## 1 Introduction
As a matter of fact, in the last reference, it is stated _\"Considering all the possible combinations of the main geometrical parameters, many configurations should be tested to find the best solution for the project. This would lead to a very large number of experimental tests... a common industrial procedure is to quickly sift and select 2 or 3 configurations with better performances,...\"_. Such heuristic design procedure might provide a feasible design when relying on the previous experience of the design team; however, in the absence of a proper assessment of the full design domain under consideration, there is a true possibility for missing more efficient designs, given the complexity of the interplay between deck geometry and gap distance. This frames the target of this piece of research: improve wind tunnel-based design techniques by proposing a rigorous design framework founded upon the application of validated CFD (Computational Fluid Dynamics) simulations in the frame of surrogate-based design to explore an ample twin-box deck shape design domain, identifying the most efficient candidate designs for the ultimate detailed design of a cable-supported bridge. A surrogate model might be considered as a \"cheap-to-evaluate\" function that emulates the \"expensive-to-evaluate\" continuous quality, cost or performance metric of a product or process. Since the evaluation of the output is so costly, only the output of a limited number of \"samples\" should be obtained, adopting this sparse set of samples to define an approximation that enables a cheap performance prediction [12]. The evaluation of aerodynamic and aeroelastic responses in wind engineering applications is a complex task, with heavy burdens, associated with experimental tests or CFD simulations. Consequently, surrogate models have been applied in a relatively limited range of wind engineering applications. In [13], the authors defined a Kriging surrogate in the frame of the shape optimization of the cross-section geometry of high-rise buildings, considering both drag and lift coefficients. A multi-fidelity surrogate model was later presented in [14] for the drag coefficient and the standard deviation of the lift coefficient of buildings, based on samples evaluated using RANS (Reynolds-averaged Navier-Stokes) and LES (Large Eddy Simulations) simulations. The surrogate model was applied in the context of an aerodynamic multi-objective optimization of tall buildings. In the study of vertical axis wind turbines, a Kriging model was defined, linking the power coefficient with two airfoil design variables, namely the maximum camber and its position [15]. In [16], the authors trained and compared six different neural network (NN) models to obtain surrogates for the aerodynamic loads on wind turbine blades. In [17, 18], the multi-objective shape optimization of the cross-sections of tall buildings was addressed, considering a Kriging surrogate model for the aerodynamic response of the buildings, based on Eurocode stipulations. Turning the focus now to surrogate modelling applications in the aeroelastic response of long span bridges, some of the authors of this work have been active in the surrogate-based optimal design of cable-supported bridges, co-authoring the articles [19, 20, 21]. These optimization works relied on the ability of the surrogate model to provide the data required for the evaluation of the aeroelastic responses of interest in the numerical optimization process for the modified designs. This framework was first reported in [22]. In this last reference, two design variables, namely the depth and the width of a box girder, were considered for the aerodynamic characterization of the deck. A set of 15 samples were defined deterministically over the design domain, and the force coefficients were obtained by means of 2D URANS (Unsteady Reynolds-averaged Navier-Stokes) simulations, validating the results of a subset of three designs using wind tunnel data.