALTY ALTERNATING DIRECTION METHODS FOR mixed-integer optimization: A NEW VIEW ON FEASIBILITY PUMPS

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SIAM JOURNAL ON optimization 2017年第3期27卷 1611-1636页

作者： Geissler, Bjorn Morsi, Antonio Schewe, Lars Schmid, Martin Friedrich Alexander Univ Erlangen Nurnberg FAU Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany

Feasibility pumps are highly effective primal heuristics for mixed-integer linear and nonlinear optimization. However, despite their success in practice there are only a few works considering their theoretical properties. We show that feasibility pumps can be seen as alternating direction methods applied to special reformulations of the original problem, inheriting the convergence theory of these methods. Moreover, we propose a novel penalty framework that encompasses this alternating direction method, which allows us to refrain from random perturbations that are applied in standard versions of feasibility pumps in case of failure. We present a convergence theory for the new penalty based alternating direction method and compare the new variant of the feasibility pump with existing versions in an extensive numerical study for mixed-integer linear and nonlinear problems.

关键词： mixed-integer nonlinear optimization mixed-integer linear optimization feasibility pump alternating direction methods penalty methods

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