## 1 Introduction
[PERSON] [17] dealt with the optimal placement strategies of the active constrained layer damping to minimize the total weight of the damping treatment by using the modal strain energy method. [PERSON] et al. [18] carried out the optimization of the constrained layer damping treatment to minimize the vibration response of cylindrical shells, which are considered to transverse force excitation. [PERSON] et al. [19] developed an optimization algorithm to optimize the loss factor of a segmented constrained layer damping beam. [PERSON] et al. [20] investigated the optimization of a constrained layer damping layout on the plates using a topology optimization tool. [PERSON] et al. [21] proposed a new 0-3 viscoelastic composite layer and the layer is arranged by an optimization algorithm. [PERSON] [22] investigated the damping effectiveness of a partially covered plate, which include multi-parameter optimization techniques. Meanwhile, due to the rapid development of computers, many novel algorithms have been developed, such as genetic algorithm, neural network algorithm and so on. Some researchers applied these algorithms to optimize the sandwich structures and acquired good results. [PERSON] et al. [23] dealt with the optimal damping of a sandwich beam covered by one or several portions and the optimization problem is solved by using a genetic algorithm. [PERSON] et al. [24] studied an optimization model to minimize the vibrational energy of a sandwich beam and employed a genetic algorithm-based penalty function to obtain the optimal solutions. [PERSON] et al. [25] considered the constrain optimization of the damping characteristics to maximize the damping loss factors based on the Feasible Arc Interior Point Algorithm. [PERSON] et al. [26] applied a genetic algorithm with a large-scale mutation method to optimize the modal loss factor; the design variables include the thicknesses of the constrained layer and the viscoelastic layer and the shear modulus of the viscoelastic. [PERSON] et al. [27] proposed a real-coded constrained genetic algorithm to optimize the damping behavior of composite laminates. [PERSON] et al. [28] employed a multiple population genetic algorithm to find the best coating location of a cantilever titanium plate, which aims to obtain the maximum modal loss factor. [PERSON] et al. [29] applied a multi-objective genetic algorithm to solve the multi-objective function of the hard-coating blisk. From the above discussion, it can be found that many researchers have done some work on the optimization of the damping loss factor of the sandwich structure based on some optimization algorithms. However, the optimal damping loss factor with the constrained damping layer position as the design variable is rare. This paper deals with the optimal location of the constrained damping layer of a sandwich plate to maximize the damping loss factor by using a multi-population genetic algorithm (MPGA). In addition, the dynamic behavior of structures under moving loads is also the focus of the engineering field, especially bridges, roads and mechanical engineering. [PERSON] [30] proposed several analytical solutions on the moving loads problem. [PERSON] et al. [31] considered a theory that has arbitrary end support and is under an arbitrary number of masses to obtain the dynamic response of beams and rectangular plates. [PERSON] et al. [32] investigated the dynamic response of a plate on a viscous Winkler foundation under moving loads of varying amplitudes and developed a formulation by using a triple Fourier transform and a double Fourier transform. [PERSON] [33] concerned the dynamic behavior of a rectangular plate under curvilinear moving loads based on the finite element method (FEM), which transforms all the external loads into equivalent forces on corresponding nodes. [PERSON] et al. [34] studied the dynamic analysis of composite plates under multi-moving loads based on a third order shear deformation theory (TSDT) and applied the 7-DOF finite element model to analyze the vibration problem. [PERSON] et al.