## 1 Introduction  
As a tool for mankind to explore and develop the ocean, the status of underwater vehicles is becoming more and more prominent. When the battery of the autonomous underwater vehicle (AUV) is about to run out, it needs to be salvaged ashore for charging, which is often troublesome. Wireless power transfer (WPT) technology can solve the energy supply problem of autonomous underwater vehicles [1; 2; 3; 4; 5]. When the underwater vehicle needs to be charged, it can go to the pre-arranged underwater wireless charging base station for energy supply without manual operation. The coupler is a crucial part of the wireless power transfer system, which determines the ability of the WPT system to transmit power [6; 7; 8]. Seawater contains a lot of sodium ion (Na\({}^{+}\)) and chloride ion (Cl\({}^{-}\)), while air has few free charges. Therefore, the seawater environment is conducive, and the air environment is non-conducive. The alternating electromagnetic field around the coupler will generate additional eddy current loss, which will reduce the transmission power and efficiency of the system [9; 10; 11; 12]. Therefore, designing a coupler suitable for the underwater environment is particularly important. The WPT coupler consists of two parts: coils and ferrite cores. Researchers have proposed a variety of excellent coupler structures and practical design methods. In [13], a coil structure suitable for an underwater vehicle with a rotating body structure is proposed, which can achieve stable output power and efficiency when charging autonomous underwater vehicles. In the worst case, 92.1% dc-dc efficiency can be achieved. In [14], a coil size optimization process is proposed for the configuration of DD coils and unipolar coils. The relationship between the size of the secondary coil and the maximum achievable efficiency under two coil topologies is studied. In [15], the design principles of loss optimization and lightweight WPT coils are proposed, using finite element simulation and statistical methods. In [16], an improved alternating current (AC) resistance evaluation method is proposed, the conductive resistance is calculated by frequency-dependent formulas, and the proximity effect resistance is calculated by an improved analytical method. In contrast with the coil part, however, the shape design of the ferrite core has not been extensively studied due to its nonlinear characteristics. In [17], the thickness and shape of the core are optimized to reduce weight, increase coupling factor and reduce loss. In [18; 19], the layout of the ferrite cores is studied for optimizing the coupler coefficient between the transmitting and receiving coils. The existence of magnetic cores makes the magnetic field distribution nonlinear and cannot be analyzed by electromagnetic theory. Therefore, many studies on coils and ferrite cores in the past are independent. For the design of the coupler, we took into account both the coils and the magnetic cores. In addition, the coupler is expected to have a large mutual inductance and a small equivalent coupler loss impedance (ECLI). Therefore, the design of the coupler is a multi-objective optimization design problem. The problem of multi-objective optimization often contains a large number of variables and objective functions. The multi-objective optimization algorithm based on Pareto optimal solution, such as the Non-dominated Sorting Genetic Algorithm (NSGA-II), has been widely applied for its excellent performance [20]. Our work is aimed at the coupler design of an underwater vehicle and comprehensively considers the effects of coil structure and core structure on the coupler performance. The multi-objective optimization design of the coupler is carried out by combining finite element analysis and Non-dominated Sorting Genetic Algorithm II. This paper considers a two-objective optimization strategy of maximizing mutual inductance and minimizing the ECLI of a WPT coupler. Section 2 describes the mechanical structure and circuit structure of the wireless power transfer system.