## 1 Introduction  
In recent years, meta-heuristic algorithms have been developed to solve not only simple engineering problems but also complex ones that present nonlinear objective functions and numerous nonlinear constraints. Biologically-inspired algorithms belong to the nature-inspired meta-heuristic algorithm group. Those algorithms can be divided into two categories: evolution-based and swarm-based methods [1]. The best-known and most used evolution-based algorithms are Genetic Algorithms (GA) [2, 3]. The most popular of the Swarm-based methods is Particle Swarm Optimization (PSO), which is inspired by the group behavior of flocks of birds in flight [4]. Physics-based meta-heuristic algorithms, another type of nature-inspired algorithm, are based on the physical laws of the universe. The most popular of these is Simulated Annealing (SA) [5]. Besides these algorithms, there are human-based algorithms, the most popular of which is Harmony Search (HS) [6]. At the same time as these new meta-heuristic algorithms were developed, a number of \"no free lunch\" (NFL) theorems were presented [7]. These NFL theorems establish that for any algorithm, any elevated performance in one type of problem is offset by performance in another type. Therefore, after a period of proposing new algorithms, some of them began to be applied and fitted to specific engineering problems. The optimum design of concrete structures, which has been widely used in building [8], road [9], rail [10], and marine [11] engineering, is one of these specific problems. In parallel to this period dedicated to the development and application of new algorithms, studies have been oriented toward detecting differences in their performance and some improvements have been proposed. PSO has been shown to be more efficient than GAs [12, 13]. The work by [PERSON] et al. [14] is oriented toward the development of a new,accurate, and efficient Decline Population Swarm Optimization (P\({}_{\text{D}}\)SO) algorithm. This new method, applied to vibro-acoustic problems, has resulted in increased performance of the standard PSO. Moreover, the Firefly Algorithm (FA), which is a swarm-based method, has been shown to be more efficient than GAs and PSO [15]. The work by [PERSON] et al. [16] shows how the use of different chaotic systems to replace the parameters of the FA improves the efficiency of the algorithm. It is also necessary to mention the work by [PERSON] et al. [17], which shows the widespread use of the FA in various fields of engineering. The works by [PERSON] et al. [18; 19] and [PERSON] et al. [20] are particularly interesting. In the case of complex structural systems, the number of variables and constraints increases considerably, so the chosen methodology must be based on efficient algorithms in order to reduce the computational cost [21; 22]. However, less effort has been made to solve structural system problems where elements subject to biaxial bending appear. It is necessary to keep in mind that under biaxial bending, the computational cost increases if the equivalent rectangular compressive stress block is not used for calculating stresses in the compressed zone of the section [23]. Thus, the need to reduce costs is increasing constantly, and the use of efficient algorithms, such as the FA, in these types of problems, is essential [24]. Many recent methods are efficient, although not all of them respond well to real problems with constraints [22]. Meta-heuristic algorithms need a long time to achieve a final design. Parallel computing strategies sharing the computation load over several processors have started to be applied to reduce this computational time. [PERSON] and [PERSON] [25] present a parallel-evolution method for structural optimization. Firstly, the problem is divided into two subproblems; one with discrete design variables and the other with continuous ones. Then, each subproblem is solved using a parallel evolution approach.