# Structural Topology Design Optimization Using the Binary Bat Algorithm
## 1 Introduction
Similar to the compliance topology optimization approaches, the stress-constrained topology optimization methods search locally, and final designs can have blurry boundaries or checkerboard patterns depending on an exponent factor. The deterministic approach described in the preceding paragraph requires gradient information of functions. The other fundamental approach to topology optimization is to use metaheuristic methods [17]. Over the last few decades, many metaheuristic optimization algorithms have been explored to solve complex optimization problems. These methods are based on simulations, and they do not require gradient information. Based on the number of solutions in each iteration, there are two types of metaheuristic: (1) single solution-based, such as the Simulating Annealing (SA) and Harmony Search (HS) algorithms, and (2) population-based, such as the Genetic Algorithm (GA). Based on the inspiration, metaheuristic algorithms can be categorized into four types: evolutionary algorithms, such as GA and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [18; 19], physical-based, such as Colliding Bodies (CB), human-based, such as Tabu Search (TS), and swarm intelligence, such as Particle Swarm Optimization (PSO) [20]. All types of metaheuristic algorithms have common features: the search in the entire design space, two searching phases--exploration and exploitation, the use of random numbers to generate new designs, and no good initial designs are required. Metaheuristic algorithms are suitable for tackling many real-life optimization problems, especially those having many local minimum designs or those in which it is not possible to calculate the gradient information of the problem. Like gradient-based algorithms, metaheuristic algorithms have some drawbacks. That is, depending on the number of design variables and the range of each design, they may require many function evaluations to obtain a reasonable solution in comparison with gradient-based optimization algorithms because the number of possible combinations drastically increases. However, this computation efficiency comparison may not be meaningful because the gradient-based approach is a local search method, and the problem of global optimization requires all local optimal solutions. Thus, the deterministic approach may become as computationally expensive as metaheuristic algorithms are [4]. The Bat Algorithm (BA) is based on observations of a natural phenomenon. It was inspired by the echo locative behavior of bats. In the BA, artificial bats (\(n\) designs of dimension \(d\)) are search agents mimicking the search nature of real bats using loudness and emission rates. Regarding some benchmark continuous design variable optimization problems, such as [PERSON]'s (\(d=16\)) and [PERSON]'s (\(d=128\)), it was proven that the BA is capable of obtaining competitive results in comparison with other well-known metaheuristic algorithms, such as GA and PSO [21]. The BA has also been used to solve some discrete design variables optimization problems, such as the symmetric and asymmetric traveling salesman problems [22] and steel frames subjected to American Institute of Steel Construction-Allowable Stress Design (AINC-ASD) design requirements [23]. The binary version of the BA was developed by [PERSON] et al. [24], who termed it the Binary Bat Algorithm (BBA). The BBA has been used to solve 22 benchmark functions. The results have shown that the BBA was able to surpass the binary PSO and GA in terms of the quality of the solutions and the total number of function evaluations required to reach the optimal design [24]. Metaheuristic algorithms for topology optimization usually use binary code (i.e., 0/1) to represent void/solid material distribution. Thus, they can be used directly to solve structural topology optimization problems because no gray area is generated.