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Structural learning of the Boltzmann machine and its application to life cycle management

NEUROCOMPUTING 2011年第12-13期74卷 2193-2200页

作者： Yaakob, Shamshul Bahar Watada, Junzo Fulcher, John Waseda Univ Grad Sch Informat Prod & Syst Kitakyushu Fukuoka 8080135 Japan Univ Wollongong Sch Comp Sci & Software Engn Wollongong NSW 2522 Australia

The objective of this research is to realise structural learning within a Boltzmann machine (BM), which enables the effective solution of problems defined as mixed integer quadratic programming. Simulation results show that computation time is reduced by up to one-fifth compared to conventional BMs. The computational efficiency of the resulting double-layer BM is approximately expressed as the ratio n divided by N, where n is the number of selected units (neurons/nodes) and N is the total number of units. The double-layer BM was applied to efficiently solve a mean-variance problem using mathematical programming with two objectives: the minimisation of risk and the maximisation of expected return. Finally, the effectiveness of our method is illustrated by way of a life cycle management example. The double-layer BM was able to more effectively select results with lower computational overhead. The results also enable us to more easily understand the internal structure of the BM. Using our proposed model, decision makers are able to select the best solution based on their risk preference from the alternative solutions provided by the proposed method. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Structural learning Hopfield network Boltzmann machine (BM) Double-layer BM mixed integer quadratic programming Life cycle management

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Real-time train regulation method for metro lines with substation peak power reduction

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年 168卷

作者： Jin, Bo Feng, Xiaoyun Wang, Qingyuan Sun, Pengfei Southwest Jiaotong Univ Sch Elect Engn Chengdu 611756 Peoples R China

In high-frequency metro lines, train delays and substation peak power often occur, affecting safe and efficient train operation. In this paper, we propose real-time train regulation methods considering substation peak power reduction, in which runtimes and dwelltimes are adjusted to minimize the timetable and headway deviations and avoid multiple train accelerating. Firstly, we proposed two indirect indicators, i.e. overlapping time between accelerating phases and overlapping quantity between accelerating phases, which are minimized to suppress substation peak power in joint optimal train regulation models. The joint optimal train regulation models are based on the traditional real-time train regulation model considering the train traffic dynamics and control constraints. For the real-time requirement of train regulation, model predictive control (MPC) algorithms are designed to solve the formulated joint optimal control models, which generate the optimal train regulation strategies at each control cycle based on the real-time updated feedback system states. Finally, numerical examples based on one of the Guangzhou metro lines are implemented to verify the effectiveness and robustness of the proposed methods. The results show that the train regulation strategy with minimizing the overlapping quantity can not only suppress train delays and substation peak power, but also meet the real-time computation requirement.

关键词： Urban rail transit Timetable rescheduling Model predictive control mixed integer quadratic programming

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On support vector machines under a multiple-cost scenario

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2019年第3期13卷 663-682页

作者： Benitez-Pena, Sandra Blanquero, Rafael Carrizosa, Emilio Ramirez-Cobo, Pepa Univ Seville Inst Matemat IMUS Seville Spain Univ Seville Dept Estadist & Invest Operat Seville Spain Univ Cadiz Dept Estadist & Invest Operat Cadiz Spain

Support vector machine (SVM) is a powerful tool in binary classification, known to attain excellent misclassification rates. On the other hand, many realworld classification problems, such as those found in medical diagnosis, churn or fraud prediction, involve misclassification costs which may be different in the different classes. However, it may be hard for the user to provide precise values for such misclassification costs, whereas it may be much easier to identify acceptable misclassification rates values. In this paper we propose a novel SVM model in which misclassification costs are considered by incorporating performance constraints in the problem formulation. Specifically, our aim is to seek the hyperplane with maximal margin yielding misclassification rates below given threshold values. Such maximal margin hyperplane is obtained by solving a quadratic convex problem with linear constraints and integer variables. The reported numerical experience shows that our model gives the user control on the misclassification rates in one class (possibly at the expense of an increase in misclassification rates for the other class) and is feasible in terms of running times.

关键词： Constrained classification Misclassification costs mixed integer quadratic programming Sensitivity specificity trade-off Support vector machines

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A novel agent-based microgrid optimal control for grid-connected, planned island and emergency island operations

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2016年第9期26卷 1999-2022页

作者： Selakov, Aleksandar Bekut, Dusko Saric, Andrija T. Fac Tech Sci Dept Power Elect & Conmmun Engn Novi Sad Serbia

This paper presents an analysis of three typical microgrid operation modes. First is the analysis of the grid-connected mode, in which the main goal is to optimize the microgrid operation (in terms of economics, carbon emissions and/or reliability) when it is connected with the main grid. Second is the analysis of the planned island mode, in which the main goal is to provide a stable and smooth transition from grid-connected to island mode while keeping both the frequency and the voltages within the required limits. Finally, the paper presents the analysis of the emergency island mode, which occurs after sudden islanding, in which the main goal is to maintain the energization of critical customers. The objectives and the operation strategies of microgrid management are different in each operation mode. This paper proposes a novel, centralized, multi-agent-based, microgrid controller architecture, which provides the coordination of all three operation modes and enables the easy configuration/combination of optimization goals that are subject to a given set of operational constraints. The microgrid controller consists of a real-time agent (responsible for closed loop control and maintenance of the system's frequency), an operation planning agent [responsible for near-term (15 minutes up to 24 hours) and short-term (1 to 7 days) optimization] and a state agent (responsible for overall monitoring, management and coordination of the other two agents). A microgrid controller with the aforementioned agents has been developed and tested. The simulation results are presented for a typical microgrid test example. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： microgrid controller software agent optimization mixed integer quadratic programming

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Globally optimal clusterwise regression by mixed logical-quadratic programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第1期212卷 213-222页

作者： Carbonneau, Real A. Caporossi, Gilles Hansen, Pierre GERAD Montreal PQ H3T 2A7 Canada HEC Montreal Montreal PQ H3T 2A7 Canada

Exact global optimization of the clusterwise regression problem is challenging and there are currently no published feasible methods for performing this clustering optimally, even though it has been over thirty years since its original proposal. This work explores global optimization of the clusterwise regression problem using mathematical programming and related issues. A mixed logical-quadratic programming formulation with implication of constraints is presented and contrasted against a quadratic formulation based on the traditional big-M, which cannot guarantee optimality because the regression line coefficients, and thus errors, may be arbitrarily large. Clusterwise regression optimization times and solution optimality for two clusters are empirically tested on twenty real datasets and three series of synthetic datasets ranging from twenty to one hundred observations and from two to ten independent variables. Additionally, a few small real datasets are clustered into three lines. (C) 2011 Elsevier B.V. All rights reserved.

关键词： mixed integer quadratic programming mixed logical-quadratic programming Global optimization Combinatorial optimization Clusterwise regression Clustering

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Global optimization algorithm for mixed integer quadratically constrained quadratic program

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2017年 319卷 159-169页

作者： Zhao, Yingfeng Liu, Sanyang Xidian Univ Sch Math & Stat Xian 710071 Peoples R China Henan Inst Sci & Technol Sch Math Sci Xinxiang 453003 Peoples R China

mixed integer quadratic programs with quadratic constraints (MIQQP) occur frequently in various areas of engineering practice and management science, but most solution methods for this kind of problems are often designed for its special cases. In this paper, we present a simple global optimization algorithm for solving problem (MIQQP). We first convert problem (MIQQP) into an equivalent generalized bilinear programming problem with integer variables (EIQQP). We next show that replacing the quadratic objective and constraint functions with their convex envelopes is dominated by an alternative methodology based on convexifying the range of the bilinear terms on the feasible region. Finally, by incorporating the reduction-correction techniques and sampling strategies into the branch and bound scheme, the proposed algorithm is developed for solving (MIQQP). Convergence and optimality of the algorithm are presented and numerical examples taken from some recent literature and MINLPLib2 are carried out to validate the performance of the proposed algorithm. (C) 2017 Elsevier B.V. All rights reserved.

关键词： mixed integer quadratic programming Global optimization Branch and bound

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Timetable optimization for maximization of regenerative braking energy utilization in traction network of urban rail transit

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年第1期183卷

作者： Sun, Pengfei Zhang, Chuanxin Jin, Bo Wang, Qingyuan Geng, Haoran Southwest Jiaotong Univ Sch Elect Engn Chengdu 611756 Peoples R China POWERCHINA Jiangxi Elect Power Engn Co LTD Nanchang 330096 Peoples R China Zhejiang Sci Res Inst Transport Hangzhou 311305 Peoples R China Sophia Univ Green Sci & Engn Div Tokyo Japan

Timetable optimization is one of the effective solution methods for urban rail transit to achieve energy-saving. Previous studies on timetable optimization only focused on the transfer and utilization of mechanical energy, which did not consider the exchange of energy and line losses in the traction network. Therefore, this paper constructs a cross-substation energy transmission and utilization model taking into account the characteristics of the actual traction power supply systems. An overlap current method is presented to increase the utilization of regenerative braking energy (RBE) of trains and reduce the energy supply of the traction substation by considering the line loss, which is achieved by compensating the current generated by accelerating and braking trains in the substation. The compensation current can be maximized by adjusting the dwell time to achieve energy-saving. The traction power supply systems with highly nonlinear dynamic characteristics are linearized to construct a mixed-integer linear programming (MILP) model, which utilizes the utilization of RBE as the objection and dwell time as the variable. The method of maximum compensation current is verified by numerical examples based on Beijing Batong Line. The results show that the energy-efficient of the method is greatly improved compared with the method of maximizing the overlap time between the accelerating train and the braking train.

关键词： Urban rail transit Traction network Timetable optimization mixed integer quadratic programming The overlap current method

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Self-scheduling of a power generating company: Carbon tax considerations

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COMPUTERS & OPERATIONS RESEARCH 2016年 66卷 384-392页

作者： Liu, Sidong Chevallier, Julien Zhu, Bangzhu Wuyi Univ Sch Math & Computat Sci Jiangmen 529020 Guangdong Peoples R China IPAG Business Sch IPAG Lab F-75006 Paris France Jinan Univ Sch Management Guangzhou 510632 Guangdong Peoples R China Univ Paris 08 LED F-93526 St Denis France

The Carbon Tax Self-Scheduling (CTSS) model for a power generating company (GENCO) is proposed in light of the deregulated electricity market environment. The model analyses the effects of GENCO profits and emissions profiles under different carbon tax scenarios, by valuing the specific part of the cost which affects the environment. The resolution method provides first a mixed integer quadratic programming (MIQP) formulation of the CTSS problem. Second, using piece-wise linearisation approximation methods, the MIQP formulation is transformed into a mixed integer Linear programming (MILP) system. Simulation results of 10-100 unit systems over 24 h show that the MILP formulation is efficient and precise when calculating problems of such a large scale. We conclude that the increase of carbon tax reduces carbon emissions and the reduction effect is more favorable in the case of relatively modest carbon tax. The profit of GENCO is unnecessarily negatively related to the carbon tax, while it is determined by the increased rate of electricity price. The increase of carbon tax may inhibit demand. However, the inhibiting effect may be weakened when considering increases in electricity prices combined with the carbon tax. (c) 2015 Elsevier Ltd. All rights reserved.

关键词： Carbon Tax Self-Scheduling model Power generating company mixed integer quadratic programming Piecewise linearisation approximation mixed integer Linear programming

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Hybrid model predictive control techniques for safety factor profile and stored energy regulation while incorporating NBI constraints

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NUCLEAR FUSION 2024年第8期64卷 086052-086052页

作者： Leard, Brian Wang, Zibo Paruchuri, Sai Tej Schuster, Eugenio Rafiq, Tariq Lehigh Univ Bethlehem PA 18015 USA

A novel hybrid Model Predictive Control (MPC) algorithm has been designed for simultaneous safety factor (q) profile and stored energy (w) control while incorporating the pulse-width-modulation constraints associated with the neutral beam injection (NBI) system. Regulation of the q-profile has been extensively shown to be a key factor for improved confinement as well as non-inductive sustainment of the plasma current. Simultaneous control of w is necessary to prevent the triggering of pressure-driven magnetohydrodynamic instabilities as the controller shapes the q profile. Conventional MPC schemes proposed for q-profile control have considered the NBI powers as continuous-time signals, ignoring the discrete-time nature of these actuators and leading in some cases to performance loss. The hybrid MPC scheme in this work has the capability of incorporating the discrete-time actuator dynamics as additional constraints. In nonlinear simulations, the proposed hybrid MPC scheme demonstrates improved q-profile+w control performance for NSTX-U operating scenarios.

关键词： hybrid system model predictive control discrete constraints pulse-width modulation mixed integer quadratic programming safety factor profile

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Flight Routing and Scheduling Under Departure and En Route Speed Uncertainty

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2020年第5期21卷 1915-1928页

作者： Sandamali, Gammana Guruge Nadeesha Su, Rong Zhang, Yicheng Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

Demand uncertainty is one critical form of uncertainty which has an adverse effect on Air traffic flow management (ATFM). This is mainly due to the deviation in departure time and aircraft speed from their scheduled values. This may lead to the arrival of aircraft to certain routes at unscheduled times, causing an unexpected demand on those routes. The uncertainty of demand creates several difficulties in air transportation systems, including higher workloads for air traffic controllers, higher delays, travel costs, as well as safety risk. In this study, we propose a robust flight routing and scheduling scheme while considering both departure and speed uncertainty present in the air traffic network. Following robust optimization, we ensure that the capacity violations are eliminated from the system. The ATFM problem is formulated as a mixed integer quadratic programming (MIQP) problem with the objective of minimizing expected total delay of the system while maintaining required in-trail separation between aircraft even under uncertainty. In addition, we use an optimal flight level assignment method and speed assignment strategy to minimize the system delay and to fully utilize the system capacity. Furthermore, a greedy strategy with parallel computation is presented with the problem decomposed into a set of maximum independent sets to reduce the computational complexity in solving large-scale ATFM problems. With the experimental results, we demonstrate the effectiveness of the model.

关键词： Uncertainty Atmospheric modeling Computational modeling Aircraft Delays Routing Safety Air traffic flow management maximum independent sets mixed integer quadratic programming optimization routing and scheduling uncertainty

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