## 2 Materials and Methods  
The algorithm proposed in this study is developed to check the printability of an arbitrary design consideration. The design evaluation algorithm is particularly developed to facilitate the assessment and enhancement of a given design across a diverse array of 3D food printers. To describe the logic and the working principles of the algorithm clearly, we define and explain the method here in a more general way, followed by a detailed description. The proposed algorithm integrates two primary computational frameworks: the Threshold Analysis Model and the Scoring System Model. The Threshold Analysis Model focuses on printer constraints, such as the nozzle diameter, to ensure that the thinnest features of the design can be produced. For example, if the design includes a thin wall of 0.5 mm, only certain printers will be capable of handling the design, while others will be excluded from the analysis. The Scoring System Model assesses various design metrics through user responses to a series of weighted questions, such as unsupported features, geometric accuracy, and post-processing requirements. Each metric is assigned a specific weight, as shown in Table 2, to reflect its relevance in determining the printability. For example, unsupported features or post-processing requirements have higher weights because they have a bigger impact on printability, while less critical factors like small surface details are assigned lower weights. This weighting helps to prioritize the key aspects that affect the overall success of the design during printing. The printability score is then calculated by summing the scores from these metrics, and the algorithm classifies the design as having a high, moderate, or low printability. The process also generates recommendations for improving design features that hinder printability, ensuring a comprehensive evaluation of the design. The process is initiated with the computational model, which is defined by the constraints of the printers in the system, setting the threshold values for the nozzle diameter (representing the ability to manufacture the width of the thinnest wall of the design) for each selected machine. These threshold values are critical since they determine the capability of each printer to handle the thinnest wall design feature. For example, if the width of thinnest wall in each design is 0.5 mm, both the Foodini by Natural Machines (Madrid, Spain) and Mmuse by Mmuse Ltd. (China) printers are not capable of manufacturing the design successfully. Therefore, the algorithm will test the design on the Foodbot S2 Multi Ingredient only. After setting up the nozzle diameter, the algorithm will interact with the user through a series of specific questions designed to collect the user input and comprehensively review the design's features, as shown in Figure 2 below. The developed method employs a set of algorithms to evaluate the printability of the product by assessing the 3D design based on the DfAM design guidelines. Moreover, the evaluation is conducted in a virtual environment that could be integrated into the slicing software, providing a real-time evaluation of the design. The integration of the proposed workflow into the design enhancement method adds significant value to this system. Once the analysis is completed, the method determines the design printability score A set of questions that are related to the performance of the design include unsupported or overhang parts, geometric accuracy, and whether post-processing is required or not. The responses to these questions will be converted to numerical values that reflect the user input and are aligned with the set criteria for the maximum printability of the selected printers. Then the design verification algorithm will calculate the printability score by summing up the assigned scores for each question. The most critical part of the computation is eliminating an incapable printer based on the width of the thinnest wall.