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Piecewise polynomial interpolations and approximations of one-dimensional functions through mixed integer linear programming

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OPTIMIZATION METHODS & SOFTWARE 2009年第4-5期24卷 783-803页

作者： Natali, Joao M. Pinto, Jose M. Polytech Univ Othmer Jacobs Dept Chem & Biol Engn Brooklyn NY 11201 USA

Piecewise polynomial functions are extensively used to approximate general nonlinear functions or sets of data. In this work, we propose a mixed integer linear programming (MILP) framework for generating optimal piecewise polynomial approximations of varying degrees to nonlinear functions of a single variable. The nonlinear functions may be represented by discrete exact samplings or by data corrupted by noise. We studied two distinct approaches to the problem: (1) the generation of interpolating piecewise polynomial functions, in which the approximating function values in the extremes of each polynomial segment coincide with the original function values;and (2) a de facto approximation strategy in which the polynomial segments are free, except for the enforcement of continuity of the overall approximation. Our results from the implemented models show that the procedure is capable of efficiently approximating nonlinear functions and it has the added capability of allowing for the straightforward implementation of further constraints on solutions, such as the convexity of polynomial segments. Finally, the models for the generation of piecewise linear approximations and interpolations were applied for the linearization of mixed integer nonlinear programming (MINLP) models extracted from the MINLP library. These models were linearized by the reformulation of their nonlinearities as piecewise linear functions with varying numbers of segments, resulting in MILP models that were solved to optimality and the solutions from the linearized models were compared with global optimal solutions from the original problems.

关键词： mixed integer linear programming one-dimensional nonlinear functions piecewise linear interpolation piecewise polynomial approximation

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SPOOFING CYBER ATTACK DETECTION IN PROBE-BASED TRAFFIC MONITORING SYSTEMS USING mixed integer linear programming

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NETWORKS AND HETEROGENEOUS MEDIA 2013年第3期8卷 783-802页

作者： Canepa, Edward S. Bayen, Alexandre M. Claudel, Christian G. King Abdullah Univ Sci & Technol Dept Elect Engn Mecca 23955 Saudi Arabia Univ Calif Berkeley Berkeley CA 94720 USA

Traffic sensing systems rely more and more on user generated (insecure) data, which can pose a security risk whenever the data is used for traffic flow control. In this article, we propose a new formulation for detecting malicious data injection in traffic flow monitoring systems by using the underlying traffic flow model. The state of traffic is modeled by the Lighthill-Whitham- Richards traffic flow model, which is a first order scalar conservation law with concave flux function. Given a set of traffic flow data generated by multiple sensors of different types, we show that the constraints resulting from this partial differential equation are mixed integer linear inequalities for a specific decision variable. We use this fact to pose the problem of detecting spoofing cyber attacks in probe-based traffic flow information systems as mixed integer linear feasibility problem. The resulting framework can be used to detect spoofing attacks in real time, or to evaluate the worst-case effects of an attack offline. A numerical implementation is performed on a cyber attack scenario involving experimental data from the Mobile Century experiment and the Mobile Millennium system currently operational in Northern California.

关键词： mixed integer linear programming hyperbolic partial differential equations cybersecurity

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LO-constrained regression using mixed integer linear programming

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2017年 165卷 29-37页

作者： Willis, Mark J. von Stosch, Moritz Newcastle Univ Sch Chem Engn & Adv Mat Newcastle Upon Tyne NE1 7RU Tyne & Wear England

In this work, sparse regression using a penalized least absolute deviations objective function is considered. Regression model sparsity is promoted using a L-0 - pseudo norm penalty (the cardinality of the model parameter vector). Implemented using mixed integer linear programming (MILP) it is demonstrated that the use of the L-0 norm (without approximation) enables efficient and accurate solutions to sparse regression problems of practical size. For model development with a large number of potential model parameters (or features) methods to relax the MILP are also developed;using nonlinear function approximations to the L-0- norm, penalty terms are linearized and solved using sequential linear programming. Experimental results (using both simulated and real data) demonstrate that these algorithms are also computationally efficient producing accurate and parsimonious model structures. Applications considered are the development of a calibration model for prediction with Near Infrared (NIR) data and the development of a model for the prediction of chemical toxicity - a quantitative structure activity relationship (QSAR).

关键词： Sparse regression mixed integer linear programming

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Optimization of Vertical Formwork Layout Plans Using mixed integer linear programming

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INTERNATIONAL JOURNAL OF CIVIL ENGINEERING 2017年第2A期15卷 125-133页

作者： Biruk, Slawomir Jaskowski, Piotr Lublin Univ Technol 40 Nadbystrzycka St PL-20618 Lublin Poland

A formwork is a structure used to contain poured concrete and to mold it to the required dimensions. Different formwork systems provide a wide range of concrete construction solutions that can be chosen to suit the needs of a particular structure. The selection of panels and the design of the formwork layout for concrete structures, especially if the panels are to be reused many times to form different work zones, are one of the most complex tasks in formwork construction. It influences the quality of work, construction time, site safety and cost. The formwork costs account for a significant part of the total costs for concrete works. The problem of the selection and layout of reusable panel forms is solved mainly based on the intuitive judgment of experienced engineers in collaboration with the form system supplier. This study proposes a mixed integer linear programming modeling approach to support the formwork planning process. The problem consists in determining the number and sizes of the panels according to the geometry of the concrete elements to minimize the rental cost of wall shuttering in a building divided into work zones that are to be completed in sequence, reusing the chosen panels. The model can be solved using typical software dedicated to mixed integer linear programs. A simple example is used to illustrate the efficiency of the proposed approach, where the formwork rental cost is 7.31 % lower than the rental costs of panels and corners optimized without consideration of the reuse in consecutive zones.

关键词： Reinforced concrete works Formwork planning Cost minimization mixed integer linear programming

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Enhancing expansion of rooftop PV systems through mixed integer linear programming and Public Tender Procedures

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RENEWABLE ENERGY 2022年第0期187卷 347-361页

作者： Georgiou, Giorgos S. Rouvas, Constantinos Nathanael, Demetris Elect Author Cyprus Dept Nonregulated Act Strovolos Cyprus Cyprus Univ Technol Dept Elect Engn Comp Engn & Informat Limassol Cyprus Elect Author Cyprus Generat Unit Strovolos Cyprus Elect Author Cyprus Procurement Dept Strovolos Cyprus

Concerning the growth rate in Renewable Energy share, especially in the EU, it is fact that Rooftop PV systems have a significant role to play. Nevertheless, it is also accepted that with current policies, schemes and scientific methods, today's Renewable Energy growth rate is still far from the desired one. Based on that, this study proposes a novel integration of a mixed-integer linear programming based model in a Public Tender Procedure, which enables the bulk installation and thus, the rapid expansion of Rooftop PV systems, in a least-cost manner. The main objective and contribution of this paper is to provide an economic solution to interested Public Bodies for utilizing the rapid growth of rooftop PV systems through novel mechanisms and hence, to better achieve the desired Renewable Energy targets. To further highlight the capabilities of the proposed method, the results from a real-life project, showed that the bulk installation of PV systems, in 404 public schools with a total PV capacity of 4.8 MWp, can be realized at an optimum cost. The main achievements are: (i) high-level competition, due to the ability of the proposed model to select multiple PV Installers, (ii) a 35% lower project cost compared to the initial estimated budget and (iii) a significantly lower unit cost of about 0.7 million euro/MWp, compared to about 0.91 and 1.54 million euro/MWp obtained from other similar projects. Finally, the outcomes of the proposed MILP model are validated by those obtained from an exhaustive optimal solution search procedure. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Building integrated PV Novel renewable energy growth mechanisms mixed integer linear programming Public procurement

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Identifying differentially expressed pathways via a mixed integer linear programming model

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IET SYSTEMS BIOLOGY 2009年第6期3卷 475-486页

作者： Qiu, Y-Q. Zhang, S. Zhang, X. -S. Chen, L. Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Chinese Acad Sci Grad Univ Beijing 100049 Peoples R China Osaka Sangyo Univ Dept Elect Engn & Elect Osaka 5748530 Japan

The identification of genes and pathways involved in biological processes is a central problem in systems biology. Recent microarray technologies and other high-throughput experiments provide information which sheds light on this problem. In this article, the authors propose a new computational method to detect active pathways, or identify differentially expressed pathways via integration of gene expression and interactomic data in a sophisticated and efficient manner. Specifically, by using signal-to-noise ratio to measure the differentially expressed level of networks, this problem is formulated as a mixed integer linear programming problem (MILP). The results on yeast and human data demonstrate that the proposed method is more accurate and robust than existing approaches.

关键词： human data computational methods mixed integer linear programming systems biology Biological Process HAND2-AS1 gene

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Comparison of mixed integer linear programming models for the resource-constrained project scheduling problem with consumption and production of resources

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FLEXIBLE SERVICES AND MANUFACTURING JOURNAL 2013年第1-2期25卷 25-47页

作者： Kone, Oumar Artigues, Christian Lopez, Pierre Mongeau, Marcel Univ Abobo Lab Math & Informat UFR SFA Abidjan 02 Cote Ivoire LAAS CNRS F-31400 Toulouse France Univ Toulouse LAAS F-31400 Toulouse France Ecole Natl Aviat Civile F-31055 Toulouse 4 France

This paper addresses an extension of the resource-constrained project scheduling problem that takes into account storage resources which may be produced or consumed by activities. To solve this problem, we propose the generalization of two existing mixed integer linear programming models for the classical resource-constrained project scheduling problem, as well as one novel formulation based on the concept of event. Computational results are reported to compare these formulations with each other, as well as with a reference method from the literature. Conclusions are drawn on the merits and drawbacks of each model according to the instance characteristics.

关键词： Resource-constrained project scheduling mixed integer linear programming Consumption and production of resources Event-based on/off formulation

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Optimization of unit commitment and economic dispatch in microgrids based on genetic algorithm and mixed integer linear programming

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APPLIED ENERGY 2018年 210卷 944-963页

作者： Nemati, Mohsen Braun, Martin Tenbohlen, Stefan Siemens AG Humboldt St 59 D-90443 Nurnberg Germany Univ Kassel Fraunhofer IWES Kassel Germany Univ Stuttgart IEH Stuttgart Germany

Energy Management System (EMS) applications of modern power networks like microgrids have to respond to a number of stringent challenges due to current energy revolution. Optimal resource dispatch tasks must be handled with specific regard to the addition of new resource types and the adoption of novel modeling considerations. In addition, due to the comprehensive changes concerning the multi cell grid structure, new policies should be fulfilled via microgrids' EMS. At the same time achieving a variety of (conflicting) goals in different microgrids requires a universal and a multi criteria optimization tool. Few of recent works in this area have considered the different perspectives of network operation with high amount of constraints and decision criteria. In this paper two dispatch-optimizers for a centralized EMS (CEMS) as a universal tool are introduced. An improved real-coded genetic algorithm and an enhanced mixed integer linear programming (MILP) based method have been developed to schedule the unit commitment and economic dispatch of microgrid units. In the proposed methods, network restrictions like voltages and equipment loadings and unit constraints have been considered. The adopted genetic algorithm features a highly flexible set of sub-functions, intelligent convergence behavior, as well as diversified searching approaches and penalty methods for constraint violations. Moreover, a novel method has been introduced to deal with the limitations of the MILP algorithm for handling the non-linear network topology constraints. A new aging model of a Lithium-Ion battery based on an event driven aging behavior has been introduced. Ultimately, the developed GA-based and MILP-based optimizers have been applied to a test microgrid model under different operation policies, and the functionality of each method has been evaluated and compared together. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Microgrids Unit commitment Economic dispatch Genetic algorithm mixed integer linear programming

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A Fast and Accurate Self-Healing Scheme for Intelligent Distribution Networks Using mixed integer linear programming

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IEEE ACCESS 2024年 12卷 21586-21595页

作者： Lu, Jiangang Su, Junni Zhao, Ruifeng Chen, Fengchao Wang, Qiujie Yan, Wei Guangdong Power Grid Co Ltd Elect Power Dispatching & Control Ctr Guangzhou 510600 Peoples R China Guangdong Power Grid Co Ltd Dongguan Power Supply Bur Dongguan 523000 Peoples R China Chongqing Univ State Key Lab Power Transmiss Equipment & Syst Sec Chongqing 400044 Peoples R China

Fast and accurate self-healing after faults is an important way to improve the reliability of distribution networks. To improve the self-healing speed and accuracy of distribution networks, this paper proposes a fast and accurate self-healing scheme for distribution networks using mixed integer linear programming. Firstly, this method constructs a centralized 5G communication network architecture, which can effectively reduce the communication delay during the self-healing process. Secondly, the principle of logical algebraic transformation is utilized to linearize the switch function in the fault location model, thereby achieving equivalent transformation of the fault location model. Thirdly, using the polyhedral approximation method, the mixed integer second-order cone programming of the power supply recovery model is transformed into a mixed integer linear programming. The proposed method was validated by distribution network systems with different nodes in MATLAB/Simulink, and the results showed that the proposed method significantly improved self-healing speed and accuracy.

关键词： Distribution networks Power supplies Fault location 5G mobile communication Location awareness Fault currents Delays mixed integer linear programming Distribution network fault location fault recovery self-healing mixed integer linear programming 5G communication

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A multi-period mixed integer linear programming model for water and energy supply planning in Kuwait

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CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY 2015年第2期17卷 485-499页

作者： AlQattan, Nael Ross, Mark Sunol, Aydin K. Univ S Florida Coll Engn Tampa FL 33620 USA

The demand for water often necessitates desalination, particularly in arid coastal environments. Desalination is often integrated with electrical cogeneration. The demands for water and electricity change over time and are subject to uncertainty. A country-wide large-scale energy and water cogeneration planning model for Kuwait is formulated as a multi-period mixed integer linear programming problem and solved to minimize the net present value over the time period of 2013-2050. Five different plant technology options were considered for desalination and cogeneration including Oil & Multi Stage Flash, Natural Gas & Multi-Effect Distillation, Natural Gas & Reverse Osmosis, Solar Energy & Multi-Effect Distillation, and Solar Energy & Reverse Osmosis. Both water and energy usage in Kuwait and data from existing plants were utilized in providing the parameters and forecasts necessary for solution of the mathematical programming model. The model provides technology choice and associated capacity decisions for existing plants, new plants at green sites, and existing plant capacity expansions as well as their timing to meet the demands.

关键词： Cogeneration mixed integer linear programming Capacity expansion Desalination

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