## 1 Introduction
[13] conducted an experimental, analytical and numerical survey on stress analysis and damages of a double-lap steel-to-CFRP joint. The data containing FEM, digital image correlation (DIC), and acoustic emission (AE) were compared, and their convergence was illustrated. On the other hand, the application of optimization algorithms in complex problems has increased in recent decades. [PERSON] and [PERSON] [14] introduced the particle swarm optimization methodology for optimizing nonlinear functions. They investigated the relations of the novel method with GA and artificial life. They introduced a novel algorithm that simulates how a flock of birds behaves in their social community. So, they called this new search method particle swarm optimization (PSO). Its initial purpose was to simulate the unforeseeable and distinguished choreography of a flock of birds graphically, to discover the patterns governing the ability of birds to fly synchronously and suddenly change direction by regrouping in an optimal formation. This simple concept was developed and led to an uncomplicated and effective optimization method. Figure 1: A 2D schematic diagram of a double lap joint. In this methodology, the particles can fly and search through a hyperdimensional space. The basis of changes in the position of particles is the social-psychological propensity of them to imitate the prosperity of others. So, these changes for every individual are affected by the knowledge and experiences of other particles in their neighborhood. Therefore, it influences individual fashions in searching the area that the others do in the swarm (so, the PSO is a symbiotic collaborative algorithm, in other words). Utilizing this type of social manner as an optimization method results in the particles returning to the prior successful areas of exploration territory stochastically. Basic particle swarm optimization formulas are  
\[v_{ij}(t+1)=\omega\times v_{ij}(t)+c_{1}\times r_{1j}(t)\times\left[y_{ij}(t)- x_{ij}(t)\right]+c_{2}\times r_{2j}(t)\times\left[\hat{g}_{j}(t)-x_{ij}(t)\right] \tag{1}\]  
\[x_{ij}(t+1)=x_{ij}(t)+v_{ij}(t+1) \tag{2}\]  
where \(v_{ij}\) is the velocity vector and \(x_{ij}\) shows the position of the particle. \(c_{1}\) and \(c_{2}\) are two constant values between 1.4 and 1.7. \(r_{1j}(t)\) and \(r_{2j}(t)\) are two random values ranging from 0 to 1. In the velocity equation,  
\[\text{Momentum part}:\ \omega\times v_{ij}(t) \tag{3}\]  
\[\text{Cognitive part}:\ c_{1}\times r_{1j}(t)\times\left[y_{ij}(t)-x_{ij}(t)\right] \tag{4}\]  
\[\text{Social part}:\ c_{2}\times r_{2j}(t)\times\left[\hat{g}_{j}(t)-x_{ij}(t)\right] \tag{5}\]  
This optimization method has two subsidiaries: global best PSO (gbest PSO) and local best PSO (lbest PSO). For the global best PSO, the neighborhood for each particle is the entire swarm, while the local best PSO utilizes a social network cluster topology with smaller vicinities for every particle. This paper uses the lbest methodology to find the optimum layups. In local best PSO, the social part indicates information interchanged within the vicinity of the particle, illustrating the local understanding of the territory. Concerning the velocity equation, the social subsidy to particle velocity corresponds to the distance between a particle, and the best position found in the vicinity of particles. The velocity can be thus calculated as  
\[v_{ij}(t+1)=\omega\times v_{ij}(t)+c1\times r_{1j}(t)\times\left[y_{ij}(t)-x_{ ij}(t)\right]+c2\times r_{2j}(t)\times\left[\hat{g}_{j}(t)-x_{ij}(t)\right] \tag{6}\]  
where \(y_{ij}(t)\) is the best position ever visited by the particle, \(x_{ij}(t)\) is the particle's current position and \(\hat{y}_{j}(t)\) shows the local best-visited position in the neighborhood. The pseudo-code of PSO is shown in Appendix B (Figure A1). [PERSON] et al. [15] explored the different modifications of the PSO methodology. The ability of these methods to find the optimum point of the objective function takes too much attention from specialists in different areas.