# An Optimization Workflow in Design for Additive Manufacturing
## 1 Introduction  
From the works of the early pioneers, additive manufacturing (AM) technologies were characterized by great growth in the last 35 years [1]. According to ISO/ASTM standards \"AM is the general term for those technologies that, based on a geometrical representation, create physical objects by successive addition of material\" [2]. Depending on the method of layer manufacturing, it is possible to organize the AM technologies in the following categories: vat photopolymerization, material jetting, binder jetting, powder bed fusion, material extrusion, directed energy deposition, and sheet lamination [2]. This technology brings new opportunities especially in design freedom, allowing very complex shapes, integrating cinematics and multi-material parts, reducing the number of components through part consolidation, and increasing mass customization. On the other hand, to fully exploit the AM technologies' potential, many needs in different sub-fields were highlighted [1, 3, 4, 5, 6, 7, 8], as summarized in Figure 1. For example, a highly skilled workforce is required, file formats for exchanging the data related to the AM workflow need enhancements [8, 9], and design methods and tools for complex structures, multi-material parts, and functionally graded materials need to be improved [10, 11]. The concerns over the structural integrity of these complex parts require static and dynamic mechanical characterization [12, 13]; also, experimental tests help to mechanically characterize the materials,and the obtained information is used in numerical simulations to predict the different mechanical behavior between the products obtained through additive manufacturing and the ones obtained by traditional techniques of material subtraction [14; 15]. More, dedicated qualification standards for AM are needed to guarantee an adequate quality of the printed parts [16; 17] and their representation in 2D drawings [18]. In a recent work, _The Economist_ claims that the value of AM products will no longer be in the physical item, but in its design [19]. These reflections lead to a reconsideration of the design approaches for AM. According to [PERSON] [20], the design process can be divided into six major phases: product discovery, project planning, product definition, conceptual design, product development, and product support. During the conceptual design phase, several concepts are generated and evaluated; however, the knowledge of the concepts is limited and the goal in this phase is to select the best alternatives with the least expenditure of time and other resources. In the product development phase, instead, once the product is generated, it is fundamental to compare its performance to the engineering specifications. This is done both with virtual simulations and physical prototypes, often resulting in a time-consuming iterative process due to part modifications and redesigns. A different approach that exploits the higher computational capabilities available nowadays is the computational design synthesis [21], where the tasks needed to obtain a solution are divided into four main steps: \"representation\" deals with the creation of a mental model of the object, \"generation\" deals with the object creation, \"evaluation\" verifies if the constraints and design goals are met, and \"guidance\" gives a feedback for the design improvements [22]. The last three phases are iteratively repeated until a final design is obtained. In design synthesis, optimization is performed in the representation and generation phases, where the design has not a specific topology yet. Usually, stochastic methods are applied to obtain different designs that satisfy the requirements [23]. Furthermore, when designing parts that are going to be produced by AM technologies, several thoughts must be considered to \"maximize product performance through the synthesis of shapes, sizes, hierarchical structures, and material compositions, subject to the capabilities of AM technologies\" [24].