## 1 Introduction  
Structures, including bridges, buildings, offshore foundations, pipelines, and vehicles, are complex engineering systems that are valuable assets to society and enrich the lives of people. These structures are subject to deterioration over time due to continuous use and exposure to factors such as deicing salts, humidity, and temperature variations. Hence, structural health monitoring (SHM) methods have been developed for evaluating the condition of a structure to avoid any failure and to plan maintenance actions without interrupting operations. One of the first types of SHM was vibration-based damage detection. Vibration-based damage detection techniques are commonly used in different structures. These techniques are based on the concept that any change in the mechanical properties of a structure is reflected by changes in its dynamic characteristics. The parameters monitored in vibration-based SHM include natural frequencies, mode shapes, mode shape derivatives, and damping properties. The key requirements for the success of the aforementioned techniques are the abilities to identify different natural frequencies, identify different mode shapes, and overcome spatial aliasing. Real structures are continuous; therefore, each real structure has an infinite number of nodes. However, in the physical world, only a finite number of sensors can be placed at a finite number of locations. In general, the more sensors one places on a structure, the more details are obtained to reveal the structural health status. However, in practical SHM, the number of sensors is typically limited and is subject to factors such as budget constraints and structural inaccessibility. Therefore, one must optimize the sensor locations to obtain as much structural information as possible. This problem is defined as the optimal sensor placement (OSP) problem. Many studies have been conducted on OSP problems by using various vibration testing techniques and criteria. [PERSON] [1] published a landmark paper in this area. Their study focused on OSP with modal identification and correlation for large structures. [PERSON] et al. [2] used a kinetic-energy-based method to select a candidate set based on the modal kinetic energy (MKE) distribution that measured the dynamic contribution of the physical degree of freedom (DOF) of each finite-element method (FEM) to each target mode shape. [PERSON] [3] applied information entropy to measure the energy content of a sensor configuration for OSP. Another commonly used OSP method is the modal assurance criterion (MAC) method [4; 5]. The MAC is defined to measure the correlation between different mode shapes from sensor placements. It can also be used for quantifying spatial aliasing. The ideal diagonal value of the MAC matrix should be 1, and the ideal off-diagonal value of this matrix should be 0. Numerous formalisms use one or more MAC matrices in OSP problems. [PERSON] and [PERSON] [6] compared the performance of two optimization objective functions, namely minimize the largest off-diagonal element and minimize the sum of the off-diagonal element least squares, for some examples. Although many approaches can be used for OSP, mode shape matrix methods are often used for analysis and computation. The OSP problem has been solved through stochastic approaches. [PERSON] et al. [7] described the details of evolutionary algorithms used for the OSP problem. These algorithms can be broadly categorized as population- or trajectory-based algorithms. They can also be classified as bioinspired, physics-inspired, and geography-based algorithms. However, the aforementioned single-objective OSP approaches only adopt only one OSP evaluation criterion. Because various quality measures of a signal might oppose each other, multiobjective evolutionary algorithms (MOEAs) aim at producing a set of Pareto-optimal solutions in a single run. Because MOEAs have broad applications, considerable research attention has been devoted to practical MOEAs. Numerous algorithms have been developed and improved.