## 1 Introduction
Meanwhile, the pressure loss of the fluids through the HE is also an important issue and should be considered since the total pressure loss has a significant impact on flow distribution and heat transfer performance. Therefore, it is crucially important to optimize the flow and heat transfer characteristics of lead-SCO\({}_{2}\) in the primary heat exchanger. With a mature theory, sufficient experimental studies and extensive industrial application experience, the shell-and-tube heat exchanger (STHE) has been widely used in different fields [14; 15]. Moreover, the shell-and-tube heat exchanger is a considerable choice of HE among the existing reactors including LFR [16; 17]. Consequently, STHE is an available type of HE with liquid lead and SCO\({}_{2}\) as a working medium. In response to the dramatic changes in the physical properties of SCO\({}_{2}\) with temperature, the subsection model is used to simulate the variation in physical properties in the design of SCO\({}_{2}\)[18]. Some heat transfer enhancement methods used for the conventional fluids such as conventional segmental baffles may not be suitable choices, because this will lead to vast dead zones and increase the risk of liquid metal solidification [10]. Straight tube HE is recommended for the safety and miniaturization of the system design of LFR [19]. In addition to the design of a heat exchanger, the optimization of its performance is another important work. In recent years, the emergence of various intelligent optimization algorithms provides a powerful tool for the optimization of a heat exchanger. In the past decade, the genetic algorithm is definitely a competitive intelligent algorithm. It is widely used in the optimization of various thermal equipment and systems [20; 21] and compared with other algorithms [22; 23]. In the optimization process of the genetic algorithm, there is commonly single or multi-objective functions to evaluate the optimization results. Some researchers focus on the efficiency, pressure drop, heat transfer area and other thermodynamic parameters of HE [24], whilst others consider the cost and economy of HE [25], and some researchers take the entropy generation and exergy based on the second law of thermodynamics as the objective function. Furthermore, many researchers ensure comprehensive consideration on the design of HE through the combination of different perspectives [26; 27]. [PERSON] et al. [28]took the ecological function and cost as the objective function, used the non-dominated sorting genetic algorithm II (NSGA-II) to optimize the shell and tube heat exchanger and obtained the Pareto solution set. [PERSON] and Cui Song and [PERSON] (2019) carried out single/multi-objective optimization on the plate fin heat exchanger with the entropy production and operation cost as the objective functions, and optimized the comprehensive performance of the heat exchanger. The result of multi-objective optimization provides a flexible solution for practical production. Specifically, some researchers also used genetic algorithm to optimize the design of a heat exchanger or energy system with SCO\({}_{2}\) or liquid metal as a working medium. [PERSON] et al. [PERSON] et al. (2019) carried out the multi-objective optimization of LFR system with thermoelectric conversion efficiency and a power generation cost as objective functions, improved the overall economy of the system and obtained the optimal geometric parameters of the intermediate heat exchanger. [PERSON] et al. [PERSON] et al. (2019) proposed a CCHP system combined with a SCO\({}_{2}\) cycle, took a unit cost and efficiency as the objective functions and carried out multi-objective optimization using NSGA-II to obtain the best design performance of the system. The exergy efficiency is improved and the unit cost of the system is reduced after optimization. The temperature of the coal-fired power plant was optimized by [PERSON] et al. [PERSON] et al. (2019) in order to improve the efficiency and the best temperatures of the cold end and hot end were obtained.