## 1 Introduction  
Wet-mix shotcrete is indispensable composite material for the application of tunneling, underground mining and building construction [1]. Apart from the excellent mechanical properties, there are other benefits with wet-mix shotcrete, including enhanced automation and reduced rebound and dust concentration. Given all these various advantages, wet-mix shotcrete will replace dry-mix shotcrete as the tendency of shotcrete development in the future. In practice, the uniaxial compressive strength (UCS) of wet-mix shotcrete is the primary concern since it is directly related to the integrity and durability of the supporting structures [2]. The UCS is mainly determined by the mix proportion of wet-mix shotcrete. Consequently, the optimal mix proportion is essential for the wide and safe application of wet-mix shotcrete. To obtain an optimal mix proportion, there are many available optimization methods, which are generally divided into two categories, i.e., empirical optimization methods and computational optimization methods. As for the empirical optimization methods, the main method is to design specific physical experiments and analyze the results. Wet-mix shotcrete is a composite material with many components, such as cement, water, aggregates and so on. The complexity of the components forces researchers to carry out several physical experiments to obtain an optimal mix proportion under designed UCS values, which makes the optimization very time consuming, cumbersome and expensive [3]. Then,in order to decrease the number of experiments and increase the efficiency of optimization, an orthogonal experimental design method was used to design and instruct experiments. [PERSON] et al. analyzed the optimal mix proportion of concrete with recycled clay brick powder by using orthogonal experimental analysis [4]. [PERSON] et al. investigated the effects of polypropylene fiber lengths on the compressive strength of wet-mix shotcrete and optimized the mix proportion by using an orthogonal experimental method [5]. [PERSON] et al. employed an orthogonal experimental method to analyze the optimal mix proportion of pavement concrete with fly ash and silica fume [6]. Although the orthogonal experimental design method has many advantages mentioned above, there is an important disadvantage that cannot be ignored; the number of mix proportion generated by the orthogonal experimental design method is very limited, and the method can only obtain the optimal mix proportion of given levels of experiments. So, this optimal mix proportion is a pseudo-optimal value. This has driven the search for easy and reliable methods to optimize the mix proportion. For computational optimization methods, the heuristic algorithm represented by particle swarm optimization (PSO) is a powerful tool to solve optimization problems. Particle swarm optimization has the advantages of strong robustness, simple operation and fast convergence. [PERSON] et al. adopted the PSO algorithm to optimize the shape of truss structures [7]. [PERSON] et al. utilized the PSO algorithm to optimize the parameters of diesel engine-organic Rankine cycle (ORC) combined system [8]. Although PSO has been widely and successfully adopted in other engineering optimization problems, it is rare to use it to optimize mix proportion of wet-mix shotcrete. Therefore, a further study is essential to investigate the application potential of PSO in optimizing the mix proportion of wet-mix shotcrete. Particle swarm optimization, like other heuristic algorithms, needs a defined objective function prior to the optimization process. In order to obtain a reasonable objective function, UCS, as one of the most important parameters, should be taken into account [9]. Many researchers have conducted a large number of studies to describe the relationship between the influencing factors and UCS, in other words, the prediction of UCS of wet-mix shotcrete. [PERSON] et al.