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mixed-integer quadratic programming approach for noninvasive estimation of respiratory effort profile during pressure support ventilation

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023年第1期39卷 e3668-e3668页

作者： Victor Jr, Marcus H. H. Maximo, Marcos R. O. A. Matsumoto, Monica M. S. Pereira, Sergio M. Tucci, Mauro R. R. Aeronaut Inst Technol Med Elect Devices Lab LabMed Elect Engn Sao Paulo Brazil Univ Sao Paulo Hosp Clin HCFMUSP Fac Med Div PneumolInst Coracao Sao Paulo Brazil Aeronaut Inst Technol Comp Sci Div Autonomous Computat Syst Lab LAB SCA Sao Paulo Brazil St Michaels Hosp Dept Anesthesia & Pain Med Toronto ON Canada Aeronaut Inst Technol Elect Engn Div Vila Acacias 50 BR-12228900 Sao Jose Dos Campos SP Brazil

Information about respiratory mechanics such as resistance, elastance, and muscular pressure is important to mitigate ventilator-induced lung injury. Particularly during pressure support ventilation, the available options to quantify breathing effort and calculate respiratory system mechanics are often invasive or complex. We herein propose a robust and flexible estimation of respiratory effort better than current methods. We developed a method for non-invasively estimating breathing effort using only flow and pressure signals. mixed-integer quadratic programming (MIQP) was employed, and the binary variables were the switching moments of the respiratory effort waveform. Mathematical constraints, based on ventilation physiology, were set for some variables to restrict feasible solutions. Simulated and patient data were used to verify our method, and the results were compared to an established estimation methodology. Our algorithm successfully estimated the respiratory effort, resistance, and elastance of the respiratory system, resulting in more robust performance and faster solver times than a previously proposed algorithm that used quadratic programming (QP) techniques. In a numerical simulation benchmark, the worst-case errors for resistance and elastance were 25% and 23% for QP versus < 0.1% and < 0.1% for MIQP, whose solver times were 4.7 s and 0.5 s, respectively. This approach can estimate several breathing effort profiles and identify the respiratory system's mechanical properties in invasively ventilated critically ill patients.

关键词： mechanical ventilation mixed-integer quadratic programming parameter estimation pressure support ventilation respiratory effort system identification

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Using dual relaxations in multiobjective mixed-integer convex quadratic programming

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JOURNAL OF GLOBAL OPTIMIZATION 2025年第1期92卷 159-186页

作者： De Santis, Marianna Eichfelder, Gabriele Patria, Daniele Warnow, Leo Univ Firenze Dipartimento Ingn informaz Via Santa Marta 3 I-50139 Florence Italy Tech Univ Ilmenau Inst Math Po 10 05 65 D-98684 Ilmenau Germany Sapienza Univ Roma Dipartimento Ingn Informat Automat & Gest Via Ariosto 25 I-00185 Rome Italy

We present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values of certain integer variables are fixed. The devised pruning conditions and a tailored preprocessing phase allow a fast enumeration of the nodes. Despite we do not require any boundedness of the feasible set, we are able to prove that the method stops after having explored a finite number of nodes. Numerical experiments on a broad set of instances with two, three, and four objectives are presented.

关键词： Multiobjective optimization Convex quadratic optimization mixed-integer quadratic programming Branch-and-bound algorithm

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A simple effective heuristic for embedded mixed-integer quadratic programming

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INTERNATIONAL JOURNAL OF CONTROL 2020年第1期93卷 2-12页

作者： Takapoui, Reza Moehle, Nicholas Boyd, Stephen Bemporad, Alberto Stanford Univ Dept Elect Engn Stanford CA 94305 USA Stanford Univ Dept Mech Engn Stanford CA 94305 USA Stanford Univ Dept Elect Engn Informat Syst Lab Stanford CA 94305 USA IMT Inst Adv Studies Lucca Lucca Italy

In this paper, we propose a fast optimisation algorithm for approximately minimising convex quadratic functions over the intersection of affine and separable constraints (i.e. the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-integer quadratic programming. Our heuristic is based on a variation of the alternating direction method of multipliers (ADMM), an algorithm for solving convex optimisation problems. We discuss the favourable computational aspects of our algorithm, which allow it to run quickly even on very modest computational platforms such as embedded processors. We give several examples for which an approximate solution should be found very quickly, such as management of a hybrid-electric vehicle drivetrain and control of switched-mode power converters. Our numerical experiments suggest that our method is very effective in finding a feasible point with small objective value;indeed, we see that in many cases, it finds the global solution.

关键词： mixed-integer quadratic programming heuristic ADMM embedded applications

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Dynamic optimization of a district energy system with storage using a novel mixed-integer quadratic programming algorithm

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OPTIMIZATION AND ENGINEERING 2019年第2期20卷 575-603页

作者： Blackburn, Landen Young, Aaron Rogers, Pratt Hedengren, John Powell, Kody Univ Utah Dept Chem Engn Salt Lake City UT 84112 USA Univ Utah Dept Min Engn Salt Lake City UT USA Brigham Young Univ Dept Chem Engn Provo UT 84602 USA

As more renewable energy is integrated into the power grid, it is increasingly important to exploit variable electricity pricing structures to minimize commercial utility costs and enable more intermittent renewables on the grid through proactive management of energy storage. Using data from a large campus district energy system, equipped with centralized chilled water plants and a thermal energy storage tank, a novel technique is proposed to optimize this system in real-time, formulated as a mixed-integer quadratic programming problem. This method, titled quadratic programming Hybrid with Augmented Constraints, is sufficiently fast to be computed in real-time for a district chiller system. This method is compared to both Branch and Bound and a simple logical decision algorithm in both speed and optimality. The proposed method for solving this mixed-integer quadratic programming problem proves very successful at achieving a near-optimal solution when compared to a standard Branch and Bound (BnB) algorithm. Although suboptimal, the proposed algorithm takes 99.96-99.99% less computational time than the standard BnB and computes an answer to within 29.9% of the BnB objective function. When compared to a simple logical decision algorithm, which represents an operator manually controlling the plant, the proposed method is estimated to yield 8.10-33.7% in savings on chiller energy costs. The quadratic programming Hybrid with Augmented Constraints algorithm shows potential for use in a real-time optimization application to exploit variable electricity pricing and significantly reduce the costs of running a chiller plant with thermal energy storage.

关键词： Dynamic optimization Chiller mixed-integer quadratic programming Thermal energy storage

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Complex portfolio selection via convex mixed-integer quadratic programming: a survey

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2019年第2期26卷 389-414页

作者： Mencarelli, Luca D'Ambrosio, Claudia Ecole Polytech CNRS LIX UMR7161 F-91128 Palaiseau France

In this paper, we review convex mixed-integer quadratic programming approaches to deal with single-objective single-period mean-variance portfolio selection problems under real-world financial constraints. In the first part, after describing the original Markowitz's mean-variance model, we analyze its theoretical and empirical limitations, and summarize the possible improvements by considering robust and probabilistic models, and additional constraints. Moreover, we report some recent theoretical convexity results for the probabilistic portfolio selection problem. In the second part, we overview the exact algorithms proposed to solve the single-objective single-period portfolio selection problem with quadratic risk measure.

关键词： portfolio selection mixed-integer quadratic programming convex MINLP robust and probabilistic optimization exact methods

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A railcar re-blocking strategy via mixed integer quadratic programming

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2022年 162卷

作者： Zu, Yue Heydari, Ruhollah Chahar, Kiran Pranoto, Yudi Cheng, Clark Norfolk Southern Corp 650 West Peachtree St Atlanta GA 30308 USA Delta Air Lines 1030 Delta Blvd Atlanta GA 30320 USA

This article presents a novel solution namely Pre-blocking through Re-waybilling to minimize railcar cuts in freight railways. The Pre-blocking through Re-waybilling Problem (PRP) can be described as follows: A freight train carrying m railcars, loaded or empty, arrives at a local classification yard where, based on the destination on their electronic waybills, railcars will be physically switched to n outbound trains. Number of railcar cuts depends on the order of railcars on train. The objective is to minimize the number of railcar cuts by means of changing the electronic waybills of empty railcars, i.e. re-assignment of empty railcars to customers, while respecting supply, demand, and feasibility constraints. In order to solve this problem, a supply-demand network is constructed first, where supply nodes and demand nodes represent railcars and destinations, respectively. The problem is then formulated as a modified transportation problem. Unlike the conventional transportation problem, a linear arc cost function is proposed to describe the adjacent cars' impact on railcar cut. The objective is converted to a quadratic function, leading to a mixed-integer quadratic programming (MIQP) problem. We improve proposed MIQP to a Convex mixed-integer quadratic programming (CMIQP) problem by adding a quadratic term to the objective function. Illustrative and realistic examples are presented to validate the feasibility and efficiency of proposed pre-blocking optimizer.

关键词： Railroad freight transportation Railcar distribution Transportation problem mixed-integer quadratic programming Pre-blocking

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On approximation algorithms for concave mixed-integer quadratic programming

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MATHEMATICAL programming 2018年第1-2期172卷 3-16页

作者： Del Pia, Alberto Univ Wisconsin Wisconsin Inst Discovery Dept Ind & Syst Engn Madison WI 53706 USA

Concave mixed- integer quadratic programming is the problem of minimizing a concave quadratic polynomial over the mixed- integer points in a polyhedral region. In this work we describe an algorithm that finds an - approximate solution to a concave mixed- integer quadratic programming problem. The running time of the proposed algorithm is polynomial in the size of the problem and in 1/ , provided that the number of integer variables and the number of negative eigenvalues of the objective function are fixed. The running time of the proposed algorithm is expected unless P = NP.

关键词： mixed-integer quadratic programming Approximation algorithms

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A Numerically Robust mixed-integer quadratic programming Solver for Embedded Hybrid Model Predictive Control

A Numerically Robust Mixed-Integer Quadratic Programming Sol...

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6th International-Federation-of-Automatic-Control (IFAC) Conference on Nonlinear-Model-Predictive-Control (NMPC)

作者： Bemporad, Alberto Naik, Vihangkumar V. IMT Sch Adv Studies Lucca Lucca Italy

The deployment of hybrid model predictive control (MPC) in practical applications requires primarily an efficient and robust on-line mixed-integer quadratic programming (MIQP) solver that runs in real time. In this paper we propose a new algorithm for solving MIQP problems which is particularly tailored to solve small-scale MIQPs, such as those that arise in embedded hybrid MPC applications. The algorithm couples a branch and bound (B&B) scheme with a recently proposed numerically robust quadratic programming (QP) solver based on nonnegative least squares (NNLS) and proximal-point iterations. The resulting MIQP solver supports positive semidefinite Hessian matrices, often appearing in hybrid MPC formulations, and warm starts with respect to both binary and real variables. We show that the speed of execution of our solver is comparable with state-of-the-art commercial solvers, while it is relatively simple to code in an embedded control system. (c) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： mixed-integer quadratic programming quadratic programming active-set methods nonnegative least squares model predictive control hybrid systems

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mixed-integer quadratic Constrained programming versus quadratic programming Methods for Distribution Network Reconfiguration

Mixed-Integer Quadratic Constrained Programming versus Quadr...

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International Conference on Advanced Electrical Engineering (ICAEE)

作者： Tami, Y. Sebaa, K. Lahdeb, M. Nouri, H. Univ Medea LSEA Medea 26000 Algeria Univ Laghouat LaACoSE Elect PB 37G Laghouat 03000 Algeria Univ West England Dept Engn Design & Math Power Syst Elect & Control Res Grp Bristol BS16 1QY Avon England

ISBN: (纸本)9781728122205

This paper will examine the solution of the minimum loss reconfiguration problem of distribution networks that determine the optimal switches, by means of a mixed-integer quadratically-constrained programming (MIQCP) model. The proposed MIQCP model is a convex formulation, which allows to find the optimal solution using optimization solvers. Our mathematical model considers the typical operating constraints of distribution networks (radial configuration, the maximum currents or the voltage plane).The accuracy of the results and the computational performance of the proposed MIQCP model are evaluated by referring to another MIQP (mixed integer quadratic programming) model already adopted for the problem of interest. We used a real distribution system of 106 nodes to show the effectiveness of the proposed model compared to another MIQP model that was tested on the same network. The mathematical model adopted has been solved using the Cplex optimization software implemented under Matlab. The overall optimality of the guaranteed solution is obtained by the convex relaxation of the continuous decision variables.

关键词： convex optimization quadratically constrained convex optimization mixed-integer quadratic programming power loss Radial distribution networks

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Dynamic OPF Considering Different Charging and Discharging Cost of Energy Storage Using mixed-integer quadratic programming 18

Dynamic OPF Considering Different Charging and Discharging C...

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International Seminar on Intelligent Technology and Its Applications (ISITIA)

作者： Wibowo, Rony Seto Purnomo, Fiona Yolita Aryani, Ni Ketut Penangsang, Ontoseno Inst Teknol Sepuluh Nopember ITS Surabaya Indonesia

ISBN: (纸本)9781538627082

This paper presents a study about optimization in microgrid with energy storage. The development of technology makes it possible for energy storage utilization as solution for energy management problem due to renewable integration. The ability of energy storage to store and supply power can be used to solve intermittency problem of renewable energy. Furthermore, the possibility of energy storage integration to make profit is researched deeper by considering charging and discharging cost. The DC Optimal Power Flow calculation is done to optimize the system with energy storage using mixed-integer quadratic programming. The output of this research are generation power and energy storage power in each period with minimum generation cost and the effect of different charging and discharging cost towards it.

关键词： battery DDCOPF microgrid mixed-integer quadratic programming charging and discharging cost

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