A Tree-Shaped Support Structure for Additive Manufacturing Generated by Using a Hybrid of Particle Swarm Optimization and Greedy Algorithm

Abstract

Reducing the volume of support structures is a critical means for saving materials and budgets of additive manufacturing, and tree structure is an effective topology for this purpose. Although a few articles in literature and commercial software have been devoted to developing tree-supports, those tree-supports are generated based on geometry optimization or user-defined parameters, which cannot guarantee a minimum volume with robust fabrication guarantee. To address this issue, we propose a set of formulas for stably growing the tree-supports with physical constraints based on 3D printing experiments using fused decomposition modelling (FDM) machines, and a volume minimization mechanism using a hybrid of particle swarm optimization (PSO) method and a greedy algorithm. We show that this combination is effective in reducing the volume of tree-supports and the simulations reveal that the volume curves monotonically descent to a constant within a short time, and our experimental results show that the models with the tree-supports can be manufactured stably.

Escaping Tree-Support (ET-Sup): minimizing contact points for tree-like support structures in additive manufacturing

“…Generating tree-supports can be described as the Euclidean Steiner Minimal Tree problem, which is at least NP-hard (Vanek et al , 2014). Zhu et al (2019b, 2019c) used a hybrid of a particle swarm optimization and a greedy algorithm to design the tree-supports. The method saves up to 8% material and 13% print time compared to the results obtained by the Autodesk Meshmixer (Schmidt and Umetani, 2014), and it has a computation time from minutes to hours.…”

Developing a New Robust Swarm-Based Algorithm for Robot Analysis

“…In additive manufacturing (3D printing), constructing over-hanging features can only be achieved by introducing some support structures beneath the overhang which can be removed afterward to get the desired shape, [3] used a hybrid variation of PSO with greedy algorithm to reduce the volume of the support structure thereby save printing time, material and minimize budget. The recent hype in groundbreaking fifth-generation (5G) wireless communication technology presents the need to improve the quality of service with massive multiple-input multiple-output (MIMO) antenna arrays, [4] used a contraction adaptive PSO to optimize the design and positions of antenna array elements.…”

“…The position and velocity vectors of the ith particle can be defined as X i and V i in Equations (1) and (2) below. The position and velocity of every particle in the swarm is updated according to Equations (3) and (4) through every iteration, the first part of the Equation 3is the previous velocity which describes the particles previous experience, the second part of the equation is the cognitive component which describes the particles personal experience while the third part of the equation is the social component which describes the entire swarms best experience. The inertia weight w is a learning coefficient associated with the previous velocity, while c 1 and c 2 are learning coefficients associated with the cognitive and social components respectively.…”

“…The inertia weight first decreases from the initial value to a predetermined value w m where it remains constant for a while before decreasing further to the final value. As shown in Figure 7b, five different scenarios were presented, and the governing equation for updating the value of the inertia weight in each of the scenarios is given in Equations (18)-(22) 3 5 t max , 4 5 t max , 3 5 t max , 4 5 t max , 3 5 t max ,…”

Multi-objective optimization of support structures for metal additive manufacturing

“…The authors proposed a set of formulas for stably growing the tree-supports and minimized the support volume using a hybrid of particle swarm optimization method and a greedy algorithm. The results found the combination to be effective in reducing the volume of tree-supports [12]. Zhang et al, 2019, used Taguchi method to analyze the effect of a block support structure (with solid cuboids geometric design parameters) on the part deformation and surface roughness during the fabrication of overhang structures by SLM.…”