###### Abstract
[13] introduced a methodology for defining compressor characteristic curves via a comprehensive surge cycle process. The experimental attainment of compressor characteristics is also essential for foundational research and application, which manipulates the exit throttle valves to change compressor performance. Recording parameters like pressure, temperature, and torque ensued after stable operation at preset valve openings. [PERSON] et al. [14] finished an experimental study on a low-speed single-stage axial compressor to explore the impact of rotating distortion on its aerodynamic stability, which was controlled by a throttling valve device positioned at the exit. [PERSON] et al. examined the influence of seal cavity leakage flow, comparing compressor performance alterations in conjunction with exhaust systems and other apparatus [15]. In addition, [PERSON] carried out centrifugal compressor experiments, where the baseline compressor was throttled to operate near surge conditions and then methodically driven into surge by gradually closing the throttle at a uniform rate [16]. Moreover, a new casing treatment method was proposed and tested by [PERSON] et al. on three different compressors. Featuring controllable bleed valves, the TA36 fan can precisely navigate operating points close to the stall and rapidly depart from it. On another compressor, throttling was executed via the exit rotary cone valve affixed to the shaft, manually regulated as stall conditions approached [17]. Furthermore, [PERSON] et al. also leveraged outlet duct throttling in their experiments, with the dynamic measurements of pressure, temperature, and acoustic noise being explored to ascertain compressor surge points [18]. The above review reveals that the advantages of obtaining compressor characteristic curves through numerical simulations lie in their speed and low cost, with the practice involving a trial-and-error approach to gradually approximate the stall point. Relatively, experimental methodologies enable the precise determination of characteristic curves, typically through the manual or motor-driven adjustment of a downstream throttling device. It is a method that, although costly, ensures precise results and is often reserved for specific studies. Consequently, by automating the solution process in conjunction with numerical simulation techniques, researchers can further enhance work efficiency in compressor design, optimization, and application studies. A crucial instrument for automated solving processes is the optimization algorithm, whose research and implementation spans across diverse industries, and is exceptional in the optimization design of compressors. During the evolution of optimization algorithms, cutting-edge optimization algorithms have continually arisen, including numerous local optimization algorithms as well as global optimization techniques [19]. Generally, optimization algorithms encompass numerical optimization methods, direct search methods, and global exploration methods. Numerical optimization methods specifically include Sequential Quadratic Programming, while the direct search methods involve the Hooke-Jeeves method, the downhill simplex method, etc. Moreover, the global exploration methods entail variable algorithms such as multiple-island genetic algorithms, simulated annealing, and particle swarm optimization [20; 21; 22]. This category of algorithms comprises stochastic search methods inspired by natural biological evolution or collective social behaviors. They operate independent of gradient information, ensuring that solutions are robust from the start. Additionally, they exhibit the characteristics of intergenerational inheritance and collective intelligence. These algorithms excel in global optimization, making them well suited for tackling large-scale, complex optimization problems with a wide scope of applications [23]. In addition, several contemporary subjects, such as artificial intelligence and machine learning [24; 25; 26], have gained a lot of attention lately.