# Enhancing Design for Additive Manufacturing Workflow: Optimization, Design and Simulation Tools
## 4 Optimization Strategy  
This phase is focused on solving the selected structural optimization process and validating the performance of the proposed design. Given a design domain, boundary constraints and loading conditions, TO describes solid mathematical method implemented through computer-aided engineering (CAE) software. The method allows finding the optimum material layout that maximizes or minimizes an objective function representing a physic response of the system subjected to constraints. In general, real systems are subjected to multiple loading conditions requiring the definition of a multi-objective criteria optimization [29]. One common approach is to solve the multi-objective problem with a single scalar function by associating weighted factors to the different loading cases [30]. This converts the problem into the so-called Pareto-optimality describing a frontier of admissible optimal solutions. In [31] a 199-line Matlab code for tracing the Pareto optimal frontier is proposed: interestingly, no sub-objective can be improved without diminishing another with the main limitation to find a priori adequate values of weight factors [32].  
Given this background, TO could be applied to a vast range of physics problems, with the conditional enforcement that the partial differential equation (PDE) of analysis might be reliably discretized and modelled using finite element method (FEM), boundary element method (BEM), finite volume method (FVM) or other domain discretization schemes [33]. Besides classic static structural analysis, the process can be applied to fluid dynamics [34], heat transfer [35], electromagnetism [36], acoustic [37] and Multiphysics combinations between them [38]. In this manner, it is possible to associate a wide number of objectives and constrains formulations including compliance, stress, frequency, displacements, Eigen frequencies, reaction forces, moment of inertia, critical buckling load, mass or volume. Typical optimization tasks for static structural problems are: compliance minimization that is equivalent to stiffness maximization with volume constraint [39]; volume minimization with stress constraint [40]; and minimizing displacement under volume constraint [41].  
The global classification of TO methods is based on the fact that the optimization process requires or does not calculate the gradient information of the objective functions. Therefore, two main groups are defined: deterministic (gradient-based) and stochastic (heuristic) methods; the later are inspired by nature and gradient calculus is not required. Gradient-based methods include homogenization, density interpolation schemes as SIMP (Solid Isotropic Material with Penalization) or RAMP (Rational Approximation of Material Properties), and level set methods. Stochastic methods include metaheuristic algorithms like evolutionary approaches as Genetic Algorithm (GA), ESO, BESO and bioinspiredalgorithms like particle swarm intelligence, human base (tabu-search) and physical-based (Colliding bodies). The reader is kindly referred to [42] for an in-depth review of these TO methods and their numerical formulation. All of the proposed algorithms have in common the definition of a discretized domain and the necessity of implement filtering techniques to ensure smooth convergence and mesh-independency results. Differences between consists in purely mathematical definition with continuous or discrete variables, linear or non-linear programming, heuristic or mathematical derivation, local or global length scale control with implicit-explicit means.  
Nowadays, software platforms allow applying several optimization strategies for maximizing performance and obtaining lightweight structures that are suitably produced by AM technologies. In this manuscript, different TO approaches are presented: traditional gradient-based sequence with density interpolation schemes, infill optimization with lattice structures and the innovative generative design approach. All of these are significantly appropriate in the frame of DfAM.