###### Abstract
These non-conventional algorithms are genetic algorithms (GA) [7], Monte Carlo simulations (MCs) [8], biogeography-based optimization [9], particle swarm optimization (PSO) [10] and derivative algorithms [11]. Of these optimization algorithms, the PSO has favorable search ability, fast convergence and no complicated evolutionary operators, but a derivative algorithm, such as improved particle swarm optimization (IPSO) has more rapid convergence speed compared to PSO [12]. By considering these two factors, many studies have been carried out to determine the problem with the WFLO. [PERSON] et al. developed a PSO with multiple adaptive methods, based on the Jensen model, to find an optimal layout, which outperformed the baseline layout of a reference wind farm by increasing the energy yield by 3.84% under constant wind speed and variable wind direction [13]. [PERSON] et al. presented an approach expected to solve the problem of WFLO based on Gaussian wake model and the GA. Their results showed that there was a small improvement under a more complex wind scenario, in which variable wind speed and wind direction were defined [14]. From the existing approaches aimed at turbine layout optimization and application, the layout optimization can produce electrical energy at a lower cost and a higher efficiency. However, these studies have only taken the wake loss model and optimization algorithm into consideration, with a fixed design of the wind turbine. Thus, it may be beneficial to minimize the COE while simultaneously optimizing the wind turbines and their layout. The wind energy extracted from the wind by a wind turbine is affected by the design parameters of the wind turbine. Recently, researchers have shown great attention to the WTDO, studying three approaches. One approach is to use optimum control algorithms in which Lidar-enhanced control [15] and model predictive control methods [16] are proposed for the torque system, and one-step model predictive control [17] and multi-step model predictive control methods [18] are proposed for the yaw system. Another approach is to optimize the blade shape, such as by an adaptive blade concept for large-scale turbines [19], and the lifting surface method, for airfoils aerodynamic shape optimization [20], so that the wind turbine can gain high energy harvesting efficiency [21]. Nevertheless, the optimization, in terms of the control algorithm and the blade shape, only contributes in some small way to the turbine design. By comparison, the last approach, namely, design optimization may achieve a low COE in an effective way, which involves the most important parameters of the overall design. The dominant methods for designing a satisfactory turbine with low COE require suitable physical and operational parameters, which are related to the wind resource at the selected site but have rarely been studied. In Reference [22], the authors presented a framework for the site-specific design optimization of a horizontal-axis onshore wind turbine, in which the blade number, rotor diameter, tower height, rotor rotational speed, rated wind speed, and rated power were optimized to match the wind condition described by the Weibull distribution and parameters. [PERSON] et al. [23] developed an iterative approach to optimize a single turbine with minimum COE, in which the capital cost was a function of all turbine components, such as rotor diameter, hub height and rated power. In the study, it was found that the onshore turbines with capacities of about 1-2 MW lowered their COE by about 45-75 \(\lx@math@degree\)/MWh. In Reference [24], [PERSON] et al. proposed a mathematical approach to minimize the COE of onshore turbines, in which the COE model was expressed as a function of rated power and rated wind speed. The above references have shown that the site-specific turbine design can achieve a low COE for onshore turbines, but studies of offshore wind turbines are lacking.