Статті в журналах: "Mixed-integer quadratic program"

1

Gondzio, Jacek, and E. Alper Yıldırım. "Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations." Journal of Global Optimization 81, no. 2 (April 20, 2021): 293–321. http://dx.doi.org/10.1007/s10898-021-01017-y.

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AbstractA standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative formulations. Our first formulation is based on casting a standard quadratic program as a linear program with complementarity constraints. We then employ binary variables to linearize the complementarity constraints. For the second formulation, we first derive an overestimating function of the objective function and establish its tightness at any global minimizer. We then linearize the overestimating function using binary variables and obtain our second formulation. For both formulations, we propose a set of valid inequalities. Our extensive computational results illustrate that the proposed mixed integer linear programming reformulations significantly outperform other global solution approaches. On larger instances, we usually observe improvements of several orders of magnitude.

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2

Kimura, Keiji, Hayato Waki, and Masaya Yasuda. "Application of mixed integer quadratic program to shortest vector problems." JSIAM Letters 9 (2017): 65–68. http://dx.doi.org/10.14495/jsiaml.9.65.

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3

Chen, Zhiping, and Zongben Xu. "Continuity and Stability of a Quadratic Mixed-Integer Stochastic Program." Numerical Functional Analysis and Optimization 30, no. 5-6 (June 30, 2009): 462–77. http://dx.doi.org/10.1080/01630560902920668.

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4

Zhao, Yingfeng, and Sanyang Liu. "Global optimization algorithm for mixed integer quadratically constrained quadratic program." Journal of Computational and Applied Mathematics 319 (August 2017): 159–69. http://dx.doi.org/10.1016/j.cam.2016.12.037.

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Feitelberg, Jacob, Amitabh Basu, and Tamás Budavári. "Fast Globally Optimal Catalog Matching using MIQCP." Astronomical Journal 166, no. 4 (September 27, 2023): 174. http://dx.doi.org/10.3847/1538-3881/acf5e2.

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Abstract We propose a novel exact method to solve the probabilistic catalog matching problem faster than previously possible. Our new approach uses mixed integer programming and introduces quadratic constraints to shrink the problem by multiple orders of magnitude. We also provide a method to use a feasible solution to dramatically speed up our algorithm. This gain in performance is dependent on how close to optimal the feasible solution is. Also, we are able to provide good solutions by stopping our mixed integer programming solver early. Using simulated catalogs, we empirically show that our new mixed integer program with quadratic constraints is able to be set up and solved much faster than previous large linear formulations. We also demonstrate our new approach on real-world data from the Hubble Source Catalog. This paper is accompanied by publicly available software to demonstrate the proposed method.

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Cvokic, Dimitrije. "A leader-follower single allocation hub location problem under fixed markups." Filomat 34, no. 8 (2020): 2463–84. http://dx.doi.org/10.2298/fil2008463c.

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This study examines a scenario in which two competitors, called a leader and a follower, sequentially create their hub and spoke networks to maximize their profits. It is assumed that a non-hub node can be allocated to at most one hub. The pricing is regulated with a fixed markup. Demand is split according to the logit model, and customers patronize their choice of route by a price. Two variants of this Stackelberg competition are addressed: deterministic and robust. In both cases, it was shown how to present the problem as a bi-level mixed-integer non-linear program. When it comes to the deterministic variant, a mixed-integer linear reformulation of the follower?s model is given. For the robust variant, it is shown how to reformulate the follower?s program as a mixed-integer conic-quadratic one. The benefits of these reformulations are that they allow the usage of state-of-the-art solvers in finding feasible solutions. As a solution approach for the leader, an alternating heuristic is proposed. Computational experiments are conducted on the set of Cinstances and thoroughly discussed, providing some managerial insights.

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Popkov, Alexander S. "Optimal program control in the class of quadratic splines for linear systems." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 16, no. 4 (2020): 462–70. http://dx.doi.org/10.21638/11701/spbu10.2020.411.

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This article describes an algorithm for solving the optimal control problem in the case when the considered process is described by a linear system of ordinary differential equations. The initial and final states of the system are fixed and straight two-sided constraints for the control functions are defined. The purpose of optimization is to minimize the quadratic functional of control variables. The control is selected in the class of quadratic splines. There is some evolution of the method when control is selected in the class of piecewise constant functions. Conveniently, due to the addition/removal of constraints in knots, the control function can be piecewise continuous, continuous, or continuously differentiable. The solution algorithm consists in reducing the control problem to a convex mixed-integer quadratically-constrained programming problem, which could be solved by using well-known optimization methods that utilize special software.

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Sadeghian, Omid, Arash Moradzadeh, Behnam Mohammadi-Ivatloo, Mehdi Abapour, and Fausto Pedro Garcia Marquez. "Generation Units Maintenance in Combined Heat and Power Integrated Systems Using the Mixed Integer Quadratic Programming Approach." Energies 13, no. 11 (June 3, 2020): 2840. http://dx.doi.org/10.3390/en13112840.

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Yearly generation maintenance scheduling (GMS) of generation units is important in each system such as combined heat and power (CHP)-based systems to decrease sudden failures and premature degradation of units. Imposing repair costs and reliability deterioration of system are the consequences of ignoring the GMS program. In this regard, this research accomplishes GMS inside CHP-based systems in order to determine the optimal intervals for predetermined maintenance required duration of CHPs and other units. In this paper, cost minimization is targeted, and violation of units’ technical constraints like feasible operation region of CHPs and power/heat demand balances are avoided by considering related constraints. Demand-response-based short-term generation scheduling is accomplished in this paper considering the maintenance intervals obtained in the long-term plan. Numerical simulation is performed and discussed in detail to evaluate the application of the suggested mixed-integer quadratic programming model that implemented in the General Algebraic Modeling System software package for optimization. Numerical simulation is performed to justify the model effectiveness. The results reveal that long-term maintenance scheduling considerably impacts short-term generation scheduling and total operation cost. Additionally, it is found that the demand response is effective from the cost perspective and changes the generation schedule.

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Yaakob, Shamshul Bahar, Mohd Zamri Hasan, and Amran Ahmed. "Structural Learning of Boltzmann Machine and its Application." Applied Mechanics and Materials 785 (August 2015): 63–67. http://dx.doi.org/10.4028/www.scientific.net/amm.785.63.

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This study proposed a way to solve problem efficiently which is through structural learning of Boltzmann machine. This method used mixed integer quadratic programming to solve the problem. An analysis is conducted by using the ideas of the reliability and risks of units assessed using a variance-covariance matrix and the effect and expanses of replacement are determined. In this study, the mean-variance analysis is formulated as a mathematical program with two objectives: (1) minimization of risk and (2) maximization of expected return. Lastly, the effectiveness of proposed method is illustrated by way of a life cycle management example. The result of this suggested method was demonstrated at the end. By using this method, more effective selection of results is gathered. Thus, this prove that the effectiveness of the decision making process can be reinforced.

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10

Sterle, Arnold, Christian A. Hans, and Jörg Raisch. "Model predictive control of wakes for wind farm power tracking." Journal of Physics: Conference Series 2767, no. 3 (June 1, 2024): 032005. http://dx.doi.org/10.1088/1742-6596/2767/3/032005.

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Abstract In this paper, a model predictive control scheme for wind farms is presented. Our approach considers wake dynamics including their influence on local wind conditions and allows the tracking of a given power reference. In detail, a Gaussian wake model is used in combination with observation points that carry wind condition information. This allows the estimation of the rotor effective wind speeds at downstream turbines, based on which we deduce their power output. Through different approximation methods, the associated finite horizon nonlinear optimization problem is reformulated in a mixed-integer quadratically-constrained quadratic program fashion. By solving the reformulated problem online, optimal yaw angles and axial induction factors are found. Closed-loop simulations indicate good power tracking capabilities over a wide range of power setpoints while distributing wind turbine infeed evenly among all units. Additionally, the simulation results underline real time capabilities of our approach.

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Melton, Kerry, and Sandeep Parepally. "Domiciling Truck Drivers More Strategically in a Transportation Network." International Journal of Applied Industrial Engineering 2, no. 1 (January 2014): 41–56. http://dx.doi.org/10.4018/ijaie.2014010103.

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The authors propose a method to better domicile truck drivers in a relay-point highway transportation network to obtain better solutions for the truck driver domiciling and sourcing problem. The authors exploit characteristics of the truckload driver routing problem over a transportation network and introduce a new approach to domicile, source, and route truck drivers while more inclusively considering performance and cost measures related to the driver, transportation carrier, and customer. Driver domicile and relay-point locations are exploited to balance driver pay and recruiting costs and driving time. A mixed integer quadratic program will determine where driver domiciles are located to base drivers, source drivers, route drivers, etc. while considering key costs related to transporting truckload freight over long distances. A method to improve driver domicile locations is introduced to enhance driving jobs and driver sourcing, but not at the expense of the transportation carrier and customer. A numerical experiment will be conducted.

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12

Zhu, Qian, Xiaoning Zhu, Pan Shang, and Lingyun Meng. "Analytical Approximation-Based Approach for Passenger Flow Control Strategy in Oversaturated Urban Rail Transit Systems." Journal of Advanced Transportation 2023 (June 23, 2023): 1–21. http://dx.doi.org/10.1155/2023/3513517.

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Focusing on a heavily congested urban rail corridor, this study investigates the passenger flow control strategy optimization problem from a mesoscopic perspective to reduce platform congestion and enhance service quality. Based on a quadratic functional approximation for passenger arrival rates, an analytical formula for calculating passenger waiting time is derived based on the classic deterministic queueing theory. We formulate the problem as a continuous nonlinear programming model to minimize the total passenger waiting time within transportation capacity constraints. A Lagrangian relaxation approach effectively transforms the original complex problem into an unconstrained minimization program. The analytical solution relating to optimal flow control strategy is derived by directly solving the unconstrained program. To further provide an integrated optimization framework from both the supply and demand sides, we extend the abovementioned passenger flow control optimization model into an integrated mixed-integer nonlinear programming model to jointly optimize the passenger-flow control strategy and train frequency setting. Numerical examples are presented to demonstrate the applicability and effectiveness of the proposed models. The computational results show that the produced high-quality passenger flow control strategy significantly reduces total passenger delay.

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13

Chen, Jun, Zheng Chang, Wenlong Guo, and Xijuan Guo. "Resource Allocation and Computation Offloading for Wireless Powered Mobile Edge Computing." Sensors 22, no. 16 (August 11, 2022): 6002. http://dx.doi.org/10.3390/s22166002.

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In this paper, we investigate a resource allocation and computation offloading problem in a heterogeneous mobile edge computing (MEC) system. In the considered system, a wireless power transfer (WPT) base station (BS) with an MEC sever is able to deliver wireless energy to the mobile devices (MDs), and the MDs can utilize the harvested energy for local computing or task offloading to the WPT BS or a Macro BS (MBS) with a stronger computing server. In particular, we consider that the WPT BS can utilize full- or half-duplex wireless energy transmission mode to empower the MDs. The aim of this work focuses on optimizing the offloading decision, full/half-duplex energy harvesting mode and energy harvesting (EH) time allocation with the objective of minimizing the energy consumption of the MDs. As the formulate problem has a non-convex mixed integer programming structure, we use the quadratically constrained quadratic program (QCQP) and semi-definite relaxation (SDR) methods to solve it. The simulation results demonstrate the effectiveness of the proposed scheme.

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14

Weissteiner, Jakob, and Sven Seuken. "Deep Learning—Powered Iterative Combinatorial Auctions." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 02 (April 3, 2020): 2284–93. http://dx.doi.org/10.1609/aaai.v34i02.5606.

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In this paper, we study the design of deep learning-powered iterative combinatorial auctions (ICAs). We build on prior work where preference elicitation was done via kernelized support vector regressions (SVRs). However, the SVR-based approach has limitations because it requires solving a machine learning (ML)-based winner determination problem (WDP). With expressive kernels (like gaussians), the ML-based WDP cannot be solved for large domains. While linear or quadratic kernels have better computational scalability, these kernels have limited expressiveness. In this work, we address these shortcomings by using deep neural networks (DNNs) instead of SVRs. We first show how the DNN-based WDP can be reformulated into a mixed integer program (MIP). Second, we experimentally compare the prediction performance of DNNs against SVRs. Third, we present experimental evaluations in two medium-sized domains which show that even ICAs based on relatively small-sized DNNs lead to higher economic efficiency than ICAs based on kernelized SVRs. Finally, we show that our DNN-powered ICA also scales well to very large CA domains.

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15

Lin, Ming-Hua, Jung-Fa Tsai, Yi-Chung Hu, and Tzu-Hsuan Su. "Optimal Allocation of Virtual Machines in Cloud Computing." Symmetry 10, no. 12 (December 15, 2018): 756. http://dx.doi.org/10.3390/sym10120756.

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Virtualization is one of the core technologies used in cloud computing to provide services on demand for end users over the Internet. Most current research allocates virtual machines to physical machines based on CPU utilization. However, for many applications that require communication between services running on different servers, communication costs influence the overall performance. Therefore, this study focuses on the optimal allocation of virtual machines across multiple geographically dispersed data centers, with the objective of minimizing communication costs. The original problem can be constructed as a quadratic assignment problem that is a classical NP-hard combinatorial optimization problem. This study adopts an efficient deterministic optimization approach to reformulate the original problem as a mixed-integer linear program that may be solved to obtain a globally optimal solution. Since the required bandwidth matrix and communication cost matrix are symmetric, the mathematical model of virtual machine placement can be simplified. Several numerical examples drawn from the literature are solved to demonstrate the computational efficiency of the proposed method for determining the optimal virtual machine allocation in cloud computing.

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16

Yuan, Yuan, Ping Yan, and Liqiang Zhao. "Continuous Time Formulation and Lagrangian Relaxation Algorithm for the Gate Assignment Problem." Mathematical Problems in Engineering 2020 (August 25, 2020): 1–11. http://dx.doi.org/10.1155/2020/5059817.

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Gates are important operating facilities and resources in civil airports. It is a core task in the airport operation management to select reasonable gates for inbound and outbound flights. We present a continuous time formulation with second-order cone programming (SOCP) for the gate assignment problem which allocates flights to available gates to optimize both the transfer time of passengers and the robustness of the airport operations schedules. The problem is formulated as a mixed integer nonlinear program, and then, the quadratic objective that minimizes the walking distance of transferring passengers is linearized, and the objective that minimizes the variance of idle time at the gates is transformed to a second-order cone constraint with a linear objective function. Then, a Lagrangian relaxation algorithm is developed by exploiting the problem structure. Computational tests are carried out to illustrate the efficiency of the model and the algorithms. It is shown that the continuous time formulation is more efficient than the existing model, and the Lagrangian relaxation algorithm can obtain better solutions faster than a commercial solver.

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17

Theodorakatos, Nikolaos P., Rohit Babu, and Angelos P. Moschoudis. "An Incomplete Observability-Constrained PMU Allocation Problem by Using Mathematical and Evolutionary Algorithms." Journal of Physics: Conference Series 2701, no. 1 (February 1, 2024): 012013. http://dx.doi.org/10.1088/1742-6596/2701/1/012013.

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Abstract The purpose of this paper is to introduce several optimization algorithms that can be used to address optimization models in the power network, where the level of observability may be either complete or incomplete. These algorithms include discrete, continuous and metaheuristic methods. Initially, the optimization problem is approached by implementing a zero-one mixed integer linear program solved by several methods, including branch and bound revised simplex and primal dual-simplex in combination with interior point algorithms. To solve the problem of depth-one-unobservability (DoOU), a nonlinear program is proposed using Sequential Quadratic Programming (SQP), Interior-Point methods (IPMs) or YALMIP\s branch-and-bound algorithm. Additionally, the paper proposes the use of metaheuristic algorithms, such as Genetic Algorithms (GAs) and Binary Particle Swarm Optimization (BPSO), to solve optimization problems under incomplete observability. The proposed algorithms are tested using simulations on IEEE standard systems to illustrate their efficiency and reliability in solving the optimization problem under partial observability. Overall, the paper concludes that these algorithms can efficiently lead to the optimum point in a reasonable runtime. Hence, this work examines the problem of putting a restricted PMUs number to make the DoOU and to give a feedback to the state estimation routine accuracy.

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18

Badenbroek, Riley, and Etienne de Klerk. "An Analytic Center Cutting Plane Method to Determine Complete Positivity of a Matrix." INFORMS Journal on Computing 34, no. 2 (March 2022): 1115–25. http://dx.doi.org/10.1287/ijoc.2021.1108.

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We propose an analytic center cutting plane method to determine whether a matrix is completely positive and return a cut that separates it from the completely positive cone if not. This was stated as an open (computational) problem by Berman et al. [Berman A, Dur M, Shaked-Monderer N (2015) Open problems in the theory of completely positive and copositive matrices. Electronic J. Linear Algebra 29(1):46–58]. Our method optimizes over the intersection of a ball and the copositive cone, where membership is determined by solving a mixed-integer linear program suggested by Xia et al. [Xia W, Vera JC, Zuluaga LF (2020) Globally solving nonconvex quadratic programs via linear integer programming techniques. INFORMS J. Comput. 32(1):40–56]. Thus, our algorithm can, more generally, be used to solve any copositive optimization problem, provided one knows the radius of a ball containing an optimal solution. Numerical experiments show that the number of oracle calls (matrix copositivity checks) for our implementation scales well with the matrix size, growing roughly like [Formula: see text] for d × d matrices. The method is implemented in Julia and available at https://github.com/rileybadenbroek/CopositiveAnalyticCenter.jl . Summary of Contribution: Completely positive matrices play an important role in operations research. They allow many NP-hard problems to be formulated as optimization problems over a proper cone, which enables them to benefit from the duality theory of convex programming. We propose an analytic center cutting plane method to determine whether a matrix is completely positive by solving an optimization problem over the copositive cone. In fact, we can use our method to solve any copositive optimization problem, provided we know the radius of a ball containing an optimal solution. We emphasize numerical performance and stability in developing this method. A software implementation in Julia is provided.

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19

de Weert, Yoran, and Konstantinos Gkiotsalitis. "A COVID-19 Public Transport Frequency Setting Model That Includes Short-Turning Options." Future Transportation 1, no. 1 (March 29, 2021): 3–20. http://dx.doi.org/10.3390/futuretransp1010002.

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The COVID-19 pandemic has had an enormous impact on the public transport sector. After the start of the pandemic, passenger demand dropped significantly for public transport services. In addition, social distancing measures have resulted in introducing pandemic-imposed capacity limitations to public transport vehicles. Consequently, public transport operators should adjust their planning to minimize the impact of the COVID-19 pandemic. This study introduces a mixed-integer quadratic program that sets the optimal frequencies of public transport lines and sublines in order to conform with the pandemic-imposed capacity. The focus is on cases where the public transport demand is high, but the crowding levels inside public transport vehicles should remain below the pandemic-imposed capacities. Of particular interest are public transport lines with skewed demand profiles that can benefit from the introduction of short-turning sublines that serve the high-demand line segments. The frequency setting model is tested on a network containing two high-demand bus lines in the Twente region in the Netherlands, and it demonstrates that the revenue losses due to social distancing can be reduced when implementing short-turning service patterns.

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20

Golmohamadi, Hessam, and Amin Asadi. "Integration of Joint Power-Heat Flexibility of Oil Refinery Industries to Uncertain Energy Markets." Energies 13, no. 18 (September 17, 2020): 4874. http://dx.doi.org/10.3390/en13184874.

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This paper proposes a novel approach to optimize the main energy consumptions of heavy oil refining industries (ORI) in response to electricity price uncertainties. The whole industrial sub-processes of the ORI are modeled mathematically to investigate the joint power-heat flexibility potentials of the industry. To model the refinery processes, an input/output flow-based model is proposed for five main refining units. Moreover, the role of storage tanks capacity in the power system flexibility is investigated. To hedge against the electricity price uncertainty, an uncertain bound for the wholesale electricity price is addressed. To optimize the industrial processes, a dual robust mixed-integer quadratic program (R-MIQP) is adopted; therefore, the ORI’s operational strategies are determined under the worst-case realization of the electricity price uncertainty. Finally, the suggested approach is implemented in the south-west sector of the Iran Energy Market that suffers from a lack of electricity in hot days of summer. The simulation results confirm that the proposed framework ensures industrial demand flexibility to the external grids when a power shortage occurs. The approach not only provides demand flexibility to the power system, but also minimizes the operation cost of the industries.

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21

Agner, Raphael, Peter Gruber, and Beat Wellig. "Model Predictive Control of Heat Pumps with Thermal Energy Storages in Industrial Processes." Energies 17, no. 19 (September 26, 2024): 4823. http://dx.doi.org/10.3390/en17194823.

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Integration of heat pumps combined with thermal energy storage provides a key pathway to decarbonizing the energy supply in the industry when the processes are not operated continuously. Yet, this integration of such novel systems introduces control challenges due to added dependencies between different process streams. This work investigates the control problem of heat pumps coupled to stratified thermal energy storage that is integrated into non-continuous industrial processes. A two-layer control strategy is proposed, where, in the higher level, a model predictive controller is developed for energy management using a linear model of the non-linear process. The resulting optimization problem is a mixed integer quadratic program. The low-level control layer is defined with standard industry controllers. The overall system is tested using a dynamic simulation model for the entire process, demonstrating its performance in three different cases. The control strategy optimizes heat recovery while ensuring system operability. The study demonstrates successful disturbance rejection and cold starts, wherein 100% of the targeted heat recovery can be confirmed under nominal conditions. Further evaluation in laboratory or field trials is recommended, and alternative, yet-to-be-defined, control concepts may be compared to the proposed approach.

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22

Windmann, Stefan, Oliver Niggemann, and Heiko Stichweh. "Computation of energy efficient driving speeds in conveying systems." at - Automatisierungstechnik 66, no. 4 (April 25, 2018): 308–19. http://dx.doi.org/10.1515/auto-2017-0094.

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AbstractThis article addresses the automatic optimization of driving speeds in conveying systems. Electric drives in existing conveying systems are usually accelerated and decelerated according to predetermined movement profiles. Such an approach is inflexible for conveying applications with changing constraints and, in many cases, not optimal with respect to energy efficiency. In the present work, a method for automatic computation of energy efficient movement profiles is proposed. The proposed method is based on accurate models for electric drives and several types of conveying applications such as roll conveyors, belt conveyors and vertical conveyors. Furthermore, joint energy efficiency optimization for two drives, which are attached to an intermediate circuit, is investigated. Thereby, additional constraints on the energy flow between the drives are imposed in order to reduce load peaks and energy feedback into the grid. The resulting optimization problem is a mixed integer quadratic program (MIQP), which can be solved in a few milliseconds. Experimental results show that energy losses of electric drives are cut down by using the obtained non-trivial movement profiles instead of standard trapezoid movement profiles. The additional constraints on the energy flow between two drives lead to further significant improvements with respect to the overall energy losses.

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23

Lieberman, Edward B., Jinil Chang, and Elena Shenk Prassas. "Formulation of Real-Time Control Policy for Oversaturated Arterials." Transportation Research Record: Journal of the Transportation Research Board 1727, no. 1 (January 2000): 77–88. http://dx.doi.org/10.3141/1727-10.

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The formulation of a real-time traffic control policy designed expressly for oversaturated arterials is presented, and the operating protocol is described. Its objectives are to ( a) maximize system throughput, ( b) fully use storage capacity, and ( c) provide equitable service. This control policy, known as RT/IMPOST (real-time/internal metering policy to optimize signal timing), is designed to control queue growth on every saturated approach by suitably metering traffic to maintain stable queues. Consistent with this approach, bounds on queue lengths and signal offsets are determined. A mixed-integer linear program (MILP) tableau is formulated to yield optimal values of signal offsets and queue length for each approach. A nonlinear (quadratic) programming formulation adjusts the arterial green-phase durations of each signal cycle so that the actual arterial queue lengths on each saturated approach will continually closely approximate the optimal queue lengths computed by the MILP formulation. The policy principles are as follows: ( a) the signal phase durations “meter” traffic at intersections servicing oversaturated approaches to control and stabilize queue lengths and to provide equitable service to competing traffic streams; and ( b) the signal coordination (i.e., offsets) controls the interaction between incoming platoons and standing queues in a way that fully uses the available storage capacity, keeps intersections clear of queue spillback, and maximizes throughput.

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24

Griffin, Robert J., and Alexander Leonessa. "Model Predictive Control for Stable Walking Using the Divergent Component of Motion with Footstep Location and Yaw Adaptation." International Journal of Humanoid Robotics 16, no. 05 (October 2019): 1950025. http://dx.doi.org/10.1142/s0219843619500257.

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This paper presents an extension of previous model predictive control (MPC) schemes for dynamic walking to the stabilization of the time-varying divergent component-of-motion (DCM). In order to address the control authority limitations caused by fixed footholds, the step positions and rotations are treated as control inputs, allowing the generation and execution of stable walking motions, both at high speeds and in the face of disturbances. The use of the time-varying DCM allows consideration of height changes on the DCM dynamics, improving the robustness of the controller over varying terrain. Footstep rotation is included to allow for better modeling of the adjustment effects on reachability for stability and navigation of complex environments. This is done by formulating a quadratically constrained mixed-integer quadratic program (MIQCQP), which, when combined with the use of the time-varying DCM to account for the effects of height changes and use of angular momentum, improves the capabilities of MPC strategies for bipedal walking. While the MIQCQP cannot be solved at the desired control frequency, a method for compensating for the DCM dynamics between solves is presented. Simulation results of fast walking over flat ground and navigating varying-height terrain is presented with the ESCHER humanoid. This is combined with experiments that recover from a variety pushes, which demonstrate the effectiveness of this approach.

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25

Bilal, Ghassan A., Mohammed K. Al-Saadi, Ghaidaa A. Al-Sultany, and Wisam Abed Kattea Al-Maliki. "Optimal Operation of CCHP Smart Distribution Grid with Integration of Renewable Energy." Applied Sciences 15, no. 3 (January 29, 2025): 1407. https://doi.org/10.3390/app15031407.

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Recently, electric distribution grids supply not only electric loads but also heating and cooling loads simultaneously to increase the efficiency of the system and reduce the emission of greenhouse gases. An energy management system (EMS) to reduce the combined total expense including environmental damage cost of the combined cooling, heating, and power (CCHP) smart distribution grids in a cooperative framework is proposed in this paper. The entire problem is modelled as a unit commitment interval mixed integer quadratic program (UCIMIQP). The UC is developed to respond to the operation of the electric, heating, and cooling systems and takes into consideration the exchange of energy between these systems. In addition, the demand response (DR) is incorporated with the optimization problem as a decision variable to shave the peak load and reduce the total system cost. The environmental damage is converted to expense, and the entire combined problem is converted to a unified function that is possible to solve in one step, where this is suitable for online operation. Furthermore, a set of realistic constraints is considered to make the approach close to a real scenario. To verify the effectiveness and robustness of the proposed model, the analysis is applied to the distribution grids, which include electrical, heating, and cooling systems, where these systems operated cooperatively. The interaction between these systems makes the operation more flexible and economical. The results show that the total cost is reduced through an exchange in energy between the systems. Additionally, the consideration of the demand response reduces the maximum load and decreases the total cost.

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26

Newby, Eric, and M. Montaz Ali. "Transformation-Based Preprocessing for Mixed-Integer Quadratic Programs." Journal of Optimization Theory and Applications 168, no. 3 (September 25, 2015): 1039–45. http://dx.doi.org/10.1007/s10957-015-0806-9.

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Ziyatdinov, N. N., I. I. Emelyanov, A. A. Ryzhova, and P. S. Chernakov. "Algorithm and software for the optimal technological design of a system of simple distillation columns." Fine Chemical Technologies 16, no. 5 (November 28, 2021): 379–89. http://dx.doi.org/10.32362/2410-6593-2021-16-5-379-389.

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Анотація:

Objectives. The formalized problem of the optimal design of distillation column systems belongs to the class of mixed integer nonlinear program problems. Discrete search variables are the number of trays in the rectifying and stripping sections of columns, whereas the continuous ones are the operating modes of columns. This study aimed to develop an algorithm and a software package for the optimal technological design of a system of simple distillation columns based on the criterion of total reduced capital and energy costs using rigorous mathematical distillation models.Methods. The solution to this problem is based on the branch and bound method. A computer model of the distillation column system was developed in the environment of the Aspen Hysys software package. The Inside–Out module was used as the distillation model. The developed algorithm is implemented in the software environment of the Matlab mathematical package. To solve the conditional optimization problem, a sequential quadratic programming method-based model was used. The interaction between software add-ins in Matlab and Aspen Hysys is implemented using a Component Object Model interface.Results. Approaches to obtain the lower and upper bounds of the optimality criterion and the branching method for the implementation of the branch and bound method have been developed. In addition, an algorithm for the optimal design of a distillation column of a given topology based on the branch and bound method has been developed. Furthermore, using Matlab, a software package that implements the developed algorithm and is integrated with the universal modeling software AspenHysys has been created.Conclusions. An algorithm and a software package have been developed and implemented that allows automating the design process of distillation column systems and integration with advanced mathematical programming packages, respectively. The performance of the algorithm and software package has been evaluated using the optimal design of the debutanization column as an example.

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Fernandez-Gonzalez, Enrique, Brian Williams, and Erez Karpas. "ScottyActivity: Mixed Discrete-Continuous Planning with Convex Optimization." Journal of Artificial Intelligence Research 62 (July 27, 2018): 579–664. http://dx.doi.org/10.1613/jair.1.11219.

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The state of the art practice in robotics planning is to script behaviors manually, where each behavior is typically generated using trajectory optimization. However, in order for robots to be able to act robustly and adapt to novel situations, they need to plan these activity sequences autonomously. Since the conditions and effects of these behaviors are tightly coupled through time, state and control variables, many problems require that the tasks of activity planning and trajectory optimization are considered together. There are two key issues underlying effective hybrid activity and trajectory planning: the sufficiently accurate modeling of robot dynamics and the capability of planning over long horizons. Hybrid activity and trajectory planners that employ mixed integer programming within a discrete time formulation are able to accurately model complex dynamics for robot vehicles, but are often restricted to relatively short horizons. On the other hand, current hybrid activity planners that employ continuous time formulations can handle longer horizons but they only allow actions to have continuous effects with constant rate of change, and restrict the allowed state constraints to linear inequalities. This is insufficient for many robotic applications and it greatly limits the expressivity of the problems that these approaches can solve. In this work we present the ScottyActivity planner, that is able to generate practical hybrid activity and motion plans over long horizons by employing recent methods in convex optimization combined with methods for planning with relaxed plan graphs and heuristic forward search. Unlike other continuous time planners, ScottyActivity can solve a broad class of robotic planning problems by supporting convex quadratic constraints on state variables and control variables that are jointly constrained and that affect multiple state variables simultaneously. In order to support planning over long horizons, ScottyActivity does not resort to time, state or control variable discretization. While straightforward formulations of consistency checks are not convex and do not scale, we present an efficient convex formulation, in the form of a Second Order Cone Program (SOCP), that is very fast to solve. We also introduce several new realistic domains that demonstrate the capabilities and scalability of our approach, and their simplified linear versions, that we use to compare with other state of the art planners. This work demonstrates the power of integrating advanced convex optimization techniques with discrete search methods and paves the way for extensions dealing with non-convex disjoint constraints, such as obstacle avoidance.

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29

Su, Lijie, Lixin Tang, David E. Bernal, and Ignacio E. Grossmann. "Improved quadratic cuts for convex mixed-integer nonlinear programs." Computers & Chemical Engineering 109 (January 2018): 77–95. http://dx.doi.org/10.1016/j.compchemeng.2017.10.011.

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30

Bemporad, Alberto. "Solving Mixed-Integer Quadratic Programs via Nonnegative Least Squares." IFAC-PapersOnLine 48, no. 23 (2015): 73–79. http://dx.doi.org/10.1016/j.ifacol.2015.11.264.

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31

Han, Youpan, and Zhiping Chen. "Continuity of parametric mixed-integer quadratic programs and its application to stability analysis of two-stage quadratic stochastic programs with mixed-integer recourse." Optimization 64, no. 9 (April 25, 2014): 1983–97. http://dx.doi.org/10.1080/02331934.2014.891033.

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32

Zheng, Xiaojin, Xiaoling Sun, Duan Li, and Xueting Cui. "Lagrangian decomposition and mixed-integer quadratic programming reformulations for probabilistically constrained quadratic programs." European Journal of Operational Research 221, no. 1 (August 2012): 38–48. http://dx.doi.org/10.1016/j.ejor.2012.03.006.

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33

Nowak, Ivo. "Lagrangian decomposition of block-separable mixed-integer all-quadratic programs." Mathematical Programming 102, no. 2 (February 6, 2004): 295–312. http://dx.doi.org/10.1007/s10107-003-0500-9.

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34

Chen, Zhiping, and Youpan Han. "Quantitative stability of mixed-integer two-stage quadratic stochastic programs." Mathematical Methods of Operations Research 75, no. 2 (January 11, 2012): 149–63. http://dx.doi.org/10.1007/s00186-010-0326-1.

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35

Ragsdale, Cliff, and Antonie Stam. "A note on solving quadratic programs using mixed-integer programming." Computers & Operations Research 16, no. 4 (January 1989): 393–95. http://dx.doi.org/10.1016/0305-0548(89)90010-5.

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36

Hijazi, Hassan, Carleton Coffrin, and Pascal Van Hentenryck. "Convex quadratic relaxations for mixed-integer nonlinear programs in power systems." Mathematical Programming Computation 9, no. 3 (October 15, 2016): 321–67. http://dx.doi.org/10.1007/s12532-016-0112-z.

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37

Lazimy, Rafael. "Improved algorithm for mixed-integer quadratic programs and a computational study." Mathematical Programming 32, no. 1 (May 1985): 100–113. http://dx.doi.org/10.1007/bf01585661.

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38

Newby, Eric, and M. M. Ali. "A Note on Convex Reformulation Schemes for Mixed Integer Quadratic Programs." Journal of Optimization Theory and Applications 160, no. 2 (May 24, 2013): 457–69. http://dx.doi.org/10.1007/s10957-013-0340-6.

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39

Newby, Eric, and M. M. Ali. "Linear transformation based solution methods for non-convex mixed integer quadratic programs." Optimization Letters 11, no. 5 (December 26, 2015): 967–81. http://dx.doi.org/10.1007/s11590-015-0988-y.

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40

Billionnet, Alain, Sourour Elloumi, and Amélie Lambert. "A Branch and Bound algorithm for general mixed-integer quadratic programs based on quadratic convex relaxation." Journal of Combinatorial Optimization 28, no. 2 (November 14, 2012): 376–99. http://dx.doi.org/10.1007/s10878-012-9560-1.

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41

Nohra, Carlos J., Arvind U. Raghunathan, and Nikolaos Sahinidis. "Spectral Relaxations and Branching Strategies for Global Optimization of Mixed-Integer Quadratic Programs." SIAM Journal on Optimization 31, no. 1 (January 2021): 142–71. http://dx.doi.org/10.1137/19m1271762.

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42

Mehmanchi, Erfan, Andrés Gómez, and Oleg A. Prokopyev. "Fractional 0–1 programs: links between mixed-integer linear and conic quadratic formulations." Journal of Global Optimization 75, no. 2 (September 6, 2019): 273–339. http://dx.doi.org/10.1007/s10898-019-00817-7.

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43

Letchford, Adam N., and Daniel J. Grainger. "A note on representations of linear inequalities in non-convex mixed-integer quadratic programs." Operations Research Letters 45, no. 6 (November 2017): 631–34. http://dx.doi.org/10.1016/j.orl.2017.10.007.

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44

Vielma, Juan Pablo, Shabbir Ahmed, and George L. Nemhauser. "A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs." INFORMS Journal on Computing 20, no. 3 (August 2008): 438–50. http://dx.doi.org/10.1287/ijoc.1070.0256.

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45

Chen, Zhi-ping, and You-pan Han. "Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs." Applied Mathematics-A Journal of Chinese Universities 25, no. 4 (December 2010): 391–99. http://dx.doi.org/10.1007/s11766-010-2202-4.

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46

Bestuzheva, Ksenia, Hassan Hijazi, and Carleton Coffrin. "Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching." INFORMS Journal on Computing 32, no. 3 (July 2020): 682–96. http://dx.doi.org/10.1287/ijoc.2019.0900.

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This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

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47

Misener, Ruth, and Christodoulos A. Floudas. "Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations." Mathematical Programming 136, no. 1 (May 24, 2012): 155–82. http://dx.doi.org/10.1007/s10107-012-0555-6.

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48

Misener, Ruth, James B. Smadbeck, and Christodoulos A. Floudas. "Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2." Optimization Methods and Software 30, no. 1 (May 21, 2014): 215–49. http://dx.doi.org/10.1080/10556788.2014.916287.

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49

Nespoli, Lorenzo, Nina Wiedemann, Esra Suel, Yanan Xin, Martin Raubal, and Vasco Medici. "National-scale bi-directional EV fleet control for ancillary service provision." Energy Informatics 6, S1 (October 19, 2023). http://dx.doi.org/10.1186/s42162-023-00281-4.

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AbstractDeploying real-time control on large-scale fleets of electric vehicles (EVs) is becoming pivotal as the share of EVs over internal combustion engine vehicles increases. In this paper, we present a Vehicle-to-Grid (V2G) algorithm to simultaneously schedule thousands of EVs charging and discharging operations, that can be used to provide ancillary services. To achieve scalability, the monolithic problem is decomposed using the alternating direction method of multipliers (ADMM). Furthermore, we propose a method to handle bilinear constraints of the original problem inside the ADMM iterations, which changes the problem class from Mixed-Integer Quadratic Program (MIQP) to Quadratic Program (QP), allowing for a substantial computational speed up. We test the algorithm using real data from the largest carsharing company in Switzerland and show how our formulation can be used to retrieve flexibility boundaries for the EV fleet. Our work thus enables fleet operators to make informed bids on ancillary services provision, thereby facilitating the integration of electric vehicles.

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50

Grübel, Julia, Richard Krug, Martin Schmidt, and Winnifried Wollner. "A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities." Journal of Optimization Theory and Applications, July 23, 2023. http://dx.doi.org/10.1007/s10957-023-02254-9.

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AbstractWe present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate them and that we know their global Lipschitz constants. The algorithm is a successive linear relaxation method in which we alternate between solving a master problem, which is a mixed-integer linear relaxation of the original problem, and a subproblem, which is designed to tighten the linear relaxation of the next master problem by using the Lipschitz information about the respective functions. By doing so, we follow the ideas of Schmidt, Sirvent, and Wollner (Math Program 178(1):449–483 (2019) and Optim Lett 16(5):1355-1372 (2022)) and improve the tackling of multivariate constraints. Although multivariate nonlinearities obviously increase modeling capabilities, their incorporation also significantly increases the computational burden of the proposed algorithm. We prove the correctness of our method and also derive a worst-case iteration bound. Finally, we show the generality of the addressed problem class and the proposed method by illustrating that both bilevel optimization problems with nonconvex and quadratic lower levels as well as nonlinear and mixed-integer models of gas transport can be tackled by our method. We provide the necessary theory for both applications and briefly illustrate the outcomes of the new method when applied to these two problems.

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