An improved harris hawks optimization algorithm based on chaotic sequence and opposite elite learning mechanism

PLOS ONE RESEARCH ARTICLE An improved harris hawks optimization algorithm based on chaotic sequence and opposite elite learning mechanism Ting Yang1☯, Jie Fang1‡, Chaochuan Jia ID2,3☯*, Zhengyu Liu2,3‡, Yu Liu2,3‡ 1 College of Electronic and Optoelectronic Engineering, West Anhui University, Lu’an, China, 2 College of Electronics and Information Engineering, West Anhui University, Lu’an, China, 3 Intelligent networked vehicle laboratory, West Anhui University, Lu’an, China a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 ☯ These authors contributed equally to this work. ‡ JF, ZL and YL also contributed equally to this work. * Abstract OPEN ACCESS Citation: Yang T, Fang J, Jia C, Liu Z, Liu Y (2023) An improved harris hawks optimization algorithm based on chaotic sequence and opposite elite learning mechanism. PLoS ONE 18(2): e0281636. https://doi.org/10.1371/journal.pone.0281636 Editor: Pijush Samui, NIT Patna: National Institute of Technology Patna, INDIA Received: March 9, 2022 Accepted: January 26, 2023 Published: February 22, 2023 Peer Review History: PLOS recognizes the benefits of transparency in the peer review process; therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. The editorial history of this article is available here: https://doi.org/10.1371/journal.pone.0281636 Copyright: © 2023 Yang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper. Funding: This work was partially supported by Natural Science research project of Universities in Anhui Province(NO.KJ2021A0953), Natural The Harris hawks optimization (HHO) algorithm is a new swarm-based natural heuristic algorithm that has previously shown excellent performance. However, HHO still has some shortcomings, which are premature convergence and falling into local optima due to an imbalance of the exploration and exploitation capabilities. To overcome these shortcomings, a new HHO variant algorithm based on a chaotic sequence and an opposite elite learning mechanism (HHO-CS-OELM) is proposed in this paper. The chaotic sequence can improve the global search ability of the HHO algorithm due to enhancing the diversity of the population, and the opposite elite learning can enhance the local search ability of the HHO algorithm by maintaining the optimal individual. Meanwhile, it also overcomes the shortcoming that the exploration cannot be carried out at the late iteration in the HHO algorithm and balances the exploration and exploitation capabilities of the HHO algorithm. The performance of the HHO-CS-OELM algorithm is verified by comparison with 14 optimization algorithms on 23 benchmark functions and an engineering problem. Experimental results show that the HHO-CS-OELM algorithm performs better than the state-of-the-art swarm intelligence optimization algorithms. 1. Introduction The optimization issues in real-world problems have received increasing attention from researchers in the fields of artificial intelligence [1], computer vision [2], compressed sensing [3, 4], decision-making [5] and engineering for practical applications [6]. Traditional algorithms are based on derivative methods due to their mathematical complexity, which can only be used to deal with small-scale problems that must be continuous and derivable [7]. Therefore, it is difficult to achieve global optimization for multimodal functions and dynamically changing, strongly nonlinear problems using traditional algorithms. To solve complex and large-scale problems, many swarm intelligence (SI) optimization algorithms that imitate PLOS ONE | https://doi.org/10.1371/journal.pone.0281636 February 22, 2023 1 / 23 PLOS ONE Science Key Scientific Research Project of West Anhui University (NO. 0041021003, WXZR201903). Competing interests: The authors have declared that no competing interests exist. An improved harris hawks optimization algorithm swarm behaviour in natural phenomena, including Cuckoo Search (CS) [8], Grey Wolf Optimizer (GWO) [9], Particle Swarm Optimization (PSO) [10], Artificial Bee Colony (ABC) [11], Suffled Frog Leaping Algorithm (SFLA) [12], Whale Optimization algorithm (WOA) [13], Gravitational Search algorithm (GSA) [14], Jaya [15] and Harris Hawk Optimization (HHO) [16] have been proposed. All SI algorithms have two search phases: global exploration, which searches the whole space for a promising area, and local exploitation, which searches a chosen area that is promising to contain the best solution. However, a single SI algorithm can not deal with all optimization problems. Still, the algorithms proposed recently or those that are not yet discovered have a wide range of application prospects. HHO is a new swarm intelligence optimization algorithm proposed by Heidari et al. [16] in 2019 that mimics the way Harris eagles find and chase prey in nature, including global exploration, local besiege and pounce behaviour. HHO has been widely applied to address the optimization of functions and engineering applications due to its gradient-free and powerful nature with high performance. Heidari et al. used HHO to optimize 29 benchmark functions and 6 engineering applications, and the results show that HHO has better competitiveness and application prospects than other SI algorithms [16]. Houssein et al. [17] used the HHO in combination with the k-nearest neighbours and the support vector machines for chemical compound activities and descriptor selection, respectively. To denoise the satellite images, Golilarz et al. [18] determined optimal wavelet coefficients by using the HHO. HHO was applied to optimize the water network distribution of Homashahr city in Iran in [19]. Abbasi et al. [20] utilized HHO to microchannel heat sinks to minimize entropy generation. Jiao et al. [21] and Liu et al. [22] used HHO to find the optimal parameters of photovoltaic models. However, similar to the other SI algorithms, the HHO still has some limitations, such as the multiplicity of solutions generated by a randomized policy that is finite in the initialization phase. Moreover, because global exploration is only performed in the first half of the iteration, it is difficult to balance the global exploration and local exploitation capacities by using the escaping energy of prey, so the algorithm may converge slowly, has low solution accuracy and prematurely falls into a local optimal solution. To conquer the limitations of HHO, many HHO variant algorithms have been proposed. For example, Ali et al. [23] used the best solution to deal with the boundary condition instead of the boundary of the search space in HHO. Hu et al. [24] also proposed an improved HHO algorithm, which embedded the velocity int (...truncated)