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Decision regions and decision boundaries of generalizedKmean algorithm based on various norm criteria

MULTIMEDIA TOOLS AND APPLICATIONS 2020年第41-42期79卷 30669-30684页

作者： Wang, Xinpeng Ling, Bingo Wing-Kuen Guangdong Univ Technol Fac Informat Engn Guangzhou 510006 Peoples R China

This paper derives the decision regions and the decision boundaries of the generalizedKmean algorithms based on theL(1)norm criterion, theL(2)norm criterion and theL(infinity)norm criterion. The decision boundaries of these three generalizedKmean algorithms are all linear hyperplanes. However, the total numbers of the decision boundaries of the generalizedKmean algorithms based on both theL(1)norm criterion and theL(infinity)norm criterion are more than that based on theL(2)norm criterion. On the other hand, the decision regions of the generalizedKmean algorithm based on theL(2)norm criterion are convex while that based on both theL(1)norm criterion and theL(infinity)norm criterion are in general nonconvex. The computer numerical simulations on a toy example demonstrate the above phenomena. Besides, two examples are illustrated. The first example on the patent image retrieval system shows that the recognition accuracies of using the generalizedKmean algorithms based on theL(2)norm criterion, theL(1)norm criterion and theL(infinity)norm criterion are 58.25%, 61% and 58.75%, respectively. The second example on the electromyogram based Parkinson's disease detection system shows that the recognition accuracies of using the generalizedKmean algorithms based on theL(2)norm criterion, theL(1)norm criterion and theL(infinity)norm criterion are 60%, 60% and 67%, respectively, if the signals are classified directly in the time domain. On the other hand, the recognition accuracies of the generalizedKmean algorithms based on theL(2)norm criterion, theL(1)norm criterion and theL(infinity)norm criterion are 60%, 87% and 60%, respectively, if the signals are classified directly in the discrete cosine transform domain. The improvements are due to the nonconvexity of the decision regions of the generalizedKmean algorithm based on theL(1)norm criterion and theL(infinity)norm criterion.

关键词： GeneralizedKmean algorithms Decision regions Decision boundaries Nonconvex set mixed integer quadratic programming mixed integer linear programming

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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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Obstacle avoidance handling and mixed integer predictive control for space robots

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ADVANCES IN SPACE RESEARCH 2018年第8期61卷 1997-2009页

作者： Zong, Lijun Luo, Jianjun Wang, Mingming Yuan, Jianping Northwestern Polytech Univ Sch Astronaut Xian Shaanxi Peoples R China Natl Key Lab Aerosp Flight Dynam Xian Shaanxi Peoples R China

This paper presents a novel obstacle avoidance constraint and a mixed integer predictive control (MIPC) method for space robots avoiding obstacles and satisfying physical limits during performing tasks. Firstly, a novel kind of obstacle avoidance constraint of space robots, which needs the assumption that the manipulator links and the obstacles can be represented by convex bodies, is proposed by limiting the relative velocity between two closest points which are on the manipulator and the obstacle, respectively. Furthermore, the logical variables are introduced into the obstacle avoidance constraint, which have realized the constraint form is automatically changed to satisfy different obstacle avoidance requirements in different distance intervals between the space robot and the obstacle. Afterwards, the obstacle avoidance constraint and other system physical limits, such as joint angle ranges, the amplitude boundaries of joint velocities and joint torques, are described as inequality constraints of a quadratic programming (QP) problem by using the model predictive control (MPC) method. To guarantee the feasibility of the obtained multi-constraint QP problem, the constraints are treated as soft constraints and assigned levels of priority based on the propositional logic theory, which can realize that the constraints with lower priorities are always firstly violated to recover the feasibility of the QP problem. Since the logical variables have been introduced, the optimization problem including obstacle avoidance and system physical limits as prioritized inequality constraints is termed as MIPC method of space robots, and its computational complexity as well as possible strategies for reducing calculation amount are analyzed. Simulations of the space robot unfolding its manipulator and tracking the end-effector's desired trajectories with the existence of obstacles and physical limits are presented to demonstrate the effectiveness of the proposed obstacle avoidance s

关键词： Space robots Obstacle avoidance Model predictive control Constraint priority mixed integer quadratic programming

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Hybrid predictive controller for overheating prevention of solar collectors

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RENEWABLE ENERGY 2019年 136卷 535-547页

作者： Elias, Tiago de Araujo da Costa Mendes, Paulo Renato Normey-Rico, Julio Elias Univ Fed Santa Catarina Dept Automat & Syst Florianopolis SC Brazil

In this paper, an advanced control algorithm is presented for avoiding fluid overheating when operating solar thermal plants. The control algorithm manipulates the fluid rate to maintain the field output temperature in the desired reference, and defocus the solar collectors when the temperature reaches a maximum limit. Several simulation scenarios are considered for the test of the proposed controller using a lumped parameters model of the solar collectors that has been validated in real plants. A discussion is carried out aiming at analyzing the behavior of the controlled solar plant, and comparing the characteristics and performance of the proposed algorithms. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Overheating control Solar energy Practical nonlinear model predictive control mixed integer quadratic programming

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A Distributed Black-Start Optimization Method for Global Transmission and Distribution Network

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第5期36卷 4471-4481页

作者： Zhao, Jinquan Zhang, Qiang Liu, Ziwen Wu, Xiaokang Hohai Univ Coll Energy & Elect Engn Nanjing 210098 Peoples R China

With the large-scale integration of distributed generators (DGs), the coupling relations between transmission network (TN) and distribution networks (DNs) are getting closer. Coordinating the black-start processes of TN and DNs is beneficial to improving restoration efficiency. Therefore, a distributed black-start optimization method for global transmission and distribution (T&D) network is proposed in this paper. Firstly, a black-start optimization model of global T&D network is established to minimize the outage costs. Then, it is decomposed into the TN black-start optimization sub-problem and several DN black-start optimization sub-problems based on the analytical target cascading (ATC). The mixed integer quadratic programming (MIQP) is used for sub-problem modeling. The models take into account the restoration operations of different grid components at each black-start time step. The transmission control center (TCC) and distribution control centers (DCCs) only need to exchange partial information including the boundary power at each time step for distributed coordination, to obtain the coordinated black-start scheme for T&D network. Finally, the effectiveness of the proposed model and method is validated using a global T&D network case.

关键词： Optimization Generators Manganese Load modeling Distribution networks Couplings Reactive power Black-start transmission and distribution coordination analytical target cascading mixed integer quadratic programming outage cost

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The generalized balanced academic curriculum problem with heterogeneous classes

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ANNALS OF OPERATIONS RESEARCH 2014年第1期218卷 147-163页

作者： Ceschia, Sara Di Gaspero, Luca Schaerf, Andrea Univ Udine DIEGM I-33100 Udine Italy

We propose an extension of the Generalized Balanced Academic Curriculum Problem (GBACP), a relevant planning problem arising in many universities. The problem consists of assigning courses to teaching terms and years, satisfying a set of precedence constraints and balancing students' load among terms. Differently from the original GBACP formulation, in our case, the same course can be assigned to different years for different curricula (i.e., the predetermined sets of courses from which a student can choose), leading to a more complex solution space. The problem is tackled by both integer programming (IP) methods and combinations of metaheuristics based on local search. The experimental analysis shows that the best results are obtained by means of a two-stage metaheuristic that first computes a solution for the underlying GBACP and then refines it by searching in the extended solution space.

关键词： Timetabling Simulated Annealing Academic Planning mixed integer quadratic programming

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A new method for mean-variance portfolio optimization with cardinality constraints

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ANNALS OF OPERATIONS RESEARCH 2013年第1期205卷 213-234页

作者： Cesarone, Francesco Scozzari, Andrea Tardella, Fabio Univ Roma Tre Dipartimento Econ I-00145 Rome Italy Univ Niccolo Cusano Fac Econ I-00182 Rome Italy Univ Roma La Sapienza Dipartimento Metodi & Modelli Econ I-00161 Rome Italy

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM) model, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model based on a reformulation as a Standard quadratic Program, on a new lower bound that we establish, and on other recent theoretical and computational results for such problem. These results lead to an exact algorithm for solving the LAM model for small size problems. For larger problems, such algorithm can be relaxed to an efficient and accurate heuristic procedure that is able to find the optimal or the best-known solutions for problems based on some standard financial data sets that are used by several other authors. We also test our method on five new data sets involving real-world capital market indices from major stock markets. We compare our results with those of CPLEX and with those obtained with very recent heuristic approaches in order to illustrate the effectiveness of our method in terms of solution quality and of computation time. All our data sets and results are publicly available for use by other researchers.

关键词： Portfolio management mixed integer quadratic programming Standard quadratic optimization Cardinality constraints

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Exact and heuristic approaches for the index tracking problem with UCITS constraints

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ANNALS OF OPERATIONS RESEARCH 2013年第1期205卷 235-250页

作者： Scozzari, Andrea Tardella, Fabio Paterlini, Sandra Krink, Thiemo Univ Niccolo Cusano Rome Italy Univ Roma La Sapienza Rome Italy Univ Modena & Reggio E Dept Econ RECent Modena Italy Univ Modena & Reggio E CEFIN Modena Italy EBS Dept Finance Accounting & Real Estate Wiesbaden Germany Allianz Global Investors Europe GmbH Frankfurt Main Germany

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far. The aim of this paper is twofold. First, we present the first mixed integer quadratic programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Differential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches.

关键词： Index tracking mixed integer quadratic programming Stochastic search heuristics Differential evolution Cardinality constraints

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Stochastic Modeling of Natural Gas Infrastructure Development in Europe under Demand Uncertainty

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ENERGY JOURNAL 2016年第3-Sup期37卷 5-32页

作者： Fodstad, Marte Egging, Ruud Midthun, Kjetil Tomasgard, Asgeir SINTEF Technol & Soc Dept Appl Econ Trondheim Norway Norwegian Univ Sci & Technol Dept Ind Econ & Technol Management Trondheim Norway

We present an analysis of the optimal development of natural gas infrastructure in Europe based on the scenario studies of Holz and von Hirschhausen (2013). We use a stochastic mixed integer quadratic model to analyze the impact of uncertainty about future natural gas consumption in Europe on optimal investments in pipelines. Our data is based on results from the PRIMES model of natural gas demand and technology scenarios discussed in Knopf et al. (2013). We present a comparison between the results from the stochastic model and the expected value model, as well as an analysis of the individual scenarios. We also performed sensitivity analyses on the probabilities of the future scenarios. Comparison of the results from the stochastic model to those of a deterministic expected value model reveals a negligible Value of the Stochastic Solution. We do, however, find structurally different infrastructure solutions in the stochastic and the deterministic models. Regarding infrastructure expansions, we find that 1) the largest pipeline investments will be towards Asia, 2) there is a trend towards a larger gas supply from Africa to Europe, and 3) within Europe, eastward connections will be strengthened. Our main finding using the stochastic approach is that there is limited option value in delaying investments in natural gas infrastructure, until more information is available regarding policy and technology in 2020, due to the low costs of overcapacity.

关键词： Natural gas Infrastructure mixed integer quadratic programming Stochastic modeling

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Numerical experience with lower bounds for MIQP branch-and-bound

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SIAM JOURNAL ON OPTIMIZATION 1998年第2期8卷 604-616页

作者： Fletcher, R Leyffer, S Univ Dundee Dept Math Dundee DD1 4HN Scotland

The solution of convex mixed-integer quadratic programming (MIQP) problems with a general branch-and-bound framework is considered. It is shown how lower bounds can be computed efficiently during the branch-and-bound process. Improved lower bounds such as the ones derived in this paper can reduce the number of quadratic programming (QP) problems that have to be solved. The branch-and-bound approach is also shown to be superior to other approaches in solving MIQP problems. Numerical experience is presented which supports these conclusions.

关键词： integer programming mixed integer quadratic programming branch-and-bound

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