## 1 Introduction
Overall, these studies have demonstrated the potential of FEM for the precise evaluation of connection behavior, enabling highly accurate design. However, achieving an optimal balance between safety and economic efficiency remains a complex task, particularly given the increasing recognition of sustainability as a fundamental concern across all sectors of modern life [25; 26; 27; 28]. Formulating this challenge as a discrete mathematical problem allows for the application of structural optimization techniques, a subject that has recently attracted growing attention in several civil engineering domains [29; 30; 31; 32]. Nevertheless, only a limited number of studies have specifically addressed this issue in relation to the optimal configuration of end-plate connections. A notable contribution is the work of [PERSON] and [PERSON] [33], who introduced a methodology to minimize the cost of the joint while satisfying predefined criteria for bending moment, shear force, and initial rotational stiffness. This was achieved by employing the equivalent T-stub method [11] discussed earlier. In a comparable study, [PERSON] et al. [34] also relied on this method to optimize the cost of composite and steel end-plate connections using a genetic algorithm. It is important to note that while both approaches enable cost minimization, the inherent simplifications of the component method [11] limit the consideration of plastic deformations, which are typically capped at 5% plastic strain, as recommended by EN 1993-1-5 [35]. Overcoming this limitation may allow for more economically efficient and structurally reliable connection designs. In this research, a comprehensive optimization algorithm is proposed for the precise design of beam-to-column end-plate connections, by which the limitations of code-based T-stub methods are addressed through the incorporation of material and geometrical nonlinear finite element analysis, including initial geometric imperfections. A high level of structural safety, along with economic efficiency, can be achieved through this approach. The implementation is carried out using a custom-developed program written in PYTHON 2.7, linked to the ABAQUS 2018 [36] finite element software and integrated with a genetic algorithm that automatically determines the optimal configuration of the investigated assembly. The mathematical formulation of the optimization problem is embedded within the code, with the primary objective of minimizing material usage while satisfying various structural criteria, including the control of plastic deformations--thereby enabling more efficient solutions. In addition, as recommended by [PERSON] et al. [20], initial geometric imperfections are considered to further enhance safety. The proposed design algorithm is tested through a benchmark problem based on the research of [PERSON] et al. [18]. The developed models are verified against the experimental results from their study. Furthermore, a sensitivity analysis is conducted to investigate the influence of key GA parameters on the convergence behavior of the optimization process and the quality of the final solution. The outcomes obtained using the proposed design framework are found to demonstrate its potential and efficiency in achieving safe and economical end-plate connection configurations, as significant material savings are realized while all structural criteria are satisfied.