# Optimization of Composite Structures with Thin Rigid Fibers Using Bioinspired Algorithms
## 1 Introduction  
Mechanical structure optimization challenges are a class of challenging and time-consuming jobs. The challenge lies in the requirement of finding a global solution and computing difficult direct problems more than once in order to determine the value of the fitness function and/or its gradient. Proposing optimization techniques based on immune system applications or the particle swarm optimizer is a crucial step in the creation of bioinspired algorithms. Both the boundary element method (BEM) and the finite-element method (FEM) can be used to tackle boundary-initial value problems. In this paper, two different optimization algorithms are used: the artificial immune system (AIS) and the particle swarm optimizer (PSO). Both algorithms were created based on observations of phenomena occurring in nature. The purpose of using two different optimization algorithms is to ensure that the obtained solutions are optimal. First, all tasks are solved using AIS, then using PSO. Obtaining the same results confirms that the results are optimal. The goal of these algorithms is to optimize composite structures with thin rigid fibers. A process found in biological immune systems serves as the foundation for the development of artificial immune systems [1]. They can make use of positive and negative selection mechanisms or of the clonal selection mechanism. The clonal selection mechanism is employed in this work. Intensive research on the development of such algorithms for application to optimization and identification problems has been carried out in recent years. Currently, in many research institutions in the world, artificial immune systems [2] and particle swarm optimizers [3] are developed and used, e.g., in relation to the optimization and classification problem. A few examples of such numerous works are the query expansion problem [4], learning neural network [1, 5, 6], and multi-objective optimization [7, 8]. Nowadays, AIS is widely used to solve a wide range of issues, even highly specialized ones, such as diagnosing heart disease using ECG analysis [9], identifying and controlling a fuel-ethanol-fermutation process [1], and choosing the best Wiener equalizers [10]. There are also other fascinating uses for AISs, such as reconstructing evolutionary trees [8]. The 'classic' artificial immune system [11] has been modified; one such modification is the Bayesian artificial immune system (BAIS), which is utilized in Refs. [12; 13]. There is additional application potential of the AIS in the context of transportation systems [14; 15]. In Ref. [16], a hybrid version of this approach is utilized to achieve faster convergence to the global optimum. Swarm algorithms mimic the social behaviors of animals that travel and reside in groups. The PSO algorithm finds answers to the optimization issue by promoting the motion of particles in a specific space. PSO employs an iterative methodology. Based on its prior experiences and the collective experiences of the group, an individual's (i.e., particle) location is established (a swarm). Furthermore, the capacity to memorize and subsequently return to previously identified regions with favorable characteristics allows the particles to adjust to their new surroundings. PSO finds extensive use in several scientific and engineering challenges, including structural optimization and mechanics. Truss optimization using the particle swarm optimizer has been accomplished successfully, as reported in Ref. [17]. The work in [18] presents a PSO for constrained engineering design challenges. In contrast, the work in [19] presents an efficient coevolutionary particle swarm optimization algorithm for limited engineering design problems. There is increasing interest in this algorithm. The main advantage of the PSO algorithm is the fact that it can be controlled using a small number of parameters. The second advantage is that it is very fast. A small number of iterations are needed for the algorithm to find a solution.