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SVRG for a non-convex problem using graduated optimization algorithm

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018年第1期34卷 153-165页

作者： Chen, Li Zhou, Shuisheng Zhang, Zhuan Xidian Univ Sch Math & Stat Xian 710071 Shaanxi Peoples R China

non-convex optimization problems with multiple local optima are frequently encountered in machine learning. Graduated optimization algorithm (GOA) is a popular method for obtaining the global optima of non-convex problems by minimizing a sequence of locally strong convex functions that smooth the original non-convex problem with increasing approximation. Recently, GradOpt, a GOA-based algorithm, has demonstrated remarkable theoretical and experimental results. However, to optimize problems consisting of both convex and non-convex parts, GradOpt considers the entire objective function as a single non-convex function, leading to significant gaps between the smoothed and original functions. In this study, we propose two new algorithms: SVRG-GOA and PSVRG-GOA. They gradually smooth the non-convex part of the problem and then minimize the smoothed function using either the stochastic variance reduced gradient (SVRG) or proximal SVRG (Prox-SVRG) method. Both the algorithms are proven to have lower iteration complexity (O(1/epsilon)) than GradOpt (O(1/epsilon(2))). Some tricks, such as larger shrinkage factor, projection step, stochastic gradient, and mini-batch skill are also applied to accelerate convergence of the proposed algorithms. Experimental results illustrate that two new algorithms with similar performance can converge to the "global" optima of a non-convex problem comparatively faster than GradOpt or non-convex Prox-SVRG.

关键词： non-convex optimization problem global optima stochastic variance reduced gradient graduated optimization

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Optimal Stochastic Injection Attack Strategy Against Discrete Time-Varying System via Moment Matrices

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 11026-11037页

作者： Gao, Sheng Gramlich, Dennis Zhang, Hao Yan, Huaicheng Ebenbauer, Christian Tongji Univ Coll Elect & Informat Engn Dept Control Sci & Engn Shanghai 200092 Peoples R China Rhein Westfal TH Aachen Chair Intelligent Control Syst D-52074 Aachen Germany Tongji Univ Shanghai Inst Intelligent Sci & Technol Shanghai 200092 Peoples R China East China Univ Sci & Technol Key Lab Adv Control & Optimizat Chem Proc Minist Educ Shanghai 200237 Peoples R China East China Univ Sci & Technol Sch Informat Sci & Engn Shanghai 200237 Peoples R China

This paper investigates injection attacks incorporating stochastic noise against linear discrete time-varying system, which is more general but also more challenging to defend than deterministic injection attacks. Based on the optimization theory and novel key defining matrices, an optimal stochastic injection attack strategy is proposed. Unlike existing strategies, this strategy is stochastic, making it harder for defenders to predict. Therefore, the newly designed attack is expected to be widely used to disrupt system performance. By leveraging estimated data from the observer and the attack input, a virtual residual system is established, which more accurately reflects changes in the system error before and after the attack than the traditional error system. Using the state and output residuals along with the stochastic attack input, two performances are defined to ensure the stealthiness and effectiveness of the attack, respectively. Subsequently, an optimal attack problem with non-convex objective function and constraint is formulated. The key to acquiring the designed optimal stochastic injection attack strategy is to apply a semi-definite relaxation involving moment matrices for transforming this non-convex optimization problem into a convex optimization problem and solving it. Finally, the effectiveness of the proposed attack strategy is validated through numerical simulation of a networked mass-spring-damper system and a V-formation experiment involving three quadrotors. Note to Practitioners-The primary objective of this paper is to focus on the cyber security of discrete time-varying systems from the perspective of the attacker, which provides insight into the way of generating attack strategies under the stochastic case. The majority of existing injection attack strategies against intelligent systems are deterministic, and this can make the attacks less effective as the attacked system reconstructs and compensates for the attack signals, and the attack s

关键词： Time-varying systems optimization Observers Linear programming Programming Estimation error Numerical simulation convex functions Control systems Automation Stochastic injection attack non-convex optimization problem moment matrices semi-definite programming

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Hybrid Gravitational Search Algorithm-Particle Swarm optimization with Time Varying Acceleration Coefficients for large scale CHPED problem

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ENERGY 2017年 126卷 841-853页

作者： Beigvand, Soheil Derafshi Abdi, Hamdi La Scala, Massimo Razi Univ Fac Engn Dept Elect Engn Kermanshah Iran Politecn Bari DEE Polytech Sch Bari Bari Italy

This paper proposes a novel optimization algorithm, namely hybrid Time Varying Acceleration Coefficients-Gravitational Search Algorithm-Particle Swarm optimization (hybrid TVAC-GSA-PSO), to solve the large-scale, highly nonlinear, non-convex, non-smooth, non-differential, non-continuous, and complex Combined Heat and Power Economic Dispatch (CHPED) problems. The suggested algorithm is based on the Newtonian laws of gravitation and motion as well as swarm behaviors. The proposed technique combines the best performances of three optimization methods (i.e. GSA, TVAC-GSA, and TVAC-PSO) in terms of their specific strategies in particle movements through a self-adoptive learning strategy. The effectiveness and robustness of the suggested algorithm are tested on a set of five benchmark functions and two large-scale CHPED problems (considering valve-point loading effect and prohibited zones of conventional power units, transmission losses, as well as special characteristic of CHP units). The obtained results by the suggested algorithm in terms of quality solution, computational performance, and convergence characteristic are compared with various algorithms to show the ability of the proposed approach and its robustness in finding a better fuel cost with a less expensive solution. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Combined Heat and power Economic Dispatch (CHPED) problem Gravitational Search Algorithm (GSA) Particle Swarm optimization (PSO) Hybrid TVAC-GSA-PSO non-convex optimization problem

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Optimal Combined Heat and Power Economic Dispatch Using Stochastic Fractal Search Algorithm

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Journal of Modern Power Systems and Clean Energy 2020年第2期8卷 276-286页

作者： Muwaffaq I.Alomoush the Department of Electrical Power Engineering Hijjawi Faculty for Engineering TechnologyYarmouk UniversityIrbidJordan

Combined heat and power(CHP)generation is a valuable scheme for concurrent generation of electrical and thermal *** interdependency of power and heat productions in CHP units introduces complications and non-convexities in their modeling and *** paper uses the stochastic fractal search(SFS)optimization technique to treat the highly non-linear CHP economic dispatch(CHPED)problem,where the objective is to minimize the total operation cost of both power and heat from generation units while fulfilling several operation interdependent limits and *** CHPED problem has bounded feasible operation regions and many local *** SFS,which is a recent metaheuristic global optimization solver,outranks many current reputable *** constraints of the CHPED is achieved by employing external penalty parameters,which penalize infeasible solution during the iterative *** confirm the strength of this algorithm,it has been tested on two different test systems that are regularly *** obtained outcomes are compared with former outcomes achieved by many different methods reported in literature of *** results of this work affirm that the SFS algorithm can achieve improved near-global solution and compare favorably with other commonly used global optimization techniques in terms of the quality of solution,handling of constraints and computation time.

关键词： Combined heat and power(CHP) economic dispatch global optimization metaheuristic algorithms non-convex optimization problem power systems stochastic fractal search

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Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term hydrothermal generation scheduling

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SOFT COMPUTING 2020年第21期24卷 16225-16248页

作者： Mohamed, Maha Youssef, Abdel-Raheem Kamel, Salah Ebeed, Mohamed South Valley Univ Fac Engn Dept Elect Engn Qena Egypt Aswan Univ Fac Engn Dept Elect Engn Aswan 81542 Egypt Sohag Univ Fac Engn Dept Elect Engn Sohag Egypt Chongqing Univ State Key Lab Power Transmiss Equipment & Syst Se Chongqing Peoples R China

Short-term hydrothermal scheduling (STHS) is considered an important problem in the field of power system economics. The solution of this problem gives the hourly output of power generation schedule of the available hydro and thermal power units, which leads to minimization of the total fuel cost of thermal units for a given period of a time. The optimal generation of STHS is considered as a complicated and nonlinear optimization problem with a set of equality and inequality constraints such as the valve point loading effect of thermal units, the power transmission loss and the load balance. This paper proposes lightning attachment procedure optimization (LAPO) algorithm for solving the nonlinear non-convex STHS optimization problem in order to minimize the operating fuel cost of thermal units with satisfying the operating constraints of the system. The performance of LAPO algorithm is validated using three different test systems considering the valve point loading effects of thermal units and the power transmission losses. The obtained results prove the effectiveness and superiority of LAPO algorithm for solving the STHS problem compared with other well-known optimization techniques.

关键词： Short-term hydrothermal scheduling non-convex optimization problem Lightning attachment procedure optimization Valve point loading effect

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Solving combined heat and power economic dispatch problem using real coded genetic algorithm with improved Muhlenbein mutation

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APPLIED THERMAL ENGINEERING 2016年 99卷 465-475页

作者： Haghrah, A. Nazari-Heris, M. Mohammadi-ivatloo, B. Univ Tabriz Fac Elect & Comp Engn Tabriz Iran

The combined heat and power economic dispatch (CHPED) is a complicated optimization problem which determines the production of heat and power units to obtain the minimum production costs of the system, satisfying the heat and power demands and considering operational constraints. This paper presents a real coded genetic algorithm with improved Muhlenbein mutation (RCGA-IMM) for solving CHPED optimization task. Muhlenbein mutation is implemented on basic RCGA for speeding up the convergence and improving the optimization problem results. To evaluate the performance features, the proposed RCGA-IMM procedure is employed on six benchmark functions. The effect of valve-point and transmission losses is considered in cost function and four test systems are presented to demonstrate the effectiveness and superiority of the proposed method. In all test cases the obtained solutions utilizing RCGA-IMM optimization method are feasible and in most instances express a marked improvement over the provided results by recent works in this area. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Combined heat and power (CHP) Economic dispatch Real code genetic algorithm (RCGA) non-convex optimization problem

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Packing Unequal Spheres into Various Containers

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CYBERNETICS AND SYSTEMS ANALYSIS 2016年第3期52卷 419-426页

作者： Stoyan, Yu. G. Scheithauer, G. Yaskov, G. N. Natl Acad Sci Ukraine AN Podgorny Inst Mech Engn Problems Kharkov Ukraine Tech Univ Dresden Inst Numer Math Dresden Germany

The paper considers an optimization problem of packing different solid spheres into containers of the following types: a cuboid, a sphere, a right circular cylinder, an annular cylinder, and a spherical layer. The radii of spheres are assumed to vary. It allows us to propose a new way to derive starting points belonging to the feasible domain of the problem, as well as to carry out a non-exhaustive search of local extrema, using a modification of the jump algorithm (JA), which implements a continuous transition from one local minimum to another with a better value of the objective function. A reduction of the solution space dimension and rearrangements of sphere pairs allow improving the objective function value. The results obtained are compared with benchmark ones.

关键词： packing sphere packing non-convex optimization problem jump algorithm

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An approach for estimating time-variable rates from geodetic time series

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JOURNAL OF GEODESY 2016年第11期90卷 1207-1221页

作者： Didova, Olga Gunter, Brian Riva, Riccardo Klees, Roland Roese-Koerner, Lutz Delft Univ Technol Stevinweg 1 NL-2624 CN Delft Netherlands Georgia Inst Technol Daniel Guggenheim Sch Aerosp Engn 270 Ferst Dr NW Atlanta GA 30332 USA Univ Bonn Inst Geodesy & Geoinformat Nussallee 17 D-53115 Bonn Germany

There has been considerable research in the literature focused on computing and forecasting sea-level changes in terms of constant trends or rates. The Antarctic ice sheet is one of the main contributors to sea-level change with highly uncertain rates of glacial thinning and accumulation. Geodetic observing systems such as the Gravity Recovery and Climate Experiment (GRACE) and the Global Positioning System (GPS) are routinely used to estimate these trends. In an effort to improve the accuracy and reliability of these trends, this study investigates a technique that allows the estimated rates, along with co-estimated seasonal components, to vary in time. For this, state space models are defined and then solved by a Kalman filter (KF). The reliable estimation of noise parameters is one of the main problems encountered when using a KF approach, which is solved by numerically optimizing likelihood. Since the optimization problem is non-convex, it is challenging to find an optimal solution. To address this issue, we limited the parameter search space using classical least-squares adjustment (LSA). In this context, we also tested the usage of inequality constraints by directly verifying whether they are supported by the data. The suggested technique for time-series analysis is expanded to classify and handle time-correlated observational noise within the state space framework. The performance of the method is demonstrated using GRACE and GPS data at the CAS1 station located in East Antarctica and compared to commonly used LSA. The results suggest that the outlined technique allows for more reliable trend estimates, as well as for more physically valuable interpretations, while validating independent observing systems.

关键词： Time-variable trend Kalman filter non-convex optimization problem Colored noise

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The non-convex Sparse problem with nonnegative Constraint for Signal Reconstruction

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JOURNAL OF optimization THEORY AND APPLICATIONS 2016年第3期170卷 1009-1025页

作者： Wang, Yong Zhou, Guanglu Zhang, Xin Liu, Wanquan Caccetta, Louis Tianjin Univ Sch Sci Dept Math Tianjin 300072 Peoples R China Curtin Univ Dept Math & Stat Perth WA Australia Curtin Univ Dept Comp Perth WA Australia

The problem of finding a sparse solution for linear equations has been investigated extensively in recent years. This is an NP-hard combinatorial problem, and one popular method is to relax such combinatorial requirement into an approximated convex problem, which can avoid the computational complexity. Recently, it is shown that a sparser solution than the approximated convex solution can be obtained by solving its non-convex relaxation rather than by solving its convex relaxation. However, solving the non-convex relaxation is usually very costive due to the non-convexity and non-Lipschitz continuity of the original problem. This difficulty limits its applications and possible extensions. In this paper, we will consider the non-convex relaxation problem with the nonnegative constraint, which has many applications in signal processing with such reasonable requirement. First, this optimization problem is formulated and equivalently transformed into a Lipschitz continuous problem, which can be solved by many existing optimization methods. This reduces the computational complexity of the original problem significantly. Second, we solve the transformed problem by using an efficient and classical limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Finally, some numerical results show that the proposed method can effectively find a nonnegative sparse solution for the given linear equations with very low computational cost.

关键词： nonnegative sparse solution non-Lipschitz continuous L-BFGS method non-convex optimization problem

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Robust controller for uncertain parameters systems

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ISA TRANSACTIONS 2012年第5期51卷 632-640页

作者： Ben Hariz, Maher Bouani, Faouzi Ksouri, Mekki Tunis Manor Univ Fac Sci Tunis Tunisia Tunis Manor Univ Natl Engn Sch Tunis Tunis Tunisia Anal Concept & Control Syst Lab Tunis Tunisia

In this paper, we present the synthesis of a robust controller for Linear Time Invariant (LTI) uncertain systems. A linear parametric uncertainties model is used to describe the system dynamic behavior. The main purpose of this controller is to guarantee some step response performances such as the settling time and the overshoot. The controller synthesis is formulated as a min-max optimization problem which takes in account the desired closed-loop performances and the uncertainties on the model parameters. Then the controller parameters represent the best solution for the worst case of all possible models. In order to emphasize its performances and its efficiency, a real time implementation of the proposed controller on a laboratory pilot plant has been presented. (C) 2012 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Robust controller Uncertain systems Step response performances non-convex optimization problem

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