## 2 Design Process  
This section presents an overview of the design process proposed in this work, which is carried out in two steps composed of three phases each: (1) Parametric model; (2) Optimisation; and (3) Decision making. The three phases are executed in a very similar way in the two steps. The following Sections (Sections 3-5) detail the method or procedure followed in each of them. The proposed design process requires establishing an initial set of available cross-section sizes and the maximum value of the bending stress that can be reached due to the curving process in a given area of the structure. In Step 1, the size of the cross-sections for which the defined maximum stress is not exceeded is obtained. In addition, this first set of solutions provides a first approximation of the minimum value of the maximum initial bending stress that can be reached for each cross-section size, as well as the improvement achieved with the optimisation process. In Step 2, once the final cross-section size is chosen, a new set of topologic configurations is obtained in which the maximum bending stress value is minimal (or near-minimal). This set of solutions provides a decision space in which other non-programmed or not-programmable issues, such as end distances or other aesthetic considerations, can be taken into account. The main aspects of each of the above-mentioned phases are summarised below:  
* Phase 1: Parametric model. In this initial phase, the parametric model is built according to the procedure described in Section 3, considering as design constraints the target surface and the study area. The target surface is an external and fixed customer input. The study area is the surface portion where the initial bending stresses are intended to be minimised. It may coincide with the entire target surface, but in general it is of interest to restrict it only to the area of the grid where the highest bending stresses due to external loads (dead loads, snow, wind, etc.) will occur. Next, the parametric model of the gridshell logic considers the design variables that will define its topology and the cross-section size of the laths, which constitute the genes of the optimisation algorithm. In Step 1, the genes are the topological variables (the origin position of the geodesic curves and the grid angle) and the cross-section size variables (depth and width). In Step 2, once the final cross-section is chosen, the genes are the topological variables only. The parametric model will be able to mesh the surface starting from a pair of geodesic curves calculated from a starting point and an angle, and to fill the surface with a full mesh by running the algorithms for geodesic curves and the ACM. To establish the ACM parameters, the algorithm first analyses the curvature of the target surface, allocating the subdivision domains according to the curvature and assigning the resolution factor \(S\). Once the parametric model is built, simulations can be run by estimating the initial bending stress both in the study area, where its minimisation will be required, and in the entire grid to verify that the predefined maximum stress is not exceeded at any point, for each individual valid solution. * Phase 2: Optimisation. The algorithm performs the optimisation routine based on the Strong Pareto Evolutionary Algorithm 2 (SPEA-2) fed with the data obtained from the parametric model for each generation. It is driven by the minimisation of a fitness function defined later on. As long as the number of generations is below the prescribed maximum and the optimisation process is still in progress, the algorithm loops back to the parametric model, tuning the genes as necessary for optimisation purposes. This phase is detailed in Section 4. * Phase 3: Decision making. In this final phase detailed in Section 5, the Decision Maker (DM) analyses the solution scope, imposes further requirements and selects the final solution.