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A TRUST-REGION algorithm FOR HETEROGENEOUS MULTIOBJECTIVE OPTIMIZATION

SIAM JOURNAL ON OPTIMIZATION 2019年第2期29卷 1017-1047页

作者： Thomann, Jana Eichfelder, Gabriele Tech Univ Ilmenau Inst Math Ilmenau Germany

This paper presents a trust-region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, given, for example, by a time-consuming simulation. For this function, derivative information cannot be used, and the computation of function values involves high computational effort. The other objective functions are given analytically, and derivatives can easily be computed. The method uses the basic trust-region approach by restricting the computations in every iteration to a local area and replacing the objective functions by suitable models. The search direction is generated in the image space by using local ideal points. The algorithm generates a sequence of iterates. It is proved that any limit point is Pareto critical. Numerical results are presented and compared to two other algorithms.

关键词： multiobjective optimization trust-region method derivative-free algorithm heterogeneous optimization Pareto critical point

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A novel hybrid trust region algorithm based on nonmonotone and LOOCV techniques

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2019年第2期72卷 499-524页

作者： Ahmadvand, M. Esmaeilbeigi, M. Kamandi, A. Yaghoobi, F. M. Islamic Azad Univ Hamedan Branch Dept Math Hamadan Iran Malayer Univ Fac Math Sci & Stat Malayer Iran Univ Sci & Technol Mazandaran Fac Math Sci Behshahr Iran

In this paper, a novel hybrid trust-region algorithm using radial basis function (RBF) interpolations is proposed. The new algorithm is an improved version of ORBIT algorithm based on two novel ideas. Because the accuracy and stability of RBF interpolation depends on a shape parameter, so it is more appropriate to select this parameter according to the optimization problem. In the new algorithm, the appropriate shape parameter value is determined according to the optimization problem based on an effective statistical approach, while the ORBIT algorithm in all problems uses a fixed shape parameter value. In addition, the new algorithm is equipped with a new intelligent nonmonotone strategy which improves the speed of convergence, while the monotonicity of the sequence of objective function values in the ORBIT may decrease the rate of convergence, especially when an iteration is trapped near a narrow curved valley. The global convergence of the new hybrid algorithm is analyzed under some mild assumptions. The numerical results significantly indicate the superiority of the new algorithm compared with the original version.

关键词： Radial basis functions Unconstrained optimization derivative-free algorithm Nonmonotone technique Trust-region framework Leave one out cross validation technique

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A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

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IEEE ACCESS 2021年 9卷 18262-18277页

作者： Abubakar, Auwal Bala Muangchoo, Kanikar Ibrahim, Abdulkarim Hassan Muhammad, Abubakar Bakoji Jolaoso, Lateef Olakunle Aremu, Kazeem Olalekan Bayero Univ Kano Fac Phys Sci Dept Math Sci Kano 700241 Nigeria Sefako Makgatho Hlth Sci Univ Dept Math & Appl Math ZA-0204 Pretoria South Africa Rajamangala Univ Technol Phra Nakhon RMUTP Fac Sci & Technol Dept Math & Stat Bangkok 10800 Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math KMUTT Fixed Point Res Lab Bangkok 10140 Thailand Gombe State Univ Fac Sci Dept Math Gombe 760214 Nigeria Usmanu Danfodiyo Univ Sokoto Dept Math Sokoto 840231 Nigeria

In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.

关键词： Optimization Mathematics Gradient methods Approximation algorithms Convergence Licenses Search problems derivative-free algorithm Monotone operator equations projection technique image restoration

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State-Dependent Sweeping Processes: Asymptotic Behavior and algorithmic Approaches

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2024年第2期202卷 932-948页

作者： Adly, Samir Cojocaru, Monica G. Le, Ba Khiet Univ Limoges Lab XLIM 123 Ave Albert Thomas F-87060 Limoges France Univ Guelph Dept Math & Stat Guelph ON N1G 2W1 Canada Ton Duc Thang Univ Fac Math & Stat Optimizat Res Grp Ho Chi Minh City Vietnam

In this paper, we investigate the asymptotic properties of a particular class of state-dependent sweeping processes. While extensive research has been conducted on the existence and uniqueness of solutions for sweeping processes, there is a scarcity of studies addressing their behavior in the limit of large time. Additionally, we introduce novel algorithms designed for the resolution of quasi-variational inequalities. As a result, we introduce a new derivative-free algorithm to find zeros of nonsmooth Lipschitz continuous mappings with a linear convergence rate. This algorithm can be effectively used in nonsmooth and nonconvex optimization problems that do not possess necessarily second-order differentiability conditions of the data.

关键词： Asymptotic analysis State-dependent sweeping processes Quasi-variational inequalities derivative-free algorithm

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Globally convergent algorithms for finding zeros of duplomonotone mappings

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OPTIMIZATION LETTERS 2015年第3期9卷 569-584页

作者： Artacho, Francisco J. Aragn Fleming, Ronan M. T. Univ Luxembourg Syst Biochem Grp Luxembourg Ctr Syst Biomed L-4362 Esch Sur Alzette Luxembourg

We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide various examples, including nonlinear duplomonotone functions arising from the study of systems of biochemical reactions. Finally, we present three variations of a derivative-free line search algorithm for finding zeros of systems of duplomonotone equations, and we prove their linear convergence to a zero of the function.

关键词： Generalized monotonicity Duplomonotone mapping Monotone mapping Global convergence Line search method derivative-free algorithm Biochemical reactions

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PENALIZED NCP-FUNCTIONS FOR NONLINEAR COMPLEMENTARITY PROBLEMS AND A SCALING algorithm

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2022年第6期18卷 4527-4550页

作者： Wang, Jueyu Gu, Chao Wang, Guoqiang Shanghai Lixin Univ Accounting & Finance Sch Stat & Math Shanghai 201209 Peoples R China Shanghai Univ Engn Sci Coll Fundamental Studies Shanghai 201620 Peoples R China

In this paper, we systematically study the properties of penalized NCP-functions in derivative-free algorithms for nonlinear complementarity problems (NCPs), and give some regular conditions for stationary points of penalized NCP-functions to be solutions of NCPs. The main contribution is to unify and generalize previous results. Based on one of above penalized NCP-functions, we analyze a scaling algorithm for NCPs. The numerical results show that the scaling can greatly improve the effectiveness of the algorithm.

关键词： Nonlinear complementarity problem penalized NCP-function regular condition scaling derivative-free algorithm

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A METHOD WITH LOW COMPUTING COST TO APPROXIMATE INCREMENTS OF DETERMINANTS NEEDED FOR derivative-free RESTRICTED MAXIMUM-LIKELIHOOD

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JOURNAL OF DAIRY SCIENCE 1995年第3期78卷 672-677页

作者： RICO, M GARCIACORTES, LA NATL INST ANIM SCI DEPT RES PIGS & HORSESDK-8830 TJELEDENMARK

Estimation of variance components by REML via derivative-free algorithms requires the determinant of the coefficient matrix of mixed model equations. A Monte Carlo-based method is proposed to approximate the increment of the logarithm of the determinant of this coefficient matrix that corresponds to increments of the ratio between residual and additive-genetic variance. The computing cost of this method is linear with the order of the coefficient matrix. Results of approximate and exact methods were compared. A bias, detected when the difference of the ratio between residual and additive genetic variance is large, vanishes as convergence is reached. The proposed procedure is accurate enough to estimate the maximum of the likelihood function, The REML estimates of variance components using the Monte Carlo approximation are also presented.

关键词： derivative-free algorithm RESTRICTED MAXIMUM LIKELIHOOD MONTE CARLO METHODS

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求解不可微箱约束变分不等式的下降算法

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高等学校计算数学学报 2002年第4期24卷 335-348页

作者：陈国庆刘水霞内蒙古大学理工学院数学系内蒙古大学理工学院数学系呼和浩特010021

1 引论设X(?)Rn是非空闭集,F:Rn→Rn连续映射,变分不等式问题VI(X,F)是指:求x∈X,使 F(x)T(y-x)≥0,　 (?)y∈X,(1)记指标集N=(1,2,…,n},当 X=[a,b]≡{x∈Rn|a≤xi≤bi,i∈N},(2)其中a={a1,a2,…,an}T,b={b1,b2,…,bn}T∈Rn时,VI(X,F... 详细信息

关键词： box constrained variational inequality with locally Lipschitzian func-tions merit functions derivative-free algorithm generalized Newton method.

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A generalized evolutionary metaheuristic (GEM) algorithm for engineering optimization

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COGENT ENGINEERING 2024年第1期11卷

作者： Yang, Xin-She Middlesex Univ London Sch Sci & Technol London England

Many optimization problems in engineering and industrial design applications can be formulated as optimization problems with highly nonlinear objectives, subject to multiple complex constraints. Solving such optimization problems requires sophisticated algorithms and optimization techniques. A major trend in recent years is the use of nature-inspired metaheustic algorithms (NIMA). Despite the popularity of nature-inspired metaheuristic algorithms, there are still some challenging issues and open problems to be resolved. Two main issues related to current NIMAs are: there are over 540 algorithms in the literature, and there is no unified framework to understand the search mechanisms of different algorithms. Therefore, this paper attempts to analyse some similarities and differences among different algorithms and then presents a generalized evolutionary metaheuristic (GEM) in an attempt to unify some of the existing algorithms. After a brief discussion of some insights into nature-inspired algorithms and some open problems, we propose a generalized evolutionary metaheuristic algorithm to unify more than 20 different algorithms so as to understand their main steps and search mechanisms. We then test the unified GEM using 15 test benchmarks to validate its performance. Finally, further research topics are briefly discussed.

关键词： algorithm derivative-free algorithm evolutionary computation metaheuristic nature-inspired computing swarm intelligence optimization

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Operational assessment of solar-wind-biomass-hydro-electrolyser hybrid microgrid for load variations using model predictive deterministic algorithm and droop controllers

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e-Prime - Advances in Electrical Engineering, Electronics and Energy 2024年 9卷

作者： Ishraque, Md. Fatin Shezan, Sk. A. Shafiullah, G.M. Muyeen, S.M. Alharbi, Talal Alenezi, Ali H Hossen, Md. Delwar Dept. of Electrical Electronic and Communication Engineering Pabna University of Science and Technology Pabna Rajapur 6600 Bangladesh Department of Electrical Engineering and Industrial Automation Engineering Institute of Technology Melbourne 3001 VIC Australia School of Engineering and Energy Murdoch University 6150 WA Australia Department of Electrical Engineering Qatar University Doha 2713 Qatar Department of Electrical Engineering College of Engineering Qassim University Buraydah 52571 Saudi Arabia Remote Sensing Unit Electrical Engineering Department Northern Border University Arar Saudi Arabia Department of Electrical and Electronic Engineering Uttara University Dhaka Bangladesh

This study presents the operation and assessment of a solar-wind-biomass-hydro-electrolyser hybrid microgrid for different types of load variations by using a proprietary derivative-free algorithm (Model Predictive Deterministic algorithm) and voltage IQ droop controller. The proposed hybrid microgrid integrates various renewable energy sources and an electrolyser to generate hydrogen and produce electricity. The objective is to optimize the microgrid's performance and provide reliable power supply to meet varying load demands. The proprietary derivative-free algorithm is used to determine the optimal dispatch of power from each energy source to meet the load demand while minimizing the overall cost of energy. Additionally, a voltage IQ droop and voltage Q droop controller are employed to regulate the voltage, frequency and active power of the microgrid and maintain its stability during load variations. The proposed hybrid microgrid is assessed under different load scenarios for both grid tied and isolated modes. The results demonstrate that the proposed hybrid microgrid with the derivative-free algorithm and voltage droop controllers can effectively operate and provide reliable power supply under different load variations while maintaining the power system stability of the microgrid. Further, the mutual performances of the controller are compared to find the best controller for the specific microgrid. The findings of this study can contribute to the development of efficient and reliable hybrid microgrid systems for sustainable energy production and distribution. © 2024 The Author(s)

关键词： derivative-free algorithm Hybrid microgrid Load variations Model Predictive Deterministic algorithm Renewable energy sources Voltage IQ droop controller Voltage Q droop controller

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