## 1 Introduction  
Planar trusses are one of the most commonly used structural forms [1; 2]. One of the classical problems in their design and optimization is finding the optimal topology configuration as well as the optimal size. Two main techniques are generally used to address this problem: continuum topology optimization and the discrete ground structure method. The first strategy, achieved through many methods such as the solid isotropic material with penalization (SIMP) method [3], the level-set method [4; 5] and evolutionary structural optimization (ESO)/bi-directional ESO (BESO) method [6; 7; 8], aims to obtain the optimal material distribution in a continuous space given in advance. Postprocessing work is always needed after obtaining the optimal material distribution, and it is sometimes difficult to obtain a clear outline shape. Although some newly developed element-based algorithms that have solved the boundary issue [9; 10], for large-scale trusses, a large amount of postprocessing work is usually unacceptable. For the second strategy, the discrete model is closer to the actual structure and does not require any postprocessing work for the terminal truss structure [11]. Based on this, a large number of design variables, large search space, and a large number of design constraints are the major preventive factors in determining optimal design in a reasonable time for large-scale trusses. These are also prominent differences from small ones. Therefore, the use of optimization algorithms to solve such difficult problems is inevitable. Traditional structure optimization methods are essentially based on mathematical programming [12] and optimality criteria [13; 14] approaches. However, they rely on cumbersome gradient-based formulations and have shortcomings in handling real-world instances with discrete design variables. Thus, metaheuristic algorithms based on population evolution are mainly used for truss optimization. They are based on a single or on multiple populations, such as the genetic algorithm (GA) [15], cuckoo search algorithm (CS) [16], salp swarm algorithm (SSA) [17], adaptive dimensional search (ADS) [18], and shuffled frog-leaping algorithm (SFLA) [19]. For large-scale trusses, [PERSON] [20] investigated a new method based on the ground structure approach with selective subsets of active bars in finding the optimal topology of large-scale Michell trusses. [PERSON] [21] proposed an enhanced hybrid harmony search (HS) algorithm for weight minimization of large-scale truss structures. [PERSON] [22] extended a recently developed design-driven heuristic method, namely, guided stochastic search (GSS), to truss optimization problems with thousands of design variables. [PERSON] [23] studied the cascade optimization method in the design optimization of truss towers with large numbers of design variables. The above evolutionary methods have a large number of individuals, which all need structural analyses. This would cost considerable calculation space and time, especially for large-scale trusses with a large number of design variables. [PERSON] and [PERSON] [24] solved this problem by combining a branched multipoint approximation (BMA) with a genetic algorithm. The objective and constraint functions of structure optimization are approximated by several structural analysis results on real design points. Thus, the large number of individuals in GA can obtain approximate fitness results directly from explicit approximate functions instead of structural analyses. This extremely decreases the burden from a large amount of structural analyses [25] and provides an outstanding advantage over metaheuristic methods without BMA. This effective method has been applied successfully in many circumstances [26]. The above efficient method has been applied to sizing and topology optimization for large-scale trusses. Size variables are continuous, and topology variables are discrete, i.e., 0/1, to represent the absence/presence of bar members.