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differential evolution with Adaptive Mutation and Parameter Control Using Lvy Probability Distribution

Journal of Computer Science & Technology 2012年第5期27卷 1035-1055页

作者：贺仁杰杨振宇 Department of Management Science and Engineering College of Information System and ManagementNational University of Defense TechnologyChangsha 410073China

differential evolution （DE） has become a very popular and effective global optimization algorithm in the area of evolutionary computation. In spite of many advantages such as conceptual simplicity, high efficiency and ease of use, DE has two main components, i.e., mutation scheme and parameter control, which significantly influence its performance. In this paper we intend to improve the performance of DE by using carefully considered strategies for both of the two components. We first design an adaptive mutation scheme, which adaptively makes use of the bias of superior individuals when generating new solutions. Although introducing such a bias is not a new idea, existing methods often use heuristic rules to control the bias. They can hardly maintain the appropriate balance between exploration and exploitation during the search process, because the preferred bias is often problem and evolution-stage dependent. Instead of using any fixed rule, a novel strategy is adopted in the new adaptive mutation scheme to adjust the bias dynamically based on the identified local fitness landscape captured by the current population. As for the other component, i.e., parameter control, we propose a mechanism by using the Levy probability distribution to adaptively control the scale factor F of DE. For every mutation in each generation, an Fi is produced from one of four different Levy distributions according to their historical performance. With the adaptive mutation scheme and parameter control using Levy distribution as the main components, we present a new DE variant called Levy DE （LDE）. Experimental studies were carried out on a broad range of benchmark functions in global numerical optimization. The results show that LDE is very competitive, and both of the two main components have contributed to its overall performance. The scalability of LDE is also discussed by conducting experiments on some selected benchmark functions with dimensions from 30 to 200.

关键词： differential evolution global optimization L6vy distribution parameter adaptation

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differential evolution with controlled search direction

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Journal of Central South University 2012年第12期19卷 3516-3523页

作者：贾丽媛何建新张弛龚文引 Department of Computer Science Hunan City University School of Computer Science China University of Geosciences

A novel and simple technique to control the search direction of the differential mutation was *** order to verify the performance of this method,ten widely used benchmark functions were chosen and the results were compared with the original differential evolution(DE)*** results indicate that the search direction controlled DE algorithm obtains better results than the original DE algorithm in term of the solution quality and convergence rate.

关键词： differential evolution evolutionary algorithm search direction numerical optimization

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A differential evolution Flower Pollination Algorithm with Dynamic Switch Probability

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Chinese Journal of Electronics 2019年第4期28卷 737-747页

作者： LIU Jingsen LIU Li LI Yu Institute of Intelligent Network system Henan University College of Software Henan University Institute of Management Science and Engineering Henan University

For the shortcomings of the basic flower pollination algorithm, this paper proposes a differential evolution flower pollination algorithm with dynamic switch probability based on the Weibull *** new algorithm improved the convergence rate and precision. The switch probability is improved by Weibull distribution function combined with the number of iterations. It can balance the relationship between the global pollination and the local pollination to improve the overall optimization performance of the *** mutation operator is merged into the global pollination process to increase diversity of the population,enhance the ability of the algorithm’s global search and avoid premature convergence. In the process of local pollination, directed mutation and crossover operation of the differential evolution are incorporated, it makes the individual flower position update with the memory function, which can choose the direction of variation reasonably. The use of cross-operation can avoid new solutions crossing the boundary. Convergence rate is improved and the algorithm can approach the global optimal solution continuously. Theoretical analysis proved the convergence and time complexity of the improved algorithm. The simulation results based on the function optimization problem show that the improved algorithm has better performance of optimization, faster convergence speed and higher convergence accuracy.

关键词： Flower pollination algorithm Dynamic switch probability Random mutation operator differential evolution Optimization accuracy Convergence rate

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On the selection of solutions for mutation in differential evolution

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Frontiers of Computer Science 2018年第2期12卷 297-315页

作者： Yong WANG Zhi-Zhong LIU Jianbin LI Han-Xiong LI Jiahai WANG School of Information Science and Engineering Central South University Changsha 410083 China School of Computer Science and Informatics De Montfort University Leicester LE1 9BH UK Institute of Information Security and Big Data Central South University Changsha 410083 China Department of Systems Engineering and Engineering Management City University of Hong Kong Hong Kong China State Key Laboratory of High Performance Complex Manufacturing Central South University Changsha 410083 China School of Data and Computer Science Sun Yat-sen University Guangzhou 510006 China

differential evolution （DE） is a kind of evolutionary algorithms, which is suitable for solving complex optimization problems. Mutation is a crucial step in DE that generates new solutions from old ones. It was argued and has been commonly adopted in DE that the solutions selected for mutation should have mutually different indices. This restrained condition, however, has not been verified either theoretically or empirically yet. In this paper, we empirically investigate the selection of solutions for mutation in DE. From the observation of the extensive experiments, we suggest that the restrained condition could be relaxed for some classical DE versions as well as some advanced DE variants. Moreover, relaxing the restrained condition may also be useful in designing better future DE algorithms.

关键词： differential evolution mutation the selection of solutions for mutation evolutionary algorithms

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Parameter estimation for chaotic systems with and without noise using differential evolution-based method

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Chinese Physics B 2011年第6期20卷 72-77页

作者：李念强潘炜闫连山罗斌徐明峰江宁 Centre for Information Photonics and Communications Southwest Jiaotong University

We present an approach in which the differential evolution （DE） algorithm is used to address identification problems in chaotic systems with or without delay terms. Unlike existing considerations, the scheme is able to simultaneously extract （i） the commonly considered parameters, （ii） the delay, and （iii） the initial state. The main goal is to present and verify the robustness against the common white Guassian noise of the DE-based method. Results of the time-delay logistic system, the Mackey Glass system and the Lorenz system are also presented.

关键词： chaotic system differential evolution noise parameter estimation

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An improved chaotic hybrid differential evolution for the short-term hydrothermal scheduling problem considering practical constraints

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Frontiers of Information Technology & Electronic Engineering 2015年第5期16卷 404-417页

作者： Tahir Nadeem MALIK Salman ZAFAR Saaqib HAROON Electrical Engineering Department University of Engineering and Technology

Short-term hydrothermal scheduling(STHTS) is a non-linear and complex optimization problem with a set of operational hydraulic and thermal constraints. Earlier, this problem has been addressed by several classical techniques; however, due to limitations such as non-linearity and non-convexity in cost curves, artificial intelligence tools based techniques are being used to solve the STHTS problem. In this paper an improved chaotic hybrid differential evolution(ICHDE) algorithm is proposed to find an optimal solution to this problem taking into account practical constraints. A self-adjusted parameter setting is obtained in differential evolution(DE) with the application of chaos theory, and a chaotic hybridized local search mechanism is embedded in DE to effectively prevent it from premature convergence. Furthermore, heuristic constraint handling techniques without any penalty factor setting are adopted to handle the complex hydraulic and thermal constraints. The superiority and effectiveness of the developed methodology are evaluated by its application in two illustrated hydrothermal test systems taken from the literature. The transmission line losses, prohibited discharge zones of hydel plants, and ramp rate limits of thermal plants are also taken into account. The simulation results reveal that the proposed technique is competent to produce an encouraging solution as compared with other recently established evolutionary approaches.

关键词： Valve-point effect Prohibited discharge zones differential evolution Chaotic sequences Constraint handling

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Design of PID controller with incomplete derivation based on differential evolution algorithm

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Journal of Systems Engineering and Electronics 2008年第3期19卷 578-583页

作者： Wu Lianghong Wang Yaonan Zhou Shaowu Tan Wen School of Information and Electric Engineering Hunan Univ. of Science and Technology Xiangtan 411201 P. R. China Coll. of Electric and Information Engineering Hunan Univ. Changsha 410082 P. R. China

To determine the optimal or near optimal parameters of PID controller with incomplete derivation, a novel design method based on differential evolution （DE） algorithm is presented. The controller is called DE-PID controller. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain is proposed. The optimization procedures employing the DE algorithm to search the optimal or near optimal PID controller parameters of a control system are demonstrated in detail. Three typical control systems are chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach has superior features of easy implementation, stable convergence characteristic, and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method is indeed more efficient and robust in improving the step response of a control system.

关键词： PID controller incomplete derivation differential evolution parameter tuning.

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Classification-based self-adaptive differential evolution and its application in multi-lateral multi-issue negotiation

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Frontiers of Computer Science 2012年第4期6卷 442-461页

作者： Xiaojun BI Jing XIAO School of Information and Communication Engineering Harbin Engineering UniversityHarbin 150001China School of Information Engineering Liaoning Provincial College of CommunicationsShenyang 110122China

Multi-lateral multi-issue negotiations are the most complex realistic negotiation problems. Automated ap- proaches have proven particularly promising for complex ne- gotiations and previous research indicates evolutionary com- putation could be useful for such complex systems. To im- prove the efficiency of realistic multi-lateral multi-issue ne- gotiations and avoid the requirement of complete informa- tion about negotiators, a novel negotiation model based on art improved evolutionary algorithm p-ADE is proposed. The new model includes a new multi-agent negotiation protocol and strategy which utilize p-ADE to improve the negotia- tion efficiency by generating more acceptable solutions with stronger suitability for all the participants. Where p-ADE is improved based on the well-known differential evolution （DE）, in which a new classification-based mutation strategy DE/rand-to-best/pbest as well as a dynamic self-adaptive pa- rameter setting strategy are proposed. Experimental results confirm the superiority of p-ADE over several state-of-the-art evolutionary optimizers. In addition, the p-ADE based multi- agent negotiation model shows good performance in solving realistic multi-lateral multi-issue negotiations.

关键词： differential evolution global optimum e-commerce agent multi-lateral multi-issue negotiation

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Classification- and Regression-Assisted differential evolution for Computationally Expensive Problems

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Journal of Computer Science & Technology 2012年第5期27卷 1024-1034页

作者：陆晓芬唐珂 Nature Inspired Computation and Applications Laboratory School of Computer Science and Technology University of Science and Technology of ChinaHefei 230027China

differential evolution （DE） has been well accepted ever, it usually involves a large number of fitness evaluations to as an effective evolutionary optimization technique. Howobtain a satisfactory solution. This disadvantage severely restricts its application to computationally expensive problems, for which a single fitness evaluation can be highly timeconsuming. In the past decade, a lot of investigations have been conducted to incorporate a surrogate model into an evolutionary algorithm （EA） to alleviate its computational burden in this scenario. However, only limited work was devoted to DE. More importantly, although various types of surrogate models, such as regression, ranking, and classification models, have been investigated separately, none of them consistently outperforms others. In this paper, we propose to construct a surrogate model by combining both regression and classification techniques. It is shown that due to the specific selection strategy of DE, a synergy can be established between these two types of models, and leads to a surrogate model that is more appropriate for DE. A novel surrogate model-assisted DE, named Classification- and Regression-Assisted DE （CRADE） is proposed on this basis. Experimental studies are carried out on a set of 16 benchmark functions, and CRADE has shown significant superiority over DE-assisted with only regression or classification models. Further comparison to three state-of-the-art DE variants, i.e., DE with global and local neighborhoods （DECL）, JADE, and composite DE （CODE）, also demonstrates the superiority of CRADE.

关键词： surrogate model differential evolution computationally expensive problem

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Multiple Elite Individual Guided Piecewise Search-Based differential evolution

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IEEE/CAA Journal of Automatica Sinica 2023年第1期10卷 135-158页

作者： Shubham Gupta Shitu Singh Rong Su Shangce Gao Jagdish Chand Bansal the School of Electrical and Electronic Engineering Nanyang Technological UniversitySingapore 639798Singapore the Department of Mathematics South Asian UniversityNew Delhi 110021India IEEE Faculty of Engineering University of ToyamaToyama-shi 930-8555Japan

The differential evolution(DE)algorithm relies mainly on mutation strategy and control parameters'*** take full advantage of top elite individuals in terms of fitness and success rates,a new mutation operator is *** control parameters such as scale factor and crossover rate are tuned based on their success rates recorded over past evolutionary *** proposed DE variant,MIDE,performs the evolution in a piecewise manner,i.e.,after every predefined evolutionary stages,MIDE adjusts its settings to enrich its diversity *** performance of the MIDE is validated on two different sets of benchmarks:CEC 2014 and CEC 2017(special sessions&competitions on real-parameter single objective optimization)using different performance *** the end,MIDE is also applied to solve constrained engineering *** efficiency and effectiveness of the MIDE are further confirmed by a set of experiments.

关键词： Control parameters differential evolution metaheuristic algorithms mutation operator

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