## 1 Introduction  
Wind energy has attracted extensive attentions for the past few decades as a sustainable energy source. In early days, wind energy was primarily utilized for the household activities, including the grain grinding and water pumping for irrigation [1]. Modern application of utilizing wind resource is mainly for producing electric power [2]. The electric power that is harvested from wind energy is achieved by wind turbines that are placed in cluster to make full use of local wind resources forming a wind farm [3]. However, grouping wind turbines in cluster causes the unavoidable wake interactions, which reduces the total wind farm power output and jeopardizes the wind farm operational performance [4]. Followed by the extraction of kinetic energy from the incoming wind, the wind velocity reduces and it takes tens of kilometers to recover to its original free-stream condition. The air-disturbed area in the flow path is called wake region. When another wind turbine is located inside the wake region of upstream wind turbines, its performance will be greatly affected, which is called the wake effect phenomenon [5]. In order to reduce the wake power losses, wind turbine locations can be optimally chosen based on the contours of the wind farm, the number and size of wind turbines, and the prevailing wind conditions [6]. The study of wind farm layout optimization can be traced back to 1994, when [PERSON] et al. [7] studied a 2 km \(\times\) 2 km square wind farm when considering three types of ideal wind conditions with discrete wind speed/direction. They divided the wind farm with 10 \(\times\) 10 grid and then used the binary number (0 or 1) to indicate whether the wind turbine exists at a particular grid cell (which is named the grid method). Following this research, [PERSON] et al. [8] studied the layout optimization of three different types of wind farms using the \((x,y)\) coordinates to represent the wind turbine positions (which is called the coordinate method). Through layout optimization, great improvements in the wind farm power output and economic return have been reported in these two pioneer studies. Over the last decade, a great number of researches on the wind farm optimization have been published. [PERSON] et al. [9] employed the aforementioned coordinate method on an offshore wind farm study while using mathematical programming techniques. [PERSON] and [PERSON] [10] proposed the random search algorithm for the layout optimization of Horns Rev wind farm using the coordinate method. In a paper by [PERSON] et al. [11], a multi-objective genetic algorithm was applied for the optimization studies with two optimization objectives: maximizing the wind farm efficiency and minimizing the cost of energy production. Apart from these studies that apply the coordinate method, others have applied the grid method for the wind farm layout optimization. [PERSON] et al. [12] proposed the mixed integer programs for optimization using the wind farm grid method and incorporating the complex constraints, including the landowner participation and noise limits. The landowner participation problem is also studied in references [13; 14] using the grid method. In addition, [PERSON] et al. [15] proposed a new mechanistic semi-empirical wake interaction model, while [PERSON] et al. [16] proposed a definite point selection technique for wind farm layout optimization studies using the grid method. Due to the representation discrepancy of the wind turbine position for the grid and coordinate methods, their pros and cons are prominent. For the grid method, the available wind turbines locations are fixed with a given grid density, while the number of wind turbines during the optimization running is variable, and hence the optimal wind turbine number can be directly obtained following optimization. The coordinate method fixes the number of wind turbines before conducting optimization, and hence it is more efficient in the optimization under a known wind turbine number.