融合浓度平衡和菲克定律的新平衡优化器算法

doi:10.3778/j.issn.1002-8331.2205-0007

摘要/Abstract

摘要： 针对平衡优化器算法（equilibrium optimizer，EO）出现的收敛速度慢、算法精度不够、开发和搜索阶段信息不平衡等问题，提出了融合浓度平衡和菲克定律的新平衡优化器算法（new equilibrium optimizer，NEO）。根据布朗运动和扩散现象，不同浓度区域的粒子采取不同的浓度平衡机制，改进算法平衡池，提高种群间的信息交流能力；在算法参数中引入幂函数和指数函数两种自适应因子，进一步平衡全局搜索和局部开发能力，使得粒子种群在解空间中进行广泛搜索和深度挖掘；根据菲克定律，在粒子位置更新公式中引入扰动机制，提高算法寻优精度和收敛速度。采用24个基准测试函数和Wilcoxon 秩和检验，将NEO算法和其他智能优化算法进行仿真实验对比，结果表明NEO算法具有良好的优化性能。

关键词: 平衡优化器算法, 浓度平衡, 自适应因子, 菲克定律

Abstract: New equilibrium optimizer algorithm（NEO）, which combines concentration equilibrium and Fick’s law, is proposed to solve the problems of slow convergence speed, insufficient accuracy and information imbalance in development and search stage of equilibrium optimizer algorithm（EO）. According to Brownian motion and diffusion phenomenon, different concentration balancing mechanism is adopted for particles in different concentration regions, and the algorithm balancing pool is improved to improve the information communication ability between populations. Then, two adaptive factors, power function and exponential function, are introduced into the algorithm parameters to further balance the global search and local development capabilities, so that the particle population can conduct extensive search and in-depth mining in the solution space. Finally, according to Fick’s law, a disturbance mechanism is introduced into the particle position updating formula to improve optimization accuracy and convergence speed of the algorithm. In addition, 24 benchmark test functions and Wilcoxon rank sum test are used to compare NEO algorithm with other intelligent optimization algorithms. The results show that NEO algorithm has good optimization performance.

Key words: equilibrium optimizer, concentration balance, adaptive factor, Fick’s law

张梦溪, 马良, 刘勇. 融合浓度平衡和菲克定律的新平衡优化器算法[J]. 计算机工程与应用, 2023, 59(3): 66-76.

ZHANG Mengxi, MA Liang, LIU Yong. New Equilibrium Optimizer Algorithm Combining Concentration Equilibrium and Fick’s Law[J]. Computer Engineering and Applications, 2023, 59(3): 66-76.

参考文献

[1] 赵世杰，高雷阜，徒君，等.耦合横纵向个体更新策略的改进MVO算法[J].控制与决策，2018，33（8）：1422-1428.
ZHAO S J，GAO L F，TU J，et al.Improved multi verse optimizer coupling horizontal-and-vertical individual updated strategies[J].Control and Decision，2018，33（8）：1422-1428.
[2] HOLLAND J H.Genetic algorithms[J].Scientific American，1992，267（1）：66-73.
[3] MIRJALILI S，LEWIS A.The whale optimization algorithm[J].Advances in Engineering Software，2016，95：51-67.
[4] 张伟康，刘升，任春慧.混合策略改进的麻雀搜索算法[J].计算机工程与应用，2021，57（24）：74-82.
ZHANG W K，LIU S，REN C H.Mixed strategy improved sparrow search algorithm[J].Computer Engineering and Applications，2021，57（24）：74-82.
[5] GOLDBERG D E.Genetic algorithms in search，optimization and machine learning[M].[S.l.]：Addion Wesley，1989.
[6] MIRJALILI S，MIRJALILI S M，HATAMLOU A.Multi-verse optimizer：a nature-inspired algorithm for global optimization[J].Neural Computing and Applications，2016，27（2）：495-513.
[7] FARAMARZI A，HEIDARINEJAD M，STEPHENS B，et al.Equilibrium optimizer：a novel optimization algorithm[J].Knowledge-Based Systems，2020，191：105190.
[8] KHARRICH M，KAMEL S，ABDEEN M，et al.Developed approach based on equilibrium optimizer for optimal design of hybrid pv/wind/diesel/battery microgrid in Dakhla，Morocco[J].IEEE Access，2021，9：13655-13670.
[9] ANG A D，HAN T，ZHOU H，et al.An improved equilibrium optimizer with application in unmanned aerial vehicle path planning[J].Sensors，2021，21（5）：1814.
[10] FAN Q，HUANG H，YANG K，et al.A modified equilibrium optimizer using opposition-based learning and novel update rules[J].Expert Systems with Applications，2021，170：114575.
[11] 刘成汉，何庆.融合振荡禁忌搜索的自适应均衡优化算法[J].计算机工程与应用，2022，58（10）：68-75.
LIU C H，HE Q.Adaptive equilibrium optimizer algorithm combining oscillating tabu search[J].Computer Engineering and Applications，2022，58（10）：68-75.
[12] GUPTA S，DEEP K，MIRJALILI S.An efficient equilibrium optimizer with mutation strategy for numerical optimization[J].Applied Soft Computing，2020，96：106542.
[13] TOO J，MIRJALILI S.General learning equilibrium optimizer：a new feature selection method for biological data classification[J].Applied Artificial Intelligence，2021，35（3）：247-263.
[14] WUNNAVA A，NAIK M K，PANDA R，et al.A novel interdependence based multilevel thresholding technique using adaptive equilibrium optimizer[J].Engineering Applications of Artificial Intelligence，2020，94：103836.
[15] SHANKAR N，SARAVANAKUMAR N，KUMAR C，et al.Opposition-based equilibrium optimizer algorithm for identification of equivalent circuit parameters of various photovoltaic models[J].Journal of Computational Electronics，2021，20（4）：1560-1587.
[16] ABDEL-BASSET M，MOHAMED R，MIRJALILI S，et al.Solar photovoltaic parameter estimation using an improved equilibrium optimizer[J].Solar Energy，2020，209：694-708.
[17] AHMED S，GHOSH K K，MIRJALILI S，et al.AIEOU：automata-based improved equilibrium optimizer with U-shaped transfer function for feature selection[J].Knowledge-Based Systems，2021，228：107283.
[18] 李守玉，何庆，陈俊.改进平衡优化器算法在约束优化问题中的应用[J/OL].计算机科学与探索：1-14[2022-07-21].http：//kns.cnki.net/kcms/detail/11.5602.TP.20210901.1435.
002.html.
LI S Y，HE Q，CHEN J.Application of improved equilibrium optimizer algorithm to constrained optimization problems[J/OL].Journal of Frontiers of Computer Science and Technology：1-14[2022-07-21].http：//kns.cnki.net/kcms/detail/11.5602.TP.20210901.1435.002.html.
[19] 秦允豪.热学：普通物理学教程[M].北京：高等教育出版社，2004.
QIN Y H.Thermology：general physics course[M].Beijing：Higher Education Press，2004.
[20] 黄昆.固体物理学[M].北京：人民教育出版社，1966.
HUANG K.Solid state physics[M].Beijing：People’s Education Press，1966.
[21] 杨文珍，何庆，杜逆索.具有扰动机制和强化莱维飞行的蝗虫优化算法[J].小型微型计算机系统，2022，43（2）：247-253.
YANG W Z，HE Q，DU N S.Locust optimization algorithm with perturbation mechanism and enhanced levi flight[J].Journal of Chinese Computer Systems，2022，43（2）：247-253.
[22] RAO R.Rao algorithms：three metaphorless simple algorithms for solving optimization problems[J].International Journal of Industrial Engineering Computations，2020，11（1）：107-130.
[23] 何佩苑，刘勇.融入社会心理学理论的教与学优化算法[J].计算机科学与探索，2022，16（6）：1362-1373.
HE P Y，LIU Y.Teaching-learning-based optimization algorithm with social psychology theory[J].Journal of Frontiers of Computer Science and Technology，2022，16（6）：1362-1373.
[24] KENNEDY J，EBERHART R.Particle swarm optimization[C]//Proceedings of International Conference on Neural Networks，1995：1942-1948.
[25] ONG K M，ONG P，SIA C K.A carnivorous plant algorithm for solving global optimization problems[J].Applied Soft Computing，2021，98：106833.
[26] ZERVOUDAKIS K，TSAFARAKIS S.A mayfly optimization algorithm[J].Computers & Industrial Engineering，2020，145：106559.
[27] 贾鹤鸣，刘宇翔，刘庆鑫，等.融合随机反向学习的黏菌与算术混合优化算法[J].计算机科学与探索，2022，16（5）：1182-1192.
JIA H M，LIU Y X，LIU Q X，et al.Hybrid algorithm of slime mould algorithm and arithmetic optimization algorithm based on random opposition-based learning[J].Journal of Frontiers of Computer Science and Technology，2022，16（5）：1182-1192.
[28] KHALAF A H，MITRAS B A.Use two hybrid SCA-AOA and fuzzy SCA-AOA algorithms in information security[J].Open Access Library Journal，2021，8（4）：1-14.
[29] XIE W，XING C，WANG J S，et al.Hybrid henry gas solubility optimization algorithm based on the harris hawk optimization[J].IEEE Access，2020，8：144665-144692.