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An adaptive differential evolution algorithm based on relaxation strategy to realize the Nash equilibrium of multi-oligopoly game

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QUAESTIONES MATHEMATICAE 2024年第8期47卷 1571-1587页

作者： Li, Huimin Xiang, Shuwen Huang, Shiguo Luo, Enquan Xuzhou Univ Technol Sch Math & Stat Xuzhou 221018 Peoples R China Guizhou Univ Coll Math & Stat Guiyang 550025 Peoples R China Guiyang Univ Coll Math & Informat Sci Guiyang 550005 Peoples R China Zhengzhou Univ Light Ind Dept Math & Informat Sci Zhengzhou 450002 Peoples R China Guizhou Univ Acad Affairs Off Guiyang 550025 Peoples R China

Inspired by the idea of game learning, this paper studies the Cournot game model of the multi-oligopoly market and studies the realization of the Nash equilibrium by using adaptive differential evolution algorithm based on relaxation strategies. The realization path of Nash equilibrium is attained through an adaptive differential evolution based on a relaxation strategy procedure applied to an objective function with best response dynamics. Among them, the objective function is derived from the sum of the payoff changes of each oligopoly under best response decisions. And theoretically proved that the Nash equilibrium is the optimal solution of the objective function.

关键词： Multi-oligopoly game Nash equilibrium best response dynamics bounded rationality improved differential evolution algorithm

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Joint inversion of VES and Rayleigh wave data based on improved DE algorithm for near surface exploration

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WORLD JOURNAL OF ENGINEERING 2024年第2期21卷 242-253页

作者： Hu, Benna Wen, Laifu Zhou, Xuemei Hebei Inst Invest & Design Water Conservancy & Hyd Geol Survey Inst Tianjin Peoples R China Hebei Univ Engn Sch Earth Sci & Engn Handan Peoples R China Hebei Univ Engn Acad Journal Editorial Off Handan Peoples R China

PurposeVertical electrical sounding (VES) and Rayleigh wave exploration are widely used in the exploration of near-surface structure, but both have limitations. This study aims to make full use of the advantages of the two methods, reduce the multiple solutions of single inversion and improve the accuracy of the inversion. Thus, a nonlinear joint inversion method of VES and Rayleigh wave exploration based on improved differential evolution (DE) algorithm was proposed. Design/methodology/approachBased on the DE algorithm, a new initialization strategy was proposed. Then, taking AK-type with high-velocity interlayer model and HA-type with low-velocity interlayer model near the surface as examples, the inversion results of different methods were compared and analyzed. Then, the proposed method was applied to the field data in Chengde, Hebei Province, China. The stratum structure was accurately depicted and verified by drilling. FindingsThe synthetic data and field data results showed that the joint inversion of VES and Rayleigh wave data based on the improved DE algorithm can effectively improve the interpretation accuracy of the single-method inversion and had strong stability and large generalizable ability in near-surface engineering problems. Originality/valueA joint inversion method of VES and Rayleigh wave data based on improved DE algorithm is proposed, which can improve the accuracy of single-method inversion.

关键词： Vertical electrical sounding Rayleigh wave exploration Near-surface exploration improved differential evolution algorithm Nonlinear joint inversion

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A New Fuzzy Sliding Mode Control Method for Permanent Magnet Synchronous Motor Servo System Based on Optimization of Fuzzy Rules

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IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2022年第12期17卷 1748-1754页

作者： Guo, Liang Zhang, Xu Zheng, Chao Zhang, Peng Wu, Xiaowen Zhejiang Sci Tech Univ Fac Mech Engn & Automat Hangzhou 310018 Peoples R China Zhejiang Fangyuan Test Grp Co Ltd Hangzhou 310018 Peoples R China

Aiming at the problems of inherent chattering of traditional sliding mode control system of permanent magnet synchronous motor and further improving the control precision, a new fuzzy exponential reaching law sliding mode control method optimized by improved differential evolution (DE) algorithm (DEFSMC) is proposed in this article. A new hyperbolic tangent function with fuzzy boundary layer is proposed to instead of the traditional switching function, and the improved DE algorithm is used to optimize the fuzzy rules of parameters in sliding mode controller. Simulation and experimental results prove that the proposed strategy can effectively reduce the chattering and overshoot, and improve the response speed and robustness of the system. (c) 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

关键词： fuzzy sliding mode control fuzzy hyperbolic tangent function improved differential evolution algorithm

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Application of machine learning and its improvement technology in modeling of total energy consumption of air conditioning water system

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2022年第5期19卷 4841-4855页

作者： Zhu, Qixin Liu, Mengyuan Liu, Hongli Zhu, Yonghong Suzhou Univ Sci & Technol Sch Mech Engn 55 Changjiang Rd Suzhou 215009 Peoples R China Suzhou Univ Sci & Technol Jiangsu Prov Key Lab Intelligent Bldg Energy Effi 1 Kerui Rd Suzhou 215009 Peoples R China Suzhou Univ Sci & Technol Sch Environm Sci & Engn 1 Kerui Rd Suzhou 215009 Peoples R China Jingdezhen Ceram Inst Sch Mech & Elect Engn Sch Mech Engn 27 Taoyang South Rd Jingdezhen 333001 Peoples R China

Accurate energy consumption model is the basis of energy saving optimal control of air conditioning system. The existing energy consumption model of air conditioning water system mainly focuses on a certain equipment or a part of the cycle. However, the coupling between water system equipment will affect the setting of optimal energy consumption of equipment. It is necessary to establish the energy consumption model of water system as a whole. However, air conditioning water system is a highly nonlinear complex system, and its precise physical model is difficult to establish. The main goal of this paper is to develop an accurate machine learning modeling and optimization technique to predict the total energy consumption of air conditioning water system by using the actual operation data collected. The main contributions of this work are as follows: (1) Three commonly used machine learning techniques, artificial neural network (ANN), support vector machine (SVM) and classification regression tree (CART), are used to build prediction models of air conditioning water system energy consumption. The results show that all the three models have fast training speed, but the ANN model has better performance in cross-validation. (2) The improved differential evolution algorithm was used to optimize the parameters (initial weights and thresholds) of the ANN, which solved the problem that the ANN is easy to fall into the local optimal solution. The simulation results show that the root mean square error (RMSE) of the improved model decreases by 20.5%, the mean absolute error (MAE) decreases by 30.2%, and the coefficient of determination (R2) increases from 0.9227 to 0.9512. (3) Sensitivity analysis of the established optimization model shows that chilled water flow, chilled water outlet temperature and air conditioning load are the main factors affecting the total energy consumption.

关键词： machine learning data-driven model artificial neural network support vector machine improved differential evolution algorithm

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Piezoelectric-based smart structures for aero-engine blade: Piezoelectric layout optimization and vibration suppression tests

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AEROSPACE SCIENCE AND TECHNOLOGY 2024年 153卷

作者： Gao, Zhiyuan Xu, Tongxin Yu, Ruichen Jiang, Jinhua Zhu, Xiaojin Shanghai Univ Sch Mechatron Engn & Automat Shanghai 200444 Peoples R China

To promote the use of piezoelectric smart structures in aero-engine blades, this paper introduces a novel method for optimizing the layout of piezoelectric elements on the blade's surface and an active vibration control method, along with vibration suppression tests. A preprocessing method is introduced for the point cloud data of inservice blades to reconstruct the blade surface. An improved parameter-adaptive differential evolution algorithm is proposed to optimize the layout of piezoelectric actuators and sensors and accurately identify the hysteresis nonlinear model of piezoelectric elements. A Hammerstein model is constructed by cascading an asymmetric Bouc-Wen model with an ARX model to describe the rate-dependent hysteresis nonlinear characteristics of piezoelectric elements. An improved variable step-size FxLMS algorithm is proposed to balance the relationship between convergence speed and steady-state error in the control algorithm. The proposed layout optimization and vibration control algorithm are validated experimentally on an experimental platform under various disturbances, with results showing improved performance of the proposed VSS-FxLMS algorithm in terms of convergence and efficiency.

关键词： Piezoelectric smart structures Surface reconstruction Layout optimization improved differential evolution algorithm Hammerstein model Active vibration control

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Fertilizer Strength Prediction Model Based on Shape Characteristics

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IEEE ACCESS 2021年 9卷 87007-87023页

作者： Zhang, Hongjian Xu, Chunbao Wang, Jinxing Shandong Agr Univ Coll Mech & Elect Engn Tai An 271018 Shandong Peoples R China Shandong Prov Key Lab Hort Machinery & Equipment Tai An 271018 Shandong Peoples R China Shandong Agr Equipment Intelligent Engn Lab Tai An 271018 Shandong Peoples R China

The accurate prediction of fertilizer strength can reduce the crushing rate in the process of transportation and utilization, ensure the efficient utilization of fertilizer, so as to realize the sustainable and clean production of crops. To achieve this goal, for the first time, a fertilizer strength prediction model based on the shape characteristics is proposed to this paper by the support vector machine and the improved differential evolution algorithm. Firstly, the fertilizer shape characteristics and strength are measured by the independently developed agricultural material shape analyzer and the digital strength tester. Secondly, a fertilizer strength prediction model based on a support vector machine is constructed, in which the optimal combined kernel function is proposed according to the Pearson correlation coefficient and the normal distribution law. Finally, a differential evolution algorithm is improved to optimize the internal parameters of the fertilizer strength prediction model. The experiment results show that the maximum error rate of the fertilizer strength prediction model is between -5% and 5%. The proposed method of this paper can lay a solid foundation for fertilizer production and quality inspection, which will help reduce fertilizer crushing, improve fertilizer utilization to realize the sustainable and clean production of crops.

关键词： Fertilizers Shape Shape measurement Predictive models Particle measurements Atmospheric measurements Pollution measurement Fertilizer strength prediction model shape characteristics support vector machine combined kernel function improved differential evolution algorithm

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An improved differential evolution algorithm for the task assignment problem

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2011年第4期24卷 616-624页

作者： Zou, Dexuan Liu, Haikuan Gao, Liqun Li, Steven Xuzhou Normal Univ Sch Elect Engn & Automat Xuzhou 221116 Jiangsu Peoples R China Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Univ S Australia Div Business Adelaide SA 5001 Australia

An improved differential evolution algorithm (IDE) is proposed to solve task assignment problem. The IDE is an improved version of differential evolution algorithm (DE), and it modifies two important parameters of DE algorithm: scale factor and crossover rate. Specially, scale factor is adaptively adjusted According to the objective function values of all candidate solutions, and crossover rate is dynamically adjusted with the increasement of iterations. The adaptive scale factor and dynamical crossover rate are combined to increase the diversity of candidate solutions, and to enhance the exploration capacity of solution space of the proposed algorithm. In addition, a usual penalty function method is adopted to trade-off the objective and the constraints. Experimental results demonstrate that the optimal solutions obtained by the IDE algorithm are all better than those obtained by the other two DE algorithms on solving some task assignment problems. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： improved differential evolution algorithm Task assignment problem differential evolution algorithm Scale factor Crossover rate Penalty function method

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A random perturbation modified differential evolution algorithm for unconstrained optimization problems

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SOFT COMPUTING 2019年第15期23卷 6307-6321页

作者： Wei, Zhaokun Xie, Xinlian Bao, Tiantian Yu, Yue Dalian Maritime Univ Transportat Management Coll Room 3181 Linghai Rd Dalian 116026 Peoples R China

To solve unconstrained optimization problems, a random search differential evolution algorithm (RPMDE) is designed based on a modified differential evolution algorithm. The efficiency of an evolutionary algorithm usually depends on its exploration competence and development capability. Considering these characteristics, an effective difference operator called DE/M_pBest-best/1' is designed, which originates from DE/best/1/' and DE/current-pbest/1'. The operator makes use of information from the best population of individuals to generate new solutions for the development of RPMDE and guarantee swarm quality during the later evolution of the algorithm, which improves its searching ability. To prevent the solutions from falling into local optima, RPMDE also adopts random perturbation to update the current solution with a better solution after difference mutation and crossover are competed. Furthermore, a levy distribution is employed to adjust the scale factor as a control parameter. All designed operators are beneficial to improve the exploration competence and the diversity of the whole population. Last, a large number of computational experiments and comparisons are conducted by employing 15 benchmark functions. The experimental results indicate that the designed algorithm, RPMDE, is more effective than other differential evolution variants in dealing with unconstrained optimization problems.

关键词： improved differential evolution algorithm Difference strategy Random perturbation Levy distribution Parameter adjustment

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Effects of land use changes on the ecological operation of the Panjiakou-Daheiting Reservoir system, China

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ECOLOGICAL ENGINEERING 2020年 152卷 105851-105851页

作者： Miao, Yuanjingjing Li, Jianzhu Feng, Ping Dong, Lixin Zhang, Ting Wu, Jiezhao Katwal, Rajeev Tianjin Univ State Key Lab Hydraul Engn Simulat & Safety Tianjin 300350 Peoples R China Tianjin Hydraul Res Inst Tianjin 300061 Peoples R China

The problem of insufficient water for ecological purposes in the Luanhe River basin requires urgent resolution. The regional hydrological cycle is affected by the Panjiakou-Daheiting Reservoir system and by changes in land use in the upper watershed. Therefore, this system was selected as a study area to simulate ecological reservoir operation and analyze the effects of changes in land use on ecological operation. A physical habitat simulation model (PHABSIM) was built to determine the minimum and suitable ecological water demand. Then, an ecological reservoir operation model using an improved differential evolution (DE) algorithm was established. Simulated inflow data under the land use conditions in 1970 and 2015 were input into the model, and the effects of changes in land use on ecological operation and on the weighted usable area (WUA) for cyprinoids were calculated. The results show that ecological reservoir operation significantly improves the ecological water supply and increases cyprinoid habitat. The changes in land use led to a decrease in annual runoff, which further reduced the urban water supply by 0.67%-2.25% and the ecological water supply by 0.45%-2.04% at different flow frequencies. The land use changes also caused the WUA to decrease by 1746-2999 m(2)/km at different flow frequencies, with a decrease rate of 1.04%-6.28%. This study could provide valuable information for water resource managers operating reservoirs in river ecosystems and planning to cope with water shortages caused by land use change in water-deficient areas.

关键词： improved differential evolution algorithm PHABSIM model Ecological reservoir operation Land use changes Ecological water demand

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Parameter Design and Analysis of Grid-connected Characteristics of Virtual Synchronous Generator

International Core Journal of Engineering

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International Core Journal of Engineering 2020年第6期6卷 169-173页

作者： Qing Zhang Xihuai Wang

The grid-connected stability of new energy power generation systems has become a hot spot in microgrid technology research. Virtual Synchronous Generator (VSG) control technology simulates the operating characteristics of synchronous generators (SGs) through grid-connected inverters, making them have inertia and damping characteristics. The design of VSG controller parameters is difficult, and the grid connection effect obtained using traditional calculation methods is not ideal. Comparing the simulation results of the power grid under frequency and voltage disturbances, it is verified that the improved differential evolution algorithm is more suitable for VSG grid connection stability than the traditional algorithm.

关键词： Microgrid Virtual synchronous generator improved differential evolution algorithm Grid stability

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