## 1 Introduction
Further, it cannot recover enough energy from the low-temperature exhaust gas to drive the high-speed motor like the ICE. Therefore, improving the aerodynamic performance of the centrifugal impeller can effectively reduce the system power consumption. According to the current study's results [7], the improvement of impeller efficiency can improve the material utilisation and comprehensive performance in FC to achieve further cost reduction. This work can be achieved through the design optimisation of the aerodynamic performance of the centrifugal impeller. In FC gas supply systems, the higher the air pressure, the better the cost reduction. Studies have shown that the platinum content can be reduced from 0.36 g to 0.2 g/kW when the inlet pressure is increased from 1.5 to 3.0 atm. Second, the higher the air pressure, the higher the system's output power [8]. Higher air pressure is beneficial to increase the energy density of the stack, reducing the size and weight of the FC system and saving the manufacturing cost. Third, higher air pressure is beneficial to the water balance [4]. However, too high a stack inlet pressure consumes additional parasitic power, which reduces the efficiency of the whole machine. Therefore, when optimising the design of the aerodynamic performance of the FC centrifugal impeller, an appropriate increase in the pressure ratio is beneficial for the overall cost reduction. As well, the mass flow has a positive correlation with the FCS. The output power of the FCS will increase with the increase of the mass flow, which is beneficial to the efficiency of the FCS. The traditional centrifugal impeller design method relies on the iterative design from 1D to 3D by experts. Since the 1990s, optimisation design methods have been introduced into the field of impeller aerodynamic design. They have been widely studied for their advantages of short design cycles, lack of dependence on expert experience, and breakthroughs from traditional design limitations [9,10]. [PERSON] et al. [9] presented a 3D multi-objective aerodynamic optimisation method by the multi-objective differential evolutionary algorithm, 3D blade parameterisation method, self-adaptive integration, and RANS. The optimisation results show that the isentropic efficiency and the total pressure ratio were increased by 3.06% and 1.26%, respectively. [PERSON] et al. [10] used a genetic algorithm (GA), a 3D blade parameterisation method, a CFD solver and an artificial neural network, presenting a method for 3D optimisation of a transonic centrifugal impeller. The isentropic efficiency increased by 0.97%, the mass flow increased by 0.65%, and the total pressure ratio increased by 0.74%. The optimisation algorithm is one of the core aspects of the centrifugal impeller aerodynamic design optimisation method, which determines the optimisation-seeking capability and convergence speed in the established design space. Optimisation algorithms for turbomachinery are generally classified into gradient methods, agent model methods (e.g., neural networks) and meta-heuristic algorithms (e.g., genetic algorithms). The gradient method is more efficient in the case of continuous and single-peaked variable space, but it can often only obtain the optimal local solution of the problem, not suitable for the optimisation search of complex multi-peaked problems. The agent model method can better reduce the computational cost, but it is very difficult to establish an agent model with sufficient accuracy since the dimensionality of decision variables increases. At the same time, the method is more difficult to deal with multi-objective multi-constraint problems. Although the meta-heuristic algorithms is computationally expensive, it has been widely used in impeller mechanical design optimisation due to it can obtain global optimisation solutions and has strong robustness [11]. It should be emphasised that the meta-heuristic algorithm is particularly suitable for the optimisation search of multi-objective multi-constraint problems due to its inherent concurrency property.