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American Control Conference

作者： Shankarachary Ragi Hans D. Mittelmann School of Mathematical and Statistical Sciences Arizona State University Tempe 85287-1804 USA

ISBN: (纸本)9781509045839

We present a mixed-integer nonlinear programming (MINLP) formulation of a UAV path optimization problem, and attempt to find the global optimum solution. As objective functions in UAV path optimization problems tend to be non-convex, traditional optimization solvers (typically local solvers) are prone to local optima, which lead to severely sub-optimal controls. For the purpose of this study, we choose a target tracking application, where the goal is to optimize the kinematic controls of UAVs while maximizing the target tracking performance. First, we compare the performance of two traditional solvers numerically - MATLAB's fmincon and knitro. Second, we formulate this UAV path optimization problem as a mixed-integer nonlinear program (MINLP). As this MINLP tends to be computationally expensive, we present two pruning methods to make this MINLP tractable. We also present numerical results to demonstrate the performance of these methods.

关键词： UAV path optimization target tracking mixed-integer nonlinear programming fmincon knitro

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Comparison of two non-convex mixed-integer nonlinear programming algorithms applied to autoregressive moving average model structure and parameter estimation

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ENGINEERING OPTIMIZATION 2016年第10期48卷 1693-1706页

作者： Uilhoorn, F. E. Warsaw Univ Technol Dept Environm Engn Warsaw Poland

In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.

关键词： mesh adaptive direct search genetic algorithm ARMA Kalman filter mixed-integer nonlinear programming

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Plunge milling time optimization via mixed-integer nonlinear programming

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COMPUTERS & INDUSTRIAL ENGINEERING 2016年第0期98卷 434-445页

作者： Cafieri, Sonia Monies, Frederic Mongeau, Marcel Bes, Christian ENAC MAIAA F-31055 Toulouse France Univ Toulouse IMT F-31400 Toulouse France Univ Toulouse 3 ICA F-31062 Toulouse France

Plunge milling is a recent and efficient production mean for machining deep workpieces, notably in aeronautics. This paper focuses on the minimization of the machining time by optimizing the values of the cutting parameters. Currently, neither Computer-Aided Manufacturing (CAM) software nor standard approaches take into account the tool path geometry and the control laws driving the tool displacements to propose optimal cutting parameter values, despite their significant impact. This paper contributes to plunge milling optimization through a mixed-integer nonlinear programming (MINLP) approach, which enables us to determine optimal cutting parameter values that evolve along the tool path. It involves both continuous (cutting speed, feed per tooth) and, in contrast with standard approaches, integer (number of plunges) optimization variables, as well as nonlinear constraints. These constraints are related to the Computer Numerical Control (CNC) machine tool and to the cutting tool, taking into account the control laws. Computational results, validated on CNC machines and on representative test cases of engine housing, show that our methodology outperforms standard industrial engineering know-how approaches by up to 55% in terms of machining time. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Plunge milling mixed-integer nonlinear programming Optimized cutting parameters Machining time optimization

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Optimal scheduling of buildings with energy generation and thermal energy storage under dynamic electricity pricing using mixed-integer nonlinear programming

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APPLIED ENERGY 2015年 147卷 49-58页

作者： Lu, Yuehong Wang, Shengwei Sun, Yongjun Yan, Chengchu Hong Kong Polytech Univ Dept Bldg Serv Engn Kowloon Hong Kong Peoples R China City Univ Hong Kong Div Bldg Sci & Technol Kowloon Hong Kong Peoples R China

The increasing complexity of building energy systems integrated with renewable energy systems requires essentially more intelligent scheduling strategy. The energy systems often have strong nonlinear characteristics and have discrete working ranges. The mixed-integer nonlinear programming approach is used to solve their optimal scheduling problems of energy systems in building integrated with energy generation and thermal energy storage in this study. The optimal scheduling strategy minimizes the overall operation cost day-ahead, including operation energy cost and cost concerning the plant on/off penalty. A case study is conducted to validate the proposed strategy based on the Hong Kong Zero Carbon Building. Four scenarios are investigated and compared to exam the performance of the optimal scheduling. Results show that the strategy can reduce operation energy cost greatly (about 25%) compared with a rule-based strategy and the reduction is even increased to about 47% when a thermal energy storage system is used. The strategy can also reduce the on/off frequency of chillers significantly. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Optimal scheduling mixed-integer nonlinear programming Zero energy building Renewable energy systems Thermal energy storage

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A multi-objective nonlinear integer programming model for mixed runway operations within the TMAs

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AERONAUTICAL JOURNAL 2024年第1320期128卷 340-370页

作者： Kaplan, Z. Cetek, C. Sarac, T. Eskisehir Tech Univ Air Traff Control Dept TR-26555 Iki Eylul Eskisehir Turkiye Eskisehir Osmangazi Univ Ind Engn Dept TR-26480 Meselik Eskisehir Turkiye

Global air traffic demand has shown rapid growth for the last three decades. This growth led to more delays and congestion within terminal manoeuvring areas (TMAs) around major airports. The efficient use of airport capacities through the careful planning of air traffic flows is imperative to overcome these problems. In this study, a mixed-integer nonlinear programming (MINLP) model with a multi-objective approach was developed to solve the aircraft sequencing and scheduling problem for mixed runway operations within the TMAs. The model contains fuel cost functions based on airspeed, altitude, bank angle, and the aerodynamic characteristics of the aircraft. The optimisation problem was solved by using the epsilon-constraint method where total delay and total fuel functions were simultaneously optimised. We tested the model with different scenarios generated based on the real traffic data of Istanbul Sabiha Gokcen Airport. The results revealed that the average total delay and average total fuel were reduced by 26.4% and 6.7%, respectively.

关键词： Multi-objective programming Air traffic management Aircraft sequencing and scheduling problem mixed-integer nonlinear programming

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Convex mixed-integer nonlinear programs derived from generalized disjunctive programming using cones

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2024年第1期88卷 251-312页

作者： Neira, David E. Bernal Grossmann, Ignacio E. Purdue Univ Davidson Sch Chem Engn 480 Stadium Mall Dr W Lafayette IN 47907 USA Univ Space Res Assoc Res Inst Adv Comp Sci 425 3rd St SWSuite 950 Washington DC 20024 USA NASA Ames Res Ctr Quantum Artificial Intelligence Lab 5000 Forbes Ave Moffett Field CA 94035 USA Carnegie Mellon Univ Chem Engn Dept 5000 Forbes Ave Pittsburgh PA 15213 USA

We propose the formulation of convex Generalized Disjunctive programming (GDP) problems using conic inequalities leading to conic GDP problems. We then show the reformulation of conic GDPs into mixed-integer Conic programming (MICP) problems through both the big-M and hull reformulations. These reformulations have the advantage that they are representable using the same cones as the original conic GDP. In the case of the hull reformulation, they require no approximation of the perspective function. Moreover, the MICP problems derived can be solved by specialized conic solvers and offer a natural extended formulation amenable to both conic and gradient-based solvers. We present the closed form of several convex functions and their respective perspectives in conic sets, allowing users to formulate their conic GDP problems easily. We finally implement a large set of conic GDP examples and solve them via the scalar nonlinear and conic mixed-integer reformulations. These examples include applications from Process Systems Engineering, Machine learning, and randomly generated instances. Our results show that the conic structure can be exploited to solve these challenging MICP problems more efficiently. Our main contribution is providing the reformulations, examples, and computational results that support the claim that taking advantage of conic formulations of convex GDP instead of their nonlinear algebraic descriptions can lead to a more efficient solution to these problems.

关键词： mixed-integer nonlinear programming Conic programming Generalized disjunctive programming Perspective function

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Optimal scheduling of combined heat and power plants using mixed-integer nonlinear programming

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ENERGY 2014年 77卷 675-690页

作者： Kim, Jong Suk Edgar, Thomas F. Univ Texas Austin McKetta Dept Chem Engn Austin TX 78712 USA Univ Texas Austin Energy Inst Austin TX 78712 USA

This paper presents the application of MINLP (mixed-integer nonlinear programming) approach for scheduling of a CHP (combined heat and power) plant in the day-ahead wholesale energy markets. This work employs first principles models to describe the nonlinear dynamics of a CHP plant and its individual components. The MINLP framework includes practical constraints such as minimum/maximum power output and steam flow restrictions, minimum up/down times, start-up and shut-down procedures, and fuel limits. Special care is given to the explicit modeling of the unit start-up types (hot, warm, and cold), which depend on the component's prior reservation time, resulting in the differences in the time-dependent start-up costs of generating units. The model also accounts for the different operating modes (synchronization, soak, dispatch, and desynchronization) during start-up and shut-down of each unit. We provide case studies involving the Hal C. Weaver power plant complex at the University of Texas at Austin to demonstrate the effectiveness of the proposed methodology. The results show that the optimized operating strategies can yield substantial net incomes from electricity sales. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Scheduling Unit commitment Economic dispatch Combined heat and power Day-ahead wholesale energy market mixed-integer nonlinear programming

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A mixed-integer nonlinear programming approach to the optimal design of heat network in a polygeneration energy system

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APPLIED ENERGY 2014年 114卷 146-154页

作者： Zhang, Jianyun Liu, Pei Zhou, Zhe Ma, Linwei Li, Zheng Ni, Weidou Tsinghua Univ Dept Thermal Engn Tsinghua BP Clean Energy Res & Educ Ctr State Key Lab Power Syst Beijing 100084 Peoples R China

A large number of heat flows at various temperature and pressure levels exist in a polygeneration plant which co-produces electricity and chemical products. Integration of these external heat flows in a heat recovery steam generator (HRSG) has great potential to further enhance energy efficiency of such a plant;however, it is a challenging problem arising from the large design space of heat exchanger network. In this paper, a mixed-integer nonlinear programming model is developed for the design optimization of a HRSG with consideration of all alternative matches between the HRSG and external heat flows. This model is applied to four polygeneration cases with different HRSG types, and results indicate that the optimized heat network mainly depends on the HRSG type and the model specification. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Heat recovery steam generator Polygeneration mixed-integer nonlinear programming Design optimization

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Design and optimization of steam power systems in industrial parks based on the distributed steam turbine system

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Chinese Journal of Chemical Engineering 2025年第1期77卷 259-272页

作者： Lingwei Zhang Ziyuan Cui Yufei Wang School of Chemical Engineering and Environment China University of Petroleum(Beijing)Beijing 102249China

Steam power systems(SPSs)in industrial parks are the typical utility systems for heat and electricity *** SPSs,electricity is generated by steam turbines,and steam is generally produced and supplied at multiple levels to serve the heat demands of consumers with different temperature grades,so that energy is utilized in *** a large number of steam levels enhances energy utilization efficiency,it also tends to cause a complex steam pipeline network in the industrial *** practice,a moderate number of steam levels is always adopted in SPSs,leading to temperature mismatches between heat supply and demand for some *** study proposes a distributed steam turbine system(DSTS)consisting of main steam turbines on the energy supply side and auxiliary steam turbines on the energy consumption side,aiming to balance the heat production costs,the distance-related costs,and the electricity generation of SPSs in industrial parks.A mixed-integer nonlinear programming model is established for the optimization of SPSs,with the objective of minimizing the total annual cost(TAC).The optimal number of steam levels and the optimal configuration of DSTS for an industrial park can be determined by solving the model.A case study demonstrates that the TAC of the SPS is reduced by 220.6×10^(3)USD(2.21%)through the arrangement of auxiliary steam *** sub-optimal number of steam levels and a non-optimal operating condition slightly increase the TAC by 0.46%and 0.28%,*** sensitivity analysis indicates that the optimal number of steam levels tends to decrease from 3 to 2 as electricity price declines.

关键词： Industrial parks Steam power systems Distributed steam turbine system mixed-integer nonlinear programming Optimization Enthalpy

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Granularity for mixed-integer Polynomial Optimization Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2025年第2期205卷 1-24页

作者： Eggen, Carl Stein, Oliver Volkwein, Stefan Univ Konstanz Dept Math & Stat Universitatsstr 10 D-78464 Constance Germany Karlsruhe Inst Technol KIT Inst Operat Res Blucherstr 17 D-76185 Karlsruhe Germany

Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sum-of-squares-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sum-of-squares-hierarchy is hereby used to solve those continuous polynomial problems, which generalizes known methods from the literature. Numerical examples from the MINLPLib illustrate our approach.

关键词： mixed-integer nonlinear programming Granularity Rounding Polynomial optimization Semidefinite programming

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