HHO Algorithm Based on Bidirectional Experience Guidance and Extreme Individual Regulation

doi:10.3778/j.issn.1673-9418.2203134

Abstract

Abstract: In order to improve the optimization accuracy and iteration speed of Harris hawks optimization (HHO) algorithm, a bidirectional experience guided and extreme individual regulated HHO algorithm (BEHHO) is proposed. Firstly, Circle chaotic mapping is used to homogenize the initial population to effectively avoid individual aggregation and improve the coverage of the Harris hawks population to the solution space region, laying foundation for algorithm optimization. Secondly, the bidirectional experience guidance strategy is introduced to strengthen the rounding mechanism of the algorithm, the evolution experience of the global optimal individual and the historical optimal individual is used to guide the individual to search for the optimal direction, and the differential disturbance term of the adaptive random individual is used to strengthen the ability of the population to explore the neighborhood and improve the convergence accuracy of the algorithm. Furthermore, considering important impact of algorithm extreme individual on the global update process, the optimal individual t - distribution variation is used to avoid algorithm into local extremum, and the reverse solution of the worst individual is generated by reverse dynamic learning to improve the convergence speed indirectly. At the same time, greedy principle is adopted to retain the dominant individual to ensure the accuracy of the algorithm’s progeny individual tends to be better. Finally, the global convergence of the algorithm is analyzed based on Markov chain. By comparing the optimization of benchmark test functions, Wilcoxon rank sum test and CEC2014 complex functions, the improved algorithm is proven to have excellent solving performance and robust robustness, and the superiority of BEHHO algorithm in practical problems is verified by welding beam design problems in engineering optimization.

Key words: Harris hawks optimization (HHO) algorithm, Circle chaotic mapping, bidirectional experience guidance, extreme individual regulation, global convergence, engineering optimization

摘要： 为进一步提升哈里斯鹰优化算法（HHO）的寻优精度和迭代速度，提出一种双向经验引导与极端个体调控的HHO算法（BEHHO）。首先采用Circle混沌映射均匀化初始种群，有效规避个体聚集情形并提升哈里斯鹰群体对解空间区域的覆盖性，奠定算法寻优基础；其次引入双向经验引导策略来强化算法的围捕机制，依托全局最优个体和历史最优个体的进化经验引导个体寻优方向，且配合自适应随机个体的差分扰动项来强化种群探索邻域能力，提升算法的收敛精度；再者考虑算法中极端个体对全局更新过程的重要影响，利用t-分布变异最优个体来避免算法陷入局部极值区，并以动态反向学习产生最差个体的反向解来间接提高算法的收敛速度，同时采用贪婪原则保留优势个体的方式确保算法子代精度趋于更优；最后基于马尔科夫链分析算法的全局收敛性。通过对基准测试函数的寻优对比分析、Wilcoxon秩和检验以及CEC2014复杂函数的对比分析，验证了改进算法优异的求解性能和健壮的鲁棒性，并以工程优化中焊接梁设计问题验证了BEHHO算法处理实际问题时的优越性。

关键词: 哈里斯鹰优化算法（HHO）, Circle混沌映射, 双向经验引导, 极端个体调控, 全局收敛性, 工程优化

CHAI Yan, REN Sheng. HHO Algorithm Based on Bidirectional Experience Guidance and Extreme Individual Regulation[J]. Journal of Frontiers of Computer Science and Technology, 2023, 17(9): 2118-2136.

柴岩, 任生. 双向经验引导与极端个体调控的HHO算法[J]. 计算机科学与探索, 2023, 17(9): 2118-2136.

References

[1] 朱佳莹, 高茂庭. 融合粒子群与改进蚁群算法的AUV路径规划算法[J]. 计算机工程与应用, 2021, 57(6): 267-273.
ZHU J Y, GAO M T. AUV path planning algorithm based on particle swarm optimization and improved ant colony algorithm[J]. Computer Engineering and Applications, 2021, 57(6): 267-273.
[2] 胡晓敏, 王明丰, 张首荣, 等. 用于文本聚类的新型差分进化粒子群算法[J]. 计算机工程与应用, 2021, 57(4): 61-67.
HU X M, WANG M F, ZHANG S R, et al. New differential evolution with particle swarm optimization algorithm for text clustering[J]. Computer Engineering and Applications, 2021, 57(4): 61-67.
[3] 张晗, 杨继斌, 张继业, 等. 基于多种群萤火虫算法的车载燃料电池直流微电网能量管理优化[J]. 中国电机工程学报, 2021, 41(3): 833-846.
ZHANG H, YANG J B, ZHANG J Y, et al. Multiple-population firefly algorithm-based energy management strategy for vehicle-mounted fuel cell DC microgrid[J]. Proceedings of the CSEE, 2021, 41(3): 833-846.
[4] ZALDíVAR D, MORALES B, RODRíGUEZ A, et al. A novel bio-inspired optimization model based on Yellow Saddle Goatfish behavior[J]. Biosystems, 2018, 174: 1-21.
[5] ARORA S, SINGH S. Butterfly optimization algorithm: a novel approach for global optimization[J]. Soft Computing, 2019, 23(3): 715-734.
[6] KAUR S, AWASTHI L K, SANGAL A L, et al. Tunicate swarm algorithm: a new bio-inspired based metaheuristic paradigm for global optimization[J]. Engineering Applications of Artificial Intelligence, 2020, 90: 103541.
[7] FARAMARZI A, HEIDARINEJAD M, MIRJALILI S, et al. Marine predators algorithm: a nature-inspired metaheuristic[J]. Expert Systems with Applications, 2020, 152: 113377.
[8] HEIDARI A A, MIRJALILI S, FARIS H, et al. Harris hawks optimization: algorithm and applications[J]. Future Generation Computer Systems, 2019, 97: 849-872.
[9] KHALIFEH S, AKBARIFARD S, KHALIFEH V. Optimization of water distribution of network systems using the Harris hawks optimization algorithm (case study: Homashahr City)[J]. MethodsX, 2020, 7: 100948.
[10] MARY A H, MIRY A H, MIRY M H. An optimal robust state feedback controller for the AVR system-based Harris hawks optimization algorithm[J]. Electric Power Components and Systems, 2021, 48(16/17): 1684-1694.
[11] ISMAEL O M, QASIM O S, ALGAMAL Z Y. A new adaptive algorithm for v-support vector regression with feature selection using Harris hawks optimization algorithm[J]. Journal of Physics Conference Series, 2021, 1897(1): 12-57.
[12] ZHANG H, NGUYEN H, BUI X N, et al. A generalized artificial intelligence model for estimating the friction angle of clays in evaluating slope stability using a deep neural network and Harris hawks optimization algorithm[J]. Engineering with Computers, 2022, 38(5): 3901-3914.
[13] JIA H M, LANG C B, OLIVA D, et al. Dynamic Harris hawks optimization with mutation mechanism for satellite image segmentation[J]. Remote Sensing, 2019, 11(12): 1421.
[14] WUNNAVA A, NAIK M K, PANDA R, et al. A differential evolutionary adaptive Harris hawks optimization for two dimensional practical Masi entropy-based multilevel image thresholding[J]. Journal of King Saud University-Computer and Information Sciences, 2020, 34: 3011-3024.
[15] GUO H R, MENG X Y, LIU Y L, et al. Improved HHO algorithm based on good point set and nonlinear convergence formula[J]. The Journal of China Universities of Posts and Telecommunications, 2021, 28(2): 48-67.
[16] 赵世杰, 高雷阜, 于冬梅, 等. 融合能量周期性递减与牛顿局部增强的改进HHO算法[J]. 控制与决策, 2021, 36(3): 629-636.
ZHAO S J, GAO L F, YU D M, et al. Improved Harris hawks optimization coupling energy cycle decline mechanism and newton local enhancement strategy[J]. Control and Decision, 2021, 36(3): 629-636.
[17] USSIEN A G, AMIN M. A self-adaptive Harris hawks optimization algorithm with opposition-based learning and chaotic local search strategy for global optimization and feature selection[J]. International Journal of Machine Learning and Cybernetics, 2022, 13(2): 309-336.
[18] HUSSAIN K, NEGGAZ N, ZHU W, et al. An effcient hybrid sine-cosine Harris hawks optimization for low and high-dimensional feature selection[J]. Expert Systems with Applications, 2021, 176: 114778.
[19] 郭雨鑫, 刘升, 高文欣, 等. 精英反向学习与黄金正弦优化的HHO算法[J]. 计算机工程与应用, 2022, 58(10): 153-161.
GUO Y X, LIU S, GAO W X, et al. Elite opposition-based learning golden-sine Harris hawks optimization[J]. Computer Engineering and Applications, 2022, 58(10): 153-161.
[20] 刘小龙, 梁彤缨. 基于方形邻域和随机数组的哈里斯鹰优化算法[J]. 控制与决策, 2022, 37(10): 2467-2476.
LIU X L, LIANG T Y. Harris hawk optimization algorithm based on square neighborhood and random array[J]. Control and Decision, 2022, 37(10): 2467-2476.
[21] 刘道华, 原思聪, 兰洋, 等. 混沌映射的粒子群优化方法[J]. 西安电子科技大学学报, 2010, 37(4): 764-769.
LIU D H, YUAN S C, LAN Y, et al. Method of particle swarm optimization based on the chaos map[J]. Journal of Xidian University, 2010, 37(4): 764-769.
[22] 单梁, 强浩, 李军, 等. 基于Tent映射的混沌优化算法[J]. 控制与决策, 2005, 20(2): 179-182.
SHAN L, QIANG H, LI J, et al. Chaotic optimization algorithm based on Tent map[J]. Control and Decision, 2005, 20(2): 179-182.
[23] 张达敏, 徐航, 王依柔, 等. 嵌入Circle映射和逐维小孔成像反向学习的鲸鱼优化算法[J]. 控制与决策, 2021, 36(5): 1173-1180.
ZHANG D M, XU H, WANG Y R, et al. Whale optimization algorithm for embedded Circle mapping and one dimensional oppositional learning based small hole imaging[J]. Control and Decision, 2021, 36(5): 1173-1180.
[24] KENNEDY J, EBERHART R C. Particle swarm optimization[C]//Proceedings of the 1995 IEEE International Conference on Neural Network, Perth, Nov 27-Dec 1, 1995. Piscataway: IEEE, 1995: 1942-1948.
[25] 周方俊, 王向军, 张民. 基于t分布变异的进化规划[J].电子学报, 2008, 36(4): 667-671.
ZHOU F J, WANG X J, ZHANG M. Evolutionary pro-gramming based on t-distribution variation[J]. Acta Elect-ronica Sinica, 2008, 36(4): 667-671.
[26] TIZHOOSH H R. Opposition-based learning: a new scheme for machine intelligence[C]//Proceedings of the 2005 Com-putational Intelligence for Modelling. Washington: IEEE Computer Society, 2005: 695-701.
[27] LONG W, JIAO J J, LIANG X M, et al. A random opposition- based learning grey wolf optimizer[J]. IEEE Access, 2019, 7: 113810-113825.
[28] GHASEMI M, AKBARI E, RAHIMNEJAD A, et al. Phasor particle swarm optimization: a simple and efficient variant of PSO[J]. Soft Computing, 2013, 23(19): 9701-9718.
[29] 何庆, 魏康园, 徐钦帅. 基于混合策略改进的鲸鱼优化算法[J]. 计算机应用研究, 2019, 36(12): 3647-3651.
HE Q, WEI K Y, XU Q S. Improved whale optimization algorithm based on hybrid strategy[J]. Application Research of Computers, 2019, 36(12): 3647-3651.
[30] MIRJALILI S. SCA: a sine cosine algorithm for solving optimization problems[J]. Knowledge-Based Systems, 2016, 96: 120-133.
[31] MIRJALILI S, GANDOMI A H, MIRJALILI S Z, et al. Salp swarm algorithm: a bio-inspired optimizer for engineering design problems[J]. Advances in Engineering Software, 2017, 114: 163-191.