A hybrid equilibrium algorithm and pattern search technique for wind farm layout optimization problem.

The layout optimization-based model is a significant issue for increasing the utilization rate of the wind farm and minimizing its cost per unit of power. For the accurate and reliable wind farm layout optimization design, a novel algorithm based on the hybridization of equilibrium optimizer (EO) and pattern search (PS) technique, named EO-PS, is proposed in this paper. The proposed EO-PS operates in two phases. The first phase implements the EO to explore the search space and reach the promising regions by using an equilibrium pool of elite particles, which contributes to maintaining the diversity of solutions. The second phase integrates the PS to guide the searching towards better vicinities and achieve a high-quality solution by using its detecting and pattern movements to boost the exploitation ability of the proposed method in the last steps. The presented EO-PS algorithm is implemented to deal with single and multi-objective optimization aspects of wind farm layout optimization using different wind speed scenarios. Furthermore, the proposed algorithm is investigated on irregular land space in the Gulf of Suez-Red Sea in Egypt to achieve the optimal layout configuration of the wind farm, which is vital for possible practical planning trends. The comprehensive results and analyses have affirmed that the proposed EO-PS can achieve competitive performance compared to the other state-of-the-state methods, especially in terms of the solution' quality and reliability.