## 1 Introduction
Three main methods are used in multi-objective optimization, according to the processing methods of searches and decision-making: the a priori preference, posterior preference, and interactive methods [24]. For complex systems, the display expression of the preference function cannot be provided in advance. Here, the decision-maker must use the posterior preference method to search for the decision first, then obtain a satisfactory solution from a series of solutions. Multi-objective evolutionary algorithms belong to this a posteriori preference method, which can be divided into the following three categories: the aggregation function method, population-based method, and Pareto-based method. The aggregation function method is used to transform multi-objective problems into single-objective problems, such as a decomposition-based multi-objective evolutionary algorithm [25]. This method needs to set each target weight, which is a challenging problem for decision-makers. The population-based method mainly relies on population evolution to realize each target function search separately, such as the multi-objective particle swarm optimization algorithm [26], pollen pollination algorithm [27], and multi-objective Grey Wolf algorithm [28]. This method will cause the partial loss of non-inferior solutions, due to the necessity of compromise in all sub-objectives [29]. At present, most evolutionary algorithms are Pareto-based, which incorporates the concept of the Pareto optimum into the selection mechanism, such as the non-dominant sequencing genetic algorithm [30; 31; 32; 33], the Niched Pareto genetic algorithm (NPGA) [34], and the Strength Pareto Evolutionary Algorithm (SPEA) [35]. The NSGA-II algorithm is a typical representative of the Pareto method, which overcomes the shortcomings of complex calculation, low efficiency, and the low robustness of the Non-dominated Sorting Genetic Algorithm (NSGA). The algorithm offers the advantages of good distribution and convergence. Therefore, NSGA-II is applied in many fields [36; 37; 38]. [PERSON] et al. optimized the key parameters of the actuating mechanism of the stepsizes air flow regulation system of a multistage reciprocating compressor with NSGA-II and obtained good results [39]. The above literature review demonstrates that the suction valve of the stepless flow control system acts as the coupling point of hydraulic, mechanical, and compressor gas systems. The optimization of the valve's motion characteristics directly affects the performance of the three systems, and there are contradictions among the objective functions of the systems. Therefore, the traditional single-system analysis model and single-objective optimization method are no longer applicable. In response to this problem, this study has established a multi-system simulation model of a reciprocating compressor stepless flow control system by analyzing the coupling points and coupling parameters among the subsystems. Multi-objective optimization was used to optimize the key parameters. The main research contributions are as follows. Through the analysis of the coupling points between the hydraulic and mechanical systems, this study has determined the two coupling factors affecting the unloader movement characteristics, namely, the oil inlet pressure and oil return pressure, which are independent factors of the mechanical system, namely the return spring stiffness. Following the operating principle of the top-opening suction valve, a mathematical model of the flow control system based on multi-system coupling was established. Based on the analysis of the influence of the change in the valve movement characteristics on other subsystems, four objective functions were determined: the ejection and withdrawal speeds of the unloader movement characteristic parameters, the indicator diagram deviation, and the displacement deviation of the compressor thermodynamic performance.