A Chaotic Local Search-Based Particle Swarm Optimizer for Large-Scale Complex Wind Farm Layout Optimization Zhenyu Lei, Shangce Gao, Senior Member, IEEE, Zhiming Zhang, Haichuan Yang, and Haotian Li Abstract—Wind energy has been widely applied in power gen- eration to alleviate climate problems. The wind turbine layout of a wind farm is a primary factor of impacting power conversion efficiency due to the wake effect that reduces the power outputs of wind turbines located in downstream. Wind farm layout opti- mization (WFLO) aims to reduce the wake effect for maximizing the power outputs of the wind farm. Nevertheless, the wake effect among wind turbines increases significantly as the number of wind turbines increases in the wind farm, which severely affect power conversion efficiency. Conventional heuristic algorithms suffer from issues of low solution quality and local optimum for large-scale WFLO under complex wind scenarios. Thus, a chaotic local search-based genetic learning particle swarm optimizer (CGPSO) is proposed to optimize large-scale WFLO problems. CGPSO is tested on four larger-scale wind farms under four complex wind scenarios and compares with eight state-of-the-art algorithms. The experiment results indicate that CGPSO signifi- cantly outperforms its competitors in terms of performance, sta- bility, and robustness. To be specific, a success and failure memo- ries-based selection is proposed to choose a chaotic map for chaotic search local. It improves the solution quality. The param- eter and search pattern of chaotic local search are also analyzed for WFLO problems. Index Terms—Chaotic local search (CLS), evolutionary computa- tion, genetic learning, particle swarm optimization (PSO), wake effect, wind farm layout optimization (WFLO).    I. Introduction T HE natural environment is annually degraded with rapid industrialization development because excessive fossil fuel consumption leads to negative effects on the environ- ment. Sustainable development is necessary for alleviating environmental problems. Therefore, renewable energy resou- rces, such as solar, wind, ocean, hydropower, and geothermal energies, have been rapidly developed instead of fossil fuels to achieve sustainable development [1]–[6]. Wind energy has become one of the most promising renewable resources with its continual development. Currently, wind energy is also worldwidely applied in the power generation. The power gen- eration capacity of a wind farm is strictly dependent on the site, wind turbine (WT), wind profile, its layout, etc. More- over, the wake effect highly affects the generation capacity, which causes power losses by 10%−20% of total power out- puts in complex wind farm [7]. It refers to that the wind energy of a wind turbine located in downwind is absorbed by its upwind wind turbine resulting in its generation capacity declination. Researchers have investigated from different aspects to improve the generation capacity of a wind farm, such as site selection, wind turbine design [8], wake effect model [9], wind speed forecast [10], and wind farm layout optimization [11]. Meanwhile, the wind turbine is more stable, efficient, and controllable with the manufacture development. Wind farm layout optimization (WFLO) problems play an essential role in improving the power outputs of a wind farm. It maximizes the power generation capacity of a wind farm via optimizing the position of wind turbines to reduce the wake effect among them. Then, researchers have proposed different wind farm and wake effect models for maximizing the out- puts of a wind farm. 10 × 10 For wind farm modeling, there are two modeling representa- tions of a wind farm, i.e., a continuous model and a discrete model. The former allows a wind turbine to be placed any- where in a wind farm, which means the model has high com- plexity and requires high computation costs. Chowdhury et al. [12] proposed a nonlinear continuous WFLO problem and used a constraint particle swarm optimization algorithm to optimize it. Guirguis et al. [13] proposed a gradient-based multi-objective algorithm for the wind farm continuous opti- mization problem. Feng and Shen [14] proposed an extended random search to solve a continuous WFLO problem. On the other hand, the latter divides a wind farm into many grids and places wind turbines in the center of grids. Mosetti et al. [15], for the first time, used genetic algorithms to solve a discrete WFLO problem. They divided a wind farm into grids in which wind turbines are placed. Marmidis et al. [16] subdi- vided a wind farm into 100 square grids, and optimized it by Monte Carlo simulation method. Turner et al. [17] developed a new mathematical method to optimize a discrete WFLO problem. Although the continuous model with the advantage Manuscript received October 5, 2022; revised November 29, 2022; accepted December 20, 2022. This work was partially supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (JP22H03643), Japan Science and Technology Agency (JST) Support for Pioneering Resea- rch Initiated by the Next Generation (SPRING) (JPMJSP2145), and JST through the Establishment of University Fellowships towards the Creation of Science Technology Innovation (JPMJFS2115). Recommended by Associate Editor Xin Luo. (Corresponding author: Shangce Gao.) Citation: Z. Y. Lei, S. C. Gao, Z. M. Zhang, H. C. Yang, and H. T. Li, “A chaotic local search-based particle swarm optimizer for large-scale complex wind farm layout optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1168–1180, May 2023. The authors are with the Faculty of Engineering, University of Toyama, Toyama 930-8555, Japan (e-mail: leizystu@outlook.com; gaosc@eng.u- toyama.ac.jp; zhangzm0128@163.com; yokaisen1994@gmail.com; 159168 8699lht@gmail.com) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2023.123387 1168 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 10, NO. 5, MAY 2023