## 1 Introduction
The second one, proposed by [PERSON] [17], is aimed at the early design phase, where the location, shape, and main elements of the bridge can be determined. The third one [18], which is in part more directly related to the study reported in this article, deals with the application of neural networks for the preliminary design of cable-stayed bridges using a database of 39 sample bridges. The proposed model uses a small number of simple input and output parameters (e.g., length, height, width, number of lanes, number of towers). The fourth one [19] implemented multiple objective particle swarm optimization and the gravitational search algorithm--support vector regression algorithms--for incrementally launched concrete bridges. The authors proposed an optimization method to determine the design parameters, such as the spacing between temporary supports and the length of the launching nose, considering the maximum local stresses for super-wide bridges and super-long steel bridges. The fifth one [20] proposed a pre-camber prediction method for long-span continuous girder bridges based on a combination of the grey model (GM) and the BP neural network (GM-BP). Despite the advances highlighted in the literature, existing research on AI applications in bridge engineering has several limitations. Most studies focus narrowly on automating damage detection, structural evaluation, and risk assessment, with limited exploration of comprehensive design processes. The few studies addressing bridge design are either restricted to specific phases, such as preliminary or conceptual design, or limited to certain bridge types and predefined parameters. Moreover, existing methods often lack integration with modern optimization techniques that can handle complex design scenarios, such as those involving prestressed concrete bridges constructed using the incremental launching method. These gaps underscore the necessity of the present research, which aims to address these limitations by developing a methodology that optimizes key design parameters, supports variant studies, and provides effective tools for both experienced and young designers in the early stages of bridge design. Bridge design is an iterative process, meaning that \"precise\" values are not the most critical aspect during the design phase. What matters most is that the user, engineer, or designer develops an understanding of the relationships between individual parameters and their mutual influences. Design, after all, is a creative process that currently surpasses the capabilities of AI. This article is organized as follows: a brief presentation is provided in this introduction section, where the objectives of the presented work are stated and the background referring to adequate literature is provided. The materials and methods section describes the incremental launching method, primary database with the main parameters of the sample bridges, proposal of empirical modeling by artificial neural networks, and extension of the primary database. Next, the theory and calculation section contains a detailed description of the proposed solution, including explicit formulae. The results and application in Section 4 show the usefulness and robustness of the proposed solution. Graphs in the form of iso-curves of equal value help practicing engineers and designers understand the complex relationships between the main bridge parameters, while the proposed application allows for quick preliminary designs and/or assistance in the design process. Finally, the discussion and conclusions of the study and future work are outlined in Section 5.