A State-of-the-Art Fractional Order-Driven Differential Evolution for Wind Farm Layout Optimization

Sichen Tao (), Sicheng Liu, Ruihan Zhao, Yifei Yang, Hiroyoshi Todo and Haichuan Yang ()
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Sichen Tao: Faculty of Engineering, University of Toyama, Toyama-shi 930-8555, Japan
Sicheng Liu: Faculty of Engineering, University of Toyama, Toyama-shi 930-8555, Japan
Ruihan Zhao: School of Mechanical Engineering, Tongji University, Shanghai 200082, China
Yifei Yang: Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8560, Japan
Hiroyoshi Todo: Wicresoft Co., Ltd., Tokyo 163-0445, Japan
Haichuan Yang: Graduate School of Technology, Industrial and Social Sciences, Tokushima University, Tokushima 770-8506, Japan

Mathematics, 2025, vol. 13, issue 2, 1-28

Abstract: The wind farm layout optimization problem (WFLOP) aims to maximize wind energy utilization efficiency and mitigate energy losses caused by wake effects by optimizing the spatial layout of wind turbines. Although Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) have been widely used in WFLOP due to their discrete optimization characteristics, they still have limitations in global exploration capability and optimization depth. Meanwhile, the Differential Evolution algorithm (DE), known for its strong global optimization ability and excellent performance in handling complex nonlinear problems, is well recognized in continuous optimization issues. However, since DE was originally designed for continuous optimization scenarios, it shows insufficient adaptability under the discrete nature of WFLOP, limiting its potential advantages. In this paper, we propose a Fractional-Order Difference-driven DE Optimization Algorithm called FODE. By introducing the memory and non-local properties of fractional-order differences, FODE effectively overcomes the adaptability issues of advanced DE variants in WFLOP’s discreteness while organically applying their global optimization capabilities for complex nonlinear problems to WFLOP to achieve more efficient overall optimization performance. Experimental results show that under 10 complex wind farm conditions, FODE significantly outperforms various current state-of-the-art WFLOP algorithms including GA, PSO, and DE variants in terms of optimization performance, robustness, and applicability. Incorporating more realistic wind speed distribution and wind condition data into modeling and experiments, further enhancing the realism of WFLOP studies presented here, provides a new technical pathway for optimizing wind farm layouts.

Keywords: sustainable energy; wind farm layout optimization; differential evolution; genetic learning competitive elimination strategy; genetic algorithm; particle swarm optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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