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A new box selection criterion in interval Bernstein global optimization algorithm for MINLPs

GRANULAR COMPUTING 2020年第2期5卷 155-168页

作者： Patil, Bhagyesh V. Zidna, Ahmed Cambridge Ctr Adv Res & Educ Singapore Ltd 1 Create Way CREATE Campus Singapore 138602 Singapore Univ Lorraine Lab Gnie Informat Prod & Maintenance LGIPM Lorraine France

mixed-integer nonlinear programming (MINLP) problems are known to be challenging due to the involvement of nonlinear mathematical relations and combinatorial complexities. In this paper, an interval form-based Bernstein global optimization algorithm is presented to solve polynomial MINLP problems. The major contribution of this paper is a new box selection criterion for this interval form-based Bernstein global optimization algorithm. This new box selection criterion promotes fast convergence of the Bernstein algorithm. Moreover, the new box selection criterion allows the construction of a hybrid branch-and-bound framework for the Bernstein algorithm, wherein a local search method is used to obtain a good upper bound on the global minimum, and the Bernstein form is employed to obtain a valid lower bound on the global minimum. We show with numerical results that it is possible to obtain a significant reduction in the number of subdivisions required with this new box selection criterion. Furthermore, the Bernstein algorithm with this new box selection criterion is evaluated numerically on a variety of small- to medium-size MINLP problem instances and its performance is compared with the previously reported Bernstein global optimization algorithm as well as with a few state-of-the-art MINLP solvers. The results of the numerical studies demonstrate satisfactory performance in terms of the chosen performance metrics. Finally, the trim-loss minimization problem from the paper industry is solved to demonstrate the practical applicability of the Bernstein algorithm.

关键词： Bernstein polynomial form Global optimization Local search mixed-integer nonlinear programming Trim-loss minimization problem

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Price-and-verify: a new algorithm for recursive circle packing using Dantzig-Wolfe decomposition

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ANNALS OF OPERATIONS RESEARCH 2020年第2期284卷 527-555页

作者： Gleixner, Ambros Maher, Stephen J. Mueller, Benjamin Pedroso, Joao Pedro Zuse Inst Berlin Takustr 7 D-14195 Berlin Germany Univ Lancaster Dept Management Sci Lancaster LA1 4YX England Univ Porto Rua Campo Alegre P-4169007 Porto Portugal

Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig-Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a "price-and-verify" algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature.

关键词： mixed-integer nonlinear programming Dantzig-Wolfe decomposition Symmetry breaking Global optimization Recursive circle packing

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Optimal Life-Cycle Resilience Enhancement of Aging Power Distribution Systems: A MINLP-Based Preventive Maintenance Planning

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IEEE ACCESS 2020年 8卷 22324-22334页

作者： Dehghani, Nariman L. Darestani, Yousef Mohammadi Shafieezadeh, Abdollah Ohio State Univ Risk Assessment & Management Struct & Infrastruct Dept Civil Environm & Geodet Engn Columbus OH 43210 USA Rice Univ Dept Civil & Environm Engn Houston TX 77005 USA

Power distribution systems in the US are commonly supported by wood utility poles. These assets require regular maintenance to enhance the reliability of power delivery to support many dependent functions of the society. Limitations in budget, however, warrant efficient allocation of limited resources based on optimal preventive maintenance plans. A few studies have developed risk-based metrics to support risk-informed decision making in preventive maintenance planning for power distribution systems. However, integration of risk-based metrics and optimization for enhancing the life-cycle resilience of distribution systems has not been explored. To address this gap, this paper proposes a mixed-integer nonlinear programming (MINLP) model to maximize the life-cycle resilience of aging power distribution systems subject to multi-occurrences of hurricane events using an optimal risk-based maintenance planning. For this purpose, a risk-based index called the Expected Outages is proposed and integrated into the optimization problem to minimize the total expected number of power outages in the entire planning horizon. Various uncertainties in the performance of poles under stochastic occurrences of hazards are taken into account through advanced fragility models and an efficient recursive formulation that models the uncertainty of precedent pole failures. The proposed approach is applied to a large, realistic power distribution system for long-term maintenance planning given a total budget limit and different levels of periodic budget constraints. The resulting optimization problems are solved through the branch and bound algorithm. Results indicate that applying the presented methodology leads to a significant enhancement of the life-cycle resilience of distribution systems compared to the commonly implemented strength-based maintenance strategy set by National Electric Safety Code.

关键词： mixed-integer nonlinear programming hurricane hazards power distribution systems preventive maintenance resilience enhancement

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A whole-year simulation study on nonlinear mixed-integer model predictive control for a thermal energy supply system with multi-use components

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APPLIED ENERGY 2020年 258卷 114064-000页

作者： Buerger, Adrian Bohlayer, Markus Hoffmann, Sarah Altmann-Dieses, Angelika Braun, Marco Diehl, Moritz Karlsruhe Univ Appl Sci Fac Management Sci & Engn Moltkestr 30 D-76133 Karlsruhe Germany Univ Freiburg Syst Control & Optimizat Lab Dept Microsyst Engn IMTEK Georges Koehler Allee 102 D-79110 Freiburg Germany Friedrich Alexander Univ Erlangen Nurnberg Sch Business & Econ Lange Gasse 20 D-90403 Nurnberg Germany Univ Freiburg Dept Math Ernst Zermelo Str 1 D-79104 Freiburg Germany

This work presents a whole-year simulation study on nonlinear mixed-integer Model Predictive Control (MPC) for a complex thermal energy supply system which consists of a heat pump, stratified water storages, free cooling facilities, and a large underground thermal storage. For solution of the arising mixed-integer Non-Linear Programs (MINLPs) we apply an existing general and optimal-control-suitable decomposition approach. To compensate deviation of forecast inputs from measured disturbances, we introduce a moving horizon estimation step within the MPC strategy. The MPC performance for this study, which consists of more than 50,000 real-time suitable MINLP solutions, is compared to an elaborate conventional control strategy for the system. It is shown that MPC can significantly reduce the yearly energy consumption while providing a similar degree of constraint satisfaction, and autonomously identify previously unknown, beneficial operation modes.

关键词： Model predictive control Energy systems mixed-integer nonlinear programming

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A comparative study of multi-objective optimization methodologies for molecular and process design

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COMPUTERS & CHEMICAL ENGINEERING 2020年 136卷 106802-000页

作者： Lee, Ye Seol Graham, Edward J. Galindo, Amparo Jackson, George Adjiman, Claire S. Imperial Coll London Ctr Proc Syst Engn Inst Mol Sci & Engn Dept Chem Engn South Kensington Campus London SW7 2AZ England

The need to consider multiple objectives in molecular design, whether based on techno-economic, environmental or health and safety metrics is increasingly recognized. There is, however, limited understanding of the suitability of different multi-objective optimization (MOO) algorithm for the solution of such design problems. In this work, we present a systematic comparison of the performance of five mixed-integer non-linear programming (MINLP) MOO algorithms on the selection of computer-aided molecular design (CAMD) and computer-aided molecular and process design (CAMPD) problems. The five methods are designed to address the discrete and nonlinear nature of the problem, with the aim of generating an accurate approximation of the Pareto front. They include: a weighted sum approach without global search phases (SWS), a weighted sum approach with simulated annealing (WSSA), a weighted sum approach with multi level single linkage (WSML), the sandwich algorithm with MLSL (SDML) and the non dominated sorting genetic algorithm-II (NSGA-II). The algorithms are compared systematically in two steps. The effectiveness of the global search methods is evaluated with SWS, WSSA and WSML. WSML is found to be most effective and a comparative analysis of WSML, SDML and NSGA-II is then undertaken. As a test set of these optimization techniques, two CAMD and one CAMPD problems of varying dimensionality are formulated as case studies. The results show that the SDML provides the most efficient generation of a diverse set of Pareto points, leading to the construction of an approximate Pareto front close to exact Pareto front. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Computer-aided molecular design Computer-aided molecular and process design Multi-objective optimization mixed-integer nonlinear programming Global optimization

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An exact MINLP model for optimal location and sizing of DGs in distribution networks: A general algebraic modeling system approach

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AIN SHAMS ENGINEERING JOURNAL 2020年第2期11卷 409-418页

作者： Danilo Montoya, Oscar Gil-Gonzalez, Walter Grisales-Norena, L. F. Univ Tecnol Bolivar Programa Ingn Elect & Ingn Elect Km 1 Via Turbaco Cartagena Colombia Univ Tecnol Pereira AA 97 Pereira 660003 Colombia Inst Tecnol Metropolitano Medellin 050012 Colombia

This paper addresses the classical problem of optimal location and sizing of distributed generators (DGs) in radial distribution networks by presenting a mixed-integer nonlinear programming (MINLP) model. To solve such model, we employ the General Algebraic Modeling System (GAMS) in conjunction with the BONMIN solver, presenting its characteristics in a tutorial style. To operate all the DGs, we assume they are dispatched with a unity power factor. Test systems with 33 and 69 buses are employed to validate the proposed solution methodology by comparing its results with multiple approaches previously reported in the specialized literature. A 27-node test system is also used for locating photovoltaic (PV) sources considering the power capacity of the Caribbean region in Colombia during a typical sunny day. Numerical results confirm the efficiency and accuracy of the MINLP model and its solution is validated through the GAMS package. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.

关键词： Distributed generation Distribution systems General algebraic modeling system mixed-integer nonlinear programming Optimal location and sizing of distributed generation

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Energy and water optimization of an integrated bioethanol production process from molasses and sugarcane bagasse: A Colombian case

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FUEL 2020年 260卷 116314-000页

作者： Valderrama, Claudia Quintero, Viviana Kafarov, Viatcheslav Ind Univ Santander Physicochem Engn Dept Chem Engn 9 St 27 Santander Colombia Marina Univ Environm Engn Calle 18 34-104 Pasto Narino Colombia

In the present paper, an integrated scheme of first and second-generation bioethanol production is proposed to increase the yield and decreasing thermal energy and freshwater requirements. In this sense, an energy consumption reduction of the integrated process was evaluated through heat exchangers network integration, applying mathematical programming. Then, to reduce freshwater consumption, streams with water disposal for reuse in the process was evaluated, formulating the problem as a mixed-integer nonlinear programming problem (MINLP). Bioethanol production from the integrated scheme increased at least 40% compared it with sugar-bioethanol production scheme. The heat exchanger network with the minimum annual cost was identified. Around of 16% of freshwater consumption was minimized using a nonconvex nonlinear programming NLP. The integration of second-generation bioethanol to a sugar-bioethanol process could increase, the bioethanol production in Colombia, without an energy and water excessive consumption.

关键词： Bioethanol Exergy analysis Heat integration Water integration mixed-integer nonlinear programming

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Automated patient-robot assignment for a robotic rehabilitation gym: a simplified simulation model

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JOURNAL OF NEUROENGINEERING AND REHABILITATION 2022年第1期19卷 126-126页

作者： Miller, Benjamin A. Adhikari, Bikranta Jiang, Chao Novak, Vesna D. Univ Wyoming Dept Elect & Comp Engn 1000 E Univ Ave Laramie WY 82071 USA Univ Cincinnati Dept Elect Engn & Comp Sci 2600 Clifton Ave Cincinnati OH 45221 USA

Background A robotic rehabilitation gym can be defined as multiple patients training with multiple robots or passive sensorized devices in a group setting. Recent work with such gyms has shown positive rehabilitation outcomes;furthermore, such gyms allow a single therapist to supervise more than one patient, increasing cost-effectiveness. To allow more effective multipatient supervision in future robotic rehabilitation gyms, we propose an automated system that could dynamically assign patients to different robots within a session in order to optimize rehabilitation outcome. Methods As a first step toward implementing a practical patient-robot assignment system, we present a simplified mathematical model of a robotic rehabilitation gym. mixed-integer nonlinear programming algorithms are used to find effective assignment and training solutions for multiple evaluation scenarios involving different numbers of patients and robots (5 patients and 5 robots, 6 patients and 5 robots, 5 patients and 7 robots), different training durations (7 or 12 time steps) and different complexity levels (whether different patients have different skill acquisition curves, whether robots have exit times associated with them). In all cases, the goal is to maximize total skill gain across all patients and skills within a session. Results Analyses of variance across different scenarios show that disjunctive and time-indexed optimization models significantly outperform two baseline schedules: staying on one robot throughout a session and switching robots halfway through a session. The disjunctive model results in higher skill gain than the time-indexed model in the given scenarios, and the optimization duration increases as the number of patients, robots and time steps increases. Additionally, we discuss how different model simplifications (e.g., perfectly known and predictable patient skill level) could be addressed in the future and how such software may eventually be used in practice. Conclu

关键词： Rehabilitation robotics Rehabilitation gym Group rehabilitation Optimization Mathematical modeling Task scheduling mixed-integer nonlinear programming

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Turnpike Properties in Discrete-Time mixed-integer Optimal Control

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IEEE CONTROL SYSTEMS LETTERS 2020年第3期4卷 704-709页

作者： Faulwasser, Timm Murray, Alexander TU Dortmund Univ Inst Energy Syst Energy Efficiency & Energy Econ D-44227 Dortmund Germany Karlsruhe Inst Technol Inst Automat & Appl Informat D-76131 Karlsruhe Germany

This note discusses properties of parametric discrete-time mixed-integer Optimal Control Problems (MIOCPs) as they often arise in model predictive control with discrete controls. We argue that, in want for a handle on similarity properties of parametric MIOCPs, the turnpike phenomenon known in optimal control is helpful. We provide sufficient turnpike conditions based on a dissipativity notion of MIOCPs, and we prove that the turnpike phenomenon allows specific and accurate guesses for the discrete controls. We also derive an easily checkable sufficient condition for dissipativity of linear-quadratic MIOCPs. Moreover, we show how the turnpike property can be used to derive efficient node-weighted branch-and-bound schemes tailored to parametric MIOCPs. We draw upon numerical examples to illustrate our findings.

关键词： Optimal control Steady-state Predictive control Optimization Sensitivity Economics Indexes Optimal control dissipativity mixed-integer optimization mixed-integer nonlinear programming

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Voltage and Reactive Power Optimization Using a Simplified Linear Equations at Distribution Networks with DG

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ENERGIES 2020年第13期13卷 3334-3334页

作者： Go, Seok-Il Yun, Sang-Yun Ahn, Seon-Ju Choi, Joon-Ho Chonnam Natl Univ Dept Elect Engn Gwangju 61186 South Korea

In this paper, the VVO (Volt/Var optimization) is proposed using simplified linear equations. For fast computation, the characteristics of voltage control devices in a distribution system are expressed as a simplified linear equation. The voltage control devices are classified according to the characteristics of voltage control and represented as the simplified linear equation. The estimated voltage of distribution networks is represented by the sum of the simplified linear equations for the voltage control devices using the superposition principle. The voltage variation by the reactive power of distributed generations (DGs) can be expressed as the matrix of reactance. The voltage variation of tap changing devices can be linearized into the control area factor. The voltage variation by capacitor banks can also be expressed as the matrix of reactance. The voltage equations expressed as simplified linear equations are formulated by quadratic programming (QP). The variables of voltage control devices are defined, and the objective function is formulated as the QP form. The constraints are set using operating voltage range of distribution networks and the control ranges of each voltage control device. In order to derive the optimal solution, mixed-integer quadratic programming (MIQP), which is a type of mixed-integer nonlinear programming (MINLP), is used. The optimal results and proposed method results are compared by using MATLAB simulation and are confirmed to be close to the optimal solution.

关键词： Volt Var optimization distributed generation OLTC (On Load Tap Changer) mixed-integer nonlinear programming quadratic programming

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