## 1 Introduction  
After an upstream wind turbine extracts kinetic energy from wind, it propagates towards downstream wind direction forming a large wake area characterized with lower wind speed and more intensive wind turbulence. This is called the wake effect [1]. When another wind turbine is located inside the wake-affected zone, its power output will be reduced to a large extent with a high fatigue load [2]. According to the real engineering observational data, this wake-affected area can cover dozens of kilometers downstream the incoming wind direction [3]. Though the wake effect is unlikely to be completely negated for downstream wind turbines, it can be alleviated by the optimal placement of wind turbines inside a wind farm. Consequently, great power losses can be regained and the cost of power production can be reduced [4]. Back in 1994, [PERSON] et al. [5] studied the wind farm layout optimization problem for an ideal square-shape wind farm using the grid-based design method. The method divides the wind farm area into a number of identical small square grids and the wind turbine can only be positioned at the center point of a specific grid. In this research, the wind farm performance under three different wind conditions (constant wind speed and constant wind direction, constant wind speed and variable wind directions, and variable wind speeds and variable wind directions) were evaluated by comparison to the random wind farm layouts, and the improvements of wind farm power output were reported for all tested wind conditions. After this pioneer work, [PERSON] et al. [6] investigated the wind farm layout optimization problem using the unrestricted coordinate wind farm design method. For this method, the Cartesian coordinates of wind turbines were directly used to represent the wind turbine locations rather than using the grids for the grid-based method. The 'expert guess' wind farm layouts, which employ a typical area value of 3-4 square rotor diameter per wind turbine, were introduced to qualitatively compare the improvements of wind farm performance with the optimized layouts. The comparative results indicated a larger increase of wind farm power output and wind farm efficiency after optimization. As the two most commonly applied wind farm design methods, the grid-based method is known as a discrete method due to the restrained and limited locations for wind turbine placements, while the unrestricted coordinate method is known as a continuous method with a continuous variation of wind turbine placements. The comparison of effectiveness of these two methods has been reported in literature [7], which claims that the coordinate method is more superior than the grid method with more flexibility of wind turbine placements and less computational cost. In recent years, a large number of studies on the wind farm layout optimization using the coordinate method have been published. [PERSON] et al. [8] applied the coordinate method for an offshore wind farm layout optimization study using mathematical programming techniques. [PERSON] and [PERSON] [9] proposed the random search algorithm for layout optimization of the Horns Rev wind farm. In a paper by [PERSON] et al. [10], a multi-objective genetic algorithm was applied for the wind farm layout optimization studies with two optimization objectives: maximizing the wind farm efficiency and minimizing the cost of power production. For the study of wind farm layout optimization using the coordinate method, most importantly, the constraints of wind farm boundary need to be carefully handled to ensure the optimized wind turbine locations are feasible within the wind farm boundary. In this regard, [PERSON] et al. [11] proposed two different means of handling the irregular boundaries of real wind farms in a layout optimization study. Moreover, the selection of the wake model that quantitatively accounts for the wake effect between wind turbines is an additional challenge in the study of wind farm layout optimization.