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Conditional gradient method for multiobjective optimization

COMPUTATIONAL optimization AND APPLICATIONS 2021年第3期78卷 741-768页

作者： Assuncao, P. B. Ferreira, O. P. Prudente, L. F. Univ Fed Goias Inst Matemat & Estat BR-74001970 Goiania Go Brazil

We analyze the conditional gradient method, also known as Frank-Wolfe method, for constrained multiobjective optimization. The constraint set is assumed to be convex and compact, and the objectives functions are assumed to be continuously differentiable. The method is considered with different strategies for obtaining the step sizes. Asymptotic convergence properties and iteration-complexity bounds with and without convexity assumptions on the objective functions are stablished. Numerical experiments are provided to illustrate the effectiveness of the method and certify the obtained theoretical results.

关键词： Conditional gradient method Multiobjective optimization Pareto optimality constrained optimization problem

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A two-step basis vector extraction strategy for multiset variable correlation analysis

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2011年第1期107卷 147-154页

作者： Zhao, Chunhui Gao, Furong Niu, Dapeng Wang, Fuli Hong Kong Univ Sci & Technol Dept Chem & Biomol Engn Kowloon Hong Kong Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang Liaoning Prov Peoples R China

In the present work, multiple data spaces, in which the same variables are measured on different sources of objects, are related with each other by a two-step analysis strategy, which focuses on finding their common structure in variable correlations. Common basis vectors, which are closely related with each other over sets, are extracted and deemed to enclose the cross-set similar correlations. Therefore, two different subspaces are separated from each other in each dataset. One is the common subspace driven by the common bases, in which, variable correlations are deemed to be consistent over sets;and the residual is the specific subspace, in which, variable correlations are unique to each definite data table. This is achieved by solving a mathematical optimization problem, in which, theoretical support is framed and the related statistical characteristics are analyzed. Its feasibility and performance are illustrated with the laboratory experiment data from the literatures. The proposed approach provides an insight into the inherent variable correlations of multiple-set data with further application potential. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Simultaneous component analysis (SCA) Common principal component analysis (CPCA) Two-step basis extraction Common structure Cross-set correlations constrained optimization problem

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Using constrained optimization algorithm for the modeling of static converter harmonics

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COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING 2012年第3期31卷 764-779页

作者： Lange, Jean-Francois Gerbaud, Laurent Hieu Nguyen-Huu Roudet, James Univ Grenoble 1 Grenoble Univ G2Elab St Martin Dheres France

Purpose - An analytical approach is preferred to carry out the harmonic modelling of power electronics converters because it is generally faster than time simulation chained with FFT. However, the difficulty of such an approach is to build the model and to manage the uncontrolled commutations that occur in the studied static converter, and also to deal with large equations. The purpose of this paper is to propose an aid in the frequency modelling of the drive elements, in the frequency domain, including all key parameters for sizing aim i.e. a way to optimize the EMC filter using different algorithms. Design/methodology/approach - The paper aims to propose an aid to create such models, and to assure its good solving, i.e. that the correct operating mode is represented. So, the solving problem is formulated as an optimization problem under constraints, to solve this difficulty. Findings - The difficulty is to be sure to deal with the good operating mode of the static converter when soft or uncontrolled commutations occur. So, the model is formulated as a constrained optimization problem. The paper proposes a symbolic approach, that allows to build automatically the frequency model. It is translated to be solved in Matlab. Research limitations/implications - The approach does not fit for static converters with a control implying numerous commutations per operating period. However, the approach deals with natural and soft commutations. Originality/value - The modelling is based on the use of linear components and ideal switches.

关键词： Electric power systems Modelling Harmonics Analytical modelling constrained optimization problem Frequency domain modelling Power electronics converters

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Crossbar-Aware Neural Network Pruning

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IEEE ACCESS 2018年 6卷 58324-58337页

作者： Liang, Ling Deng, Lei Zeng, Yueling Hu, Xing Ji, Yu Ma, Xin Li, Guoqi Xie, Yuan Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA Tsinghua Univ Dept Comp Sci & Technol Beijing 100084 Peoples R China Tsinghua Univ Ctr Brain Inspired Comp Res Dept Precis Instrument Beijing 100084 Peoples R China

Crossbar architecture has been widely adopted in neural network accelerators due to the efficient implementations on vector-matrix multiplication operations. However, in the case of convolutional neural networks (CNNs), the efficiency is compromised dramatically because of the large amounts of data reuse. Although some mapping methods have been designed to achieve a balance between the execution throughput and resource overhead, the resource consumption cost is still huge while maintaining the throughput. Network pruning is a promising and widely studied method to shrink the model size, whereas prior work for CNNs compression rarely considered the crossbar architecture and the corresponding mapping method and cannot be directly utilized by crossbar-based neural network accelerators. This paper proposes a crossbar-aware pruning framework based on a formulated L-0-norm constrained optimization problem. Specifically, we design an L-0-norm constrained gradient descent with relaxant probabilistic projection to solve this problem. Two types of sparsity are successfully achieved: 1) intuitive crossbar-grain sparsity and 2) column-grain sparsity with output recombination, based on which we further propose an input feature maps reorder method to improve the model accuracy. We evaluate our crossbar-aware pruning framework on the median-scale CIFAR10 data set and the large-scale ImageNet data set with VGG and ResNet models. Our method is able to reduce the crossbar overhead by 44%-72% with insignificant accuracy degradation. This paper significantly reduce the resource overhead and the related energy cost and provides a new co-design solution for mapping CNNs onto various crossbar devices with much better efficiency.

关键词： Crossbar architecture convolutional neural networks neural network pruning constrained optimization problem

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Resource-Aware Large-Scale Cooperative Three-Dimensional Mapping Using Multiple Mobile Devices

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IEEE TRANSACTIONS ON ROBOTICS 2018年第5期34卷 1349-1369页

作者： Guo, Chao X. Sartipi, Kourosh DuToit, Ryan C. Georgiou, Georgios A. Li, Ruipeng O'Leary, John Nerurkar, Esha D. Hesch, Joel A. Roumeliotis, Stergios, I Google Daydream Mountain View CA 94043 USA Univ Minnesota Dept Comp Sci & Engn Minneapolis MN 55455 USA GM Cruise San Francisco CA 94103 USA Lawrence Livermore Natl Lab Ctr Appl Sci Comp Livermore CA 94551 USA Apple Sunnyvale CA 94085 USA Facebook Oculus Menlo Pk CA 94025 USA

In this paper, we address the problem of cooperative mapping (CM) using datasets collected by multiple users at different times, when the transformation between the users' starting poses is unknown. Specifically, we formulate CM as a constrained optimization problem, in which each user's independently estimated trajectory and map are merged together by imposing geometric constraints between commonly observed point and line features. Additionally, we provide an algorithm for efficiently solving the CM problem, by taking advantage of its structure. The proposed solution is proven to be batch-least-squares (BLS) optimal over all users' datasets, while it is less memory demanding and lends itself to parallel implementations. In particular, our solution is shown to be faster than the standard BLS solution, when the overlap between the users' data is small. Furthermore, our algorithm is resource-aware as it is able to consistently trade accuracy for lower processing cast, by retaining only an informative subset of the common-feature constraints. Experimental results based on visual and inertial measurements collected from multiple users within large buildings are used to assess the performance of the proposed CM algorithm.

关键词： Cooperative mapping (CM) constrained optimization problem resource-aware system three-dimensional (3-D) mapping visual and inertial sensor fusion

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A practical codification and its analysis for the generalized reconfiguration problem

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ELECTRIC POWER SYSTEMS RESEARCH 2013年 97卷 19-33页

作者： Nogueira de Resende Barbosa, Carlos Henrique Alexandre, Rafael Frederico de Vasconcelos, Joao Antonio Univ Fed Ouro Preto Dept Ciencias Exatas & Aplicadas BR-35931026 Joao Monlevade MG Brazil Univ Fed Minas Gerais Grad Program Elect Engn BR-31270901 Belo Horizonte MG Brazil

Distribution network reconfiguration problem is simply aimed at finding the best set of radial configurations among a huge number of possibilities. Each solution of this set ensures optimal operation of the system without violating any prescribed constraint. To solve such problem, it is important to count on efficient procedure to enforce radiality. In this paper, we propose a reliable approach to deal properly with topology constraint enabling algorithm convergence toward optimal or quasi-optimal solutions. A simple and practical codification of individuals used in evolutionary algorithms to solve the generalized reconfiguration problem is detailed in this paper. Mathematical formulation, algorithm, and simulation results are presented for the distribution reconfiguration problem, incorporating a new representation scheme which is immune to topologically unfeasible possibilities. The individual interpretation procedure is straight and it demands no additional data structure or graph preprocessing. Comparisons are made for five well-known distribution systems to demonstrate the efficacy of the proposed methodology. It is also demonstrated that optimal configurations are properly surveyed when single or multiple sources are dealt. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Radial distribution networks Multi-objective constrained optimization problem Graph theory

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Approximation Algorithms for Capacitated Minimum Forest problems in Wireless Sensor Networks with a Mobile Sink

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IEEE TRANSACTIONS ON COMPUTERS 2013年第10期62卷 1932-1944页

作者： Liang, Weifa Schweitzer, Pascal Xu, Zichuan Australian Natl Univ Res Sch Comp Sci Canberra ACT 0200 Australia Inst Mittag Leffler SE-18260 Djursholm Sweden

To deploy a wireless sensor network for the purpose of large-scale monitoring, in this paper, we propose a heterogeneous and hierarchical wireless sensor network architecture. The architecture consists of sensor nodes, gateway nodes, and mobile sinks. The sensors transmit their sensing data to the gateway nodes for temporary storage through multihop relays, while the mobile sinks travel along predetermined trajectories to collect data from nearby gateway nodes. Under this paradigm of data gathering, we formulate a novel constrained optimization problem, namely, the capacitated minimum forest (CMF) problem, for the decision version of which we first show NP-completeness. We then devise approximation algorithms and provide upper bounds for their approximation ratios. We finally evaluate the performance of the proposed algorithms through experimental simulation. In our experiments, the approximation ratio delivered by the proposed algorithms is always less than 2. In the case of arbitrary gateway capacities, this contrasts our theoretical results which show that the approximation ratio is at most linear in the number of gateways. Our experiments thus indicate that for realistic inputs, our worst case analysis of the approximation ratio is very conservative. The proposed algorithms are the first approximation algorithms for the CMF problem, and our techniques may be applicable to other constrained optimization problems beyond wireless sensor networks.

关键词： Wireless sensor networks sink mobility data gathering constrained optimization problem capacitated minimum forest problem

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Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

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Advances in Atmospheric Sciences 2010年第6期27卷 1311-1321页

作者：孙国栋穆穆张雅乐 The State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of Sciences Key Laboratory of Ocean Circulation and Wave Institute of OceanologyChinese Academy of Sciences Graduate University of the Chinese Academy of Sciences

The conditional nonlinear optimal perturbation （CNOP）, which is a nonlinear generalization of the linear singular vector （LSV）, is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming （SQP） algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno （L-BFGS） algorithm, and the spectral projected gradients （SPG2） algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.

关键词： conditional nonlinear optimal perturbation constrained optimization problem unconstrainedoptimization problem

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Synthesis and analysis of the steering system of an adjustable tread-width four-wheel tractor

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MECHANISM AND MACHINE THEORY 2007年第5期42卷 526-540页

作者： Simionescu, P. A. Talpasanu, Ilie Univ Tulsa Dept Mech Engn Tulsa OK 74104 USA Wentworth Inst Technol Dept Elect & Mech Boston MA 02115 USA

In this paper the problem of synthesizing the Ackermann linkage and the steering control mechanism of an adjustable tread-width tractor is presented. Several conflicting requirements were simultaneously considered as follows: ensuring minimum wheel-slip and symmetric steering control for left and right turns, ensuring minimum cross-coupling between steering and axle oscillation, maintaining favorable pressure angles in the joints, and avoiding interference between the moving parts of the mechanism and between these and the body of the vehicle. This difficult multi-criteria optimization problem was solved in a simplified manner by sizing the Ackermann linkage first, followed by an optimum synthesis of the steering control mechanism, assuming it has the drag link removed. The removal of the drag link induced the extra degree of freedom which allowed the steering arm and the pitman arm to be exactly coordinated over the whole working range of the mechanism. An objective function based on the variation of the distance between the centers of the drag-link joints in several essential configurations of the steering control mechanism, was defined and further minimized in the presence of interference avoidance and pressure angle constrains. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： adjustable tread-width vehicle Ackermann linkage steering control mechanism constrained optimization problem search algorithm

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constrained multi-objective population extremal optimization based economic-emission dispatch incorporating renewable energy resources

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RENEWABLE ENERGY 2019年第0期143卷 277-294页

作者： Chen, Min-Rong Zeng, Guo-Qiang Lu, Kang-Di South China Normal Univ Sch Comp Sci Guangzhou 510631 Guangdong Peoples R China Wenzhou Univ Natl Local Joint Engn Lab Digitalize Elect Design Wenzhou 325035 Peoples R China Donghua Univ Coll Informat Sci & Technol Dept Automat Shanghai 201620 Peoples R China

Economic emission dispatch (EED) problem of an electrical power system can be considered as one of the most popular constrained multi-objective optimization problems to minimize the cost and emission simultaneously subjecting to various constraints. Although many approaches have been presented to deal with this problem, it is still a challenge issue especially when more and more renewable energy sources such as wind power and solar power are incorporated into the system due to their intermittence and uncertainty. To improve the EED performance with those renewable power generations, a constrained multi-objective population extremal optimization algorithm called CMOPEO-EED is proposed by utilizing an advanced constraint handling technique, i.e., the superiority of feasible solution approach. To demonstrate the effectiveness of the proposed method, three versions of a modified IEEE 30-bus and 6 generator system with renewable power generations are considered as the test systems. The comprehensive experimental results and analyses fully validate that the proposed CMOPEO-EED method in this paper outperforms these recently reported single-objective success history based adaptive differential evolutionary algorithm (SHADE)-based EED method and constrained non-dominated sorting genetic algorithm-based EED (CNSGAII-EED) method in terms of cost and emission indices. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Economic-emission dispatch Renewable energy resources constrained multi-objective population extremal optimization constrained optimization problem

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