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 piece...
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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 mixedinteger nonlinearprogramming (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.
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 detect...
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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 mixedintegerlinear 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 mixedintegerlinear 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.
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 param...
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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 linearprogramming. 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).
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 ne...
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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 mixedintegerlinear 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.
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...
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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-integerlinearprogramming 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.
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 l...
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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.
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...
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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.
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 handle...
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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.
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 ...
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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 mixedinteger 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.
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 an...
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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.
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