全局与局部模型交替辅助的差分进化算法

doi:10.19678/j.issn.1000-3428.0060693

摘要/Abstract

摘要： 为求解实际复杂工程应用中的高维计算费时优化问题，提出一种全局与局部代理模型交替辅助的差分进化算法。利用历史样本训练全局和局部代理模型，通过交替搜索全局和局部代理模型得到模型最优解并对其进行真实目标函数评价，实现探索和开采的平衡以减少真实目标函数的计算次数，同时通过针对性地选择个体进行真实目标函数计算，辅助算法快速找到目标函数的较优解。在15个低维测试问题和14个高维测试问题上的实验结果表明，在有限的计算资源情况下，该算法在12个低维测试问题上相较于最优重启策略代理辅助的社会学习粒子群优化算法、基于主动学习的代理模型辅助的粒子群优化算法等表现更好，在7个高维测试问题上相较于高斯过程辅助的进化算法、代理模型辅助的分层粒子群优化算法、求解高维费时问题的代理辅助的多种群优化算法等能找到目标函数的更优解。

关键词: 全局代理模型, 局部代理模型, 差分进化算法, 计算费时优化问题, 径向基函数网络

Abstract: To solve high-dimensional, computationally expensive optimization problems in practical complex engineering applications, a Differential Evolution(DE) algorithm assisted by the alternate optimization of global proxy and local proxy models is proposed.Therefore, a global or local proxy model is trained based on historical data and optimized alternatingly to assist the algorithm in finding the optimal solution of the original problem.A balance between exploration and exploitation can be achieved by alternatingly searching for the optimal solution of the global and local proxy models.The optimal solutions of global and local proxy models can be evaluated using the real objective function, which helps reduce the number of objective evaluations.Furthermore, it can accelerate the time required to find the optimal solution by selecting target individuals for real objective evaluation.The performance of the algorithm was tested on 15 low-dimensional and 14 high-dimensional test problems.Experimental results show that when computational resources are limited, the proposed algorithm performs better on 12 low-dimensional problems compared to the GORS-SSLPSO, CAL-SAPSO and other algorithms, and can find better optimal solutions for 7 high-dimensional problems than the MGP-SLPSO, SHPSO, SAMSO and other algorithms.

Key words: global proxy model, local proxy model, Differential Evolution(DE) algorithm, computationally expensive optimization problem, Radial Basis Function Network(RBFN)

中图分类号:

TP18

于成龙, 付国霞, 孙超利, 张国晨. 全局与局部模型交替辅助的差分进化算法[J]. 计算机工程, 2022, 48(3): 115-123.

YU Chenglong, FU Guoxia, SUN Chaoli, ZHANG Guochen. Differential Evolution Algorithm Alternately Assisted by Global and Local Models[J]. Computer Engineering, 2022, 48(3): 115-123.

http://www.ecice06.com/CN/Y2022/V48/I3/115

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参考文献

[1] DEL VALLE Y, VENAYAGAMOORTHY G K.Particle swarm optimization:basic concepts, variants and applications in power systems[J].IEEE Transactions on Evolutionary Computation, 2008, 12(2):171-195.
[2] 吕铭晟, 沈洪远, 李志高, 等.多变异策略差分进化算法的研究与应用[J].计算机工程, 2014, 40(12):146-150. LÜ M S, SHEN H Y, LI Z G, et al.Research and application of differential evolution algorithm under multiple mutation strategy[J].Computer Engineering, 2014, 40(12):146-150.(in Chinese)
[3] SOLTANI S, MURCH R D.A compact planar printed MIMO antenna design[J].IEEE Transactions on Antennas and Propagation, 2015, 63(3):1140-1149.
[4] MILLIGAN T A.Modern antenna design[M].Hoboken, USA:John Wiley & Sons, Inc., 2005.
[5] REGIS R G.Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions[J].IEEE Transactions on Evolutionary Computation, 2014, 18(3):326-347.
[6] ONG Y S, NAIR P B, KEANE A J.Evolutionary optimization of computationally expensive problems via surrogate modeling[J].AIAA Journal, 2003, 41(4):687-696.
[7] LIM D, JIN Y C, ONG Y S, et al.Generalizing surrogate-assisted evolutionary computation[J].IEEE Transactions on Evolutionary Computation, 2010, 14(3):329-355.
[8] QUEIPO N V, HAFTKA R T, SHYY W, et al.Surrogate-based analysis and optimization[J].Progress in Aerospace Sciences, 2005, 41(1):1-28.
[9] WORTMANN T, COSTA A, NANNICINI G, et al.Advantages of surrogate models for architectural design optimization[J].Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 2015, 29(4):471-481.
[10] TANG Y F, CHEN J Q, WEI J H.A surrogate-based particle swarm optimization algorithm for solving optimization problems with expensive black box functions[J].Engineering Optimization, 2013, 45(5):557-576.
[11] SUN C L, JIN Y C, CHENG R, et al.Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems[J].IEEE Transactions on Evolutionary Computation, 2017, 21(4):644-660.
[12] TIAN J, TAN Y, ZENG J C, et al.Multiobjective infill criterion driven Gaussian process-assisted particle swarm optimization of high-dimensional expensive problems[J].IEEE Transactions on Evolutionary Computation, 2019, 23(3):459-472.
[13] 张宗华, 赵京湘, 卢享, 等.基于遗传算法的BP神经网络在电力负载预测中的应用[J].计算机工程, 2017, 43(10):277-282, 288. ZHANG Z H, ZHAO J X, LU X, et al.Application of BP neural network based on genetic algorithm in power load forecasting[J].Computer Engineering, 2017, 43(10):277-282, 288.(in Chinese)
[14] JIN Y C, OLHOFER M, SENDHOFF B.A framework for evolutionary optimization with approximate fitness functions[J].IEEE Transactions on Evolutionary Computation, 2002, 6(5):481-494.
[15] JIN Y.A comprehensive survey of fitness approximation in evolutionary computation[J].Soft Computing, 2005, 9(1):3-12.
[16] LIU B, ZHANG Q F, GIELEN G G E.A Gaussian process surrogate model assisted evolutionary algorithm for medium scale expensive optimization problems[J].IEEE Transactions on Evolutionary Computation, 2013, 18(2):180-192.
[17] SCHNEIDER P I, SANTIAGO X G, ROCKSTUHL C, et al.Global optimization of complex optical structures using Bayesian optimization based on Gaussian processes[EB/OL].[2020-12-15].http://arxiv.org/pdf/1707.08479.
[18] YU H B, TAN Y, SUN C L, et al.A generation-based optimal restart strategy for surrogate-assisted social learning particle swarm optimization[J].Knowledge-Based Systems, 2019, 163:14-25.
[19] SUN C L, ZENG J C, PAN J, et al.A new fitness estimation strategy for particle swarm optimization[J].Information Sciences, 2013, 221:355-370.
[20] SUN C L, DING J L, ZENG J C, et al.A fitness approximation assisted competitive swarm optimizer for large scale expensive optimization problems[J].Memetic Computing, 2018, 10(2):123-134.
[21] WANG H D, JIN Y C, DOHERTY J.Committee-based active learning for surrogate-assisted particle swarm optimization of expensive problems[J].IEEE Transactions on Cybernetics, 2017, 47(9):2664-2677.
[22] YU H B, TAN Y, ZENG J C, et al.Surrogate-assisted hierarchical particle swarm optimization[J].Information Sciences, 2018, 454/455:59-72.
[23] LI F, CAI X, GAO L, et al.A surrogate-assisted multiswarm optimization algorithm for high-dimensional computationally expensive problems[J].IEEE Transactions on Cybernetics, 2021, 51(3):1390-1402.
[24] LIAO P, SUN C L, ZHANG G C, et al.Multi-surrogate multi-tasking optimization of expensive problems[EB/OL].[2020-12-15].https://www.researchgate.net/publication/343051439_Multi-surrogate_multi-tasking_optimization_of_expensive_problems.
[25] ER M J, WU S Q, LU J W, et al.Face recognition with Radial Basis Function(RBF) neural networks[J].IEEE Transactions on Neural Networks, 2002, 13(3):697-710.
[26] KATTAN A, GALVAN E.Evolving radial basis function networks via GP for estimating fitness values using surrogate models[C]//Proceedings of 2012 IEEE Congress on Evolutionary Computation.Washington D.C., USA:IEEE Press, 2012:1-7.
[27] GUTMANN H M.A radial basis function method for global optimization[J].Journal of Global Optimization, 2001, 19(3):201-227.
[28] STORN R, PRICE K.Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces[J].Journal of Global Optimization, 1997, 11(4):341-359.
[29] 代瑞瑞, 马永杰, 摆玉龙, 等.基于动态模式搜索的差分进化算法[J].计算机工程, 2016, 42(9):163-167. DAI R R, MA Y J, BAI Y L, et al.Differential evolution algorithm based on dynamic pattern search[J].Computer Engineering, 2016, 42(9):163-167.(in Chinese)
[30] ZHANG J Q, SANDERSON A C.JADE:adaptive differential evolution with optional external archive[J].IEEE Transactions on Evolutionary Computation, 2009, 13(5):945-958.
[31] SUN C L, JIN Y C, ZENG J C, et al.A two-layer surrogate-assisted particle swarm optimization algorithm[J].Soft Computing, 2015, 19(6):1461-1475.
[32] SUGANTHAN P N, HANSEN N, LIANG J J, et al.Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization[EB/OL].[2020-12-15].http://www.al-roomi.org/multimedia/CEC_Database/CEC2013/RealParameterOptimization/CEC2013_RealParameterOptimization_TechnicalReport.pdf.
[33] HENLEY S.Principles and procedure of statistics:a biometrical approach[J].Computers & Geosciences, 1983, 9(2):275.
[34] WANG H D, JIN Y C, SUN C L, et al.Offline data-driven evolutionary optimization using selective surrogate ensembles[J].IEEE Transactions on Evolutionary Computation, 2019, 23(2):203-216.

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