# Efficient Sizing and Layout Optimization of Truss Benchmark Structures Using ISRES Algorithm
## 1 Introduction  
Optimization is in our lives everywhere we turn. Athletes preserve their breath to run/swim longer/faster, people use the shortest path to their office in order to spend less time on the road, and engineers design more green and eco-friendly buildings to save energy while satisfying consumers' needs. In all these examples, the main goal is to use existing resources wisely and economically. Structural optimization basically relies on the same fundamentals. The aim of structural optimization is to perform better underspecified goals while meeting variable constraints. In previous studies, gradient-based algorithms were used considerably for structural optimization [1; 2]. While these types of algorithms can sometimes help to reach a solution, without a decent starting point obtaining a solution is not guaranteed. Meta-heuristic algorithms, on the other hand, are free from this restriction. These types of algorithms need initial data, decision and state variables, constraints, etc. Initial states can be calculated, assigned randomly, or used as default [3]. Structural optimization is practiced under three different categories, namely: size, shape, and topology. The aim for optimization in truss elements is to reduce the structures' weight. While optimization could be carried out with the use of a single category of these above-mentioned options, it can be also reached with different combinations of any two or altogether. Size is the largely applied category for truss optimization, followed by shape and topology [3]. The research gap falls between topology and shape, with very little work available in the literature. In truss optimization, weight, geometry, stress, stiffness, nodal displacements, and buckling problems are the most largely studied types of functions [4]. While the aim is reducing the weight of the truss with optimization, different optimization categories offer different types of solutions. In sizing optimization, the aim is to find the optimum cross-sectional area of the truss. In shape optimization, in changing the coordinates of the nodals, finding an optimum position is possible, and finally, in topology optimization, removing the structural members from their original position allows for minimizing the volume of the truss [5]. Meta-heuristic algorithms have been applied to truss optimization for a long time. Meta-heuristic algorithms used by researchers frequently are as follows: genetic algorithm [6], Cuckoo Search [7], Big Bang-Big Crunch [8], particle swarm optimization [9], the Firefly algorithm [10], Harmony search [11], differential evolution [12], and the bat algorithm [13]. [PERSON] et al. [14] used the Firefly algorithm in truss structures to optimize simultaneously size, shape, and topology. Four benchmark problems such as 11-bar, 39-bar, 25-bar, and 15-bar trusses were studied. As a result, it was decided that this method is useable for mixed-optimization problems. [PERSON] et al., 2023, [15] examined the effectiveness of eight population-based meta-heuristic approaches: the African Vultures Optimization Algorithm (AVOA), the Flow Direction Algorithm (FDA), the Arithmetic Optimization Algorithm (AOA), Generalized Normal Distribution Optimization (GNDO), the Stochastic Paint Optimizer (SPO), the Chaos Game Optimizer (CGO), the Crystal Structure Algorithm (CRY), and the Material Generation Algorithm (MGO). The objective is to optimize the dimensions of three aluminum truss structures with the goal of minimizing the weight of truss members while satisfying specified displacement and stress constraints. The study evaluates the performance of these methods by applying them to three established truss-structure benchmarks under certain constraints. The findings indicate that the Stochastic Paint Optimizer (SPO) outperforms the other algorithms in terms of both accuracy and convergence rate. [PERSON] and [PERSON] [16] applied hybrid genetic programming (HGP) to truss structures with different static and dynamic constraints.