Enhanced Chaotic Manta Ray Foraging Algorithm for Function Optimization and Optimal Wind Farm Layout Problem

Manta ray foraging optimization (MRFO) algorithm is relatively a novel bio-inspired optimization technique directed to given real-world engineering problems. In this present work, wind turbines layout (WTs) inside a wind farm is considered a real nonlinear optimization problem. In spite of the better convergence of MRFO, it gets stuck into local optima for large problems. The chaotic sequences are among the performed techniques used to tackle this shortcoming and improve the global search ability. Therefore, ten chaotic maps have been embedded into MRFO. To affirm the performance of the suggested chaotic approach CMRFO, it was first assessed using the IEEE CEC-2017 benchmark functions. This examination has been systematically compared to eight well-known optimization algorithms and the original MRFO. The non-parametric Wilcoxon statistical analysis significantly demonstrates the superiority of CMRFO as it ranks first in most test suites. Secondly, the MRFO and its best enhanced chaotic version were tested on the complex problem of finding the optimal locations of wind turbines within a wind farm. Besides, the application of the CMRFO to the wind farm layout optimization (WFLO) problem aims to minimize the cost per unit power output and increase the wind-farm efficiency and the electrical power engendered by all WTs. Two representative scenarios of the problem have been dealt with a square-shaped farm installed on an area of 2 km
$\times2$
km, including variable wind direction with steady wind speed, and both wind direction and speed are variable. The WFLO outcomes reveal the CMRFO capability to find the optimal locations of WTs, which generates a maximum power for the minimum cost compared to three stochastic approaches and other previous studies. At last, the suggested CMRFO with Singer chaotic sequence has been successfully enhanced by accelerating the convergence and providing better accuracy to find the global optimum.