# Efficient Sizing and Layout Optimization of Truss Benchmark Structures Using ISRES Algorithm
## 1 Introduction
Five different numerical examples, namely, 10-bar, 25-bar, 200-bar, 18-bar, and 354-bar, were considered for efficiency analyses. The authors' goal was to rule out penalty functions. Performing selected benchmark problems showed that the proposed procedure displayed effective solutions for optimization. Particle swarm optimization (PSO) is one of the frequently used meta-heuristic algorithms for truss optimization. Researchers used this algorithm for different benchmark problems, modified and improved over the years [26; 27; 28; 29; 30]. [PERSON] et al. [26] proposed an enhanced version of PSO in truss structures to decrease the structural-analysis process. Size and shape optimization was considered. The results stated that enhanced PSO reduces the computational time required for optimization without sacrificing any search capability. In truss structures, [PERSON] and [PERSON] [27] investigated the optimization process under different constraints such as deflection, stress, and kinematic stability with two-stage particle swarm optimization. It is reported that this approach outperformed other methodologies reported in the literature. [PERSON] et al. [28] used heuristic particle swarm optimization (HPSO) based on standard particle swarm optimization (PSO) for truss structures. They noted that HPSO was able to expedite convergence speed and can be efficient for steel structures. [PERSON] [29] applied PSO and compared it with other algorithms and emphasized that the optimization results obtained with PSO are similar to other known algorithms, or, in some benchmark problems, even better. Some researchers such as [PERSON] and [PERSON] [30] proposed a modified and improved version of PSO for truss optimization. Another algorithm considered in this study was differential evolution (DE). DE is a widely used algorithm for optimization problems [31; 32; 33; 34; 35; 36; 37; 38]. Over the years, authors contributed to the efficiency of the algorithm with different approaches. [PERSON] et al. [36] suggested a new plan to enhance DE performance by altering the mutation operator. [PERSON] et al. [35] proposed teaching-based DE, while [PERSON] et al. [37] used DE based on a roulette selection for trusses. From the moment it was introduced to the literature, the genetic algorithm (GA) has been used for all kinds of optimization problems. In this section, a GA focused on truss optimization in recent years is presented [39; 40; 41; 42; 43; 44; 45; 46]. [PERSON] et al. [39] used the GA to minimize the cross-section area of truss systems; [PERSON] and [PERSON] [40] proposed a hybrid intelligent genetic algorithm (HIGA) and reported that the new method is a convenient tool for truss optimization. [PERSON] et al. [41] and [PERSON] et al. [42] proposed a new approach to improve the GA, while [PERSON] et al. [43] used the GA for size and topology optimization, and [PERSON] et al. [46] introduced a new mutant operator for the GA. In this study, our main objective is to perform a single-objective optimization of truss benchmark structures using the Improved Stochastic Ranking Evolution Strategy (ISRES) algorithm. Truss structures are widely used in engineering and architecture, and optimizing their designs for a specific objective can lead to more efficient and cost-effective solutions. The ISRES algorithm is a powerful optimization technique that belongs to the class of evolutionary algorithms. It efficiently explores the solution space to search for the optimal solution, focusing on a single objective in this case. The ISRES algorithm utilizes selection, mutation, and recombination operations to iteratively improve the candidate solutions until convergence to the optimal solution is achieved. The optimization process will begin by formulating the truss-design problem as a single-objective optimization task. The key design variables, such as the cross-sectional areas and the lengths of truss members, will be considered as decision variables to be optimized.