_Applied_  
_sciences_  
_Article_  
**Improving Surface Roughness of Additively**  
**Manufactured Parts Using a Photopolymerization**  
**Model and Multi-Objective Particle**  
**Swarm Optimization**  
**[PERSON] 1,*,+, [PERSON] 2,+, [PERSON] 2\(\copyright\), [PERSON] 2\(\copyright\) and [PERSON] 2,*(\copyright\)**  
Footnote 1: [[https://github.com/journals/j](https://github.com/journals/j)]([https://github.com/journals/j](https://github.com/journals/j))  
changing from prototyping to manufacturing of end products, replacing traditional manufacturing processes [1; 2; 3]. Furthermore, AM enables manufacturing of complex geometries that are impossible to produce with traditional subtractive manufacturing techniques [4; 5; 6; 7]. In addition, there exists a distinctive advantage in manufacturing time as well. The manufacturing time of a subtractive process is highly dependent on the geometrical complexity of parts, while process time and cost in AM are relatively less dependent of part geometry. Given these advantages, AM has been creating new opportunities in various areas; personalized healthcare products [8], reducing environmental impact for sustainability by saving raw materials, simplification of supply chain and responsiveness in demand fulfillment [9]. However, achieving dimensional accuracy in AM parts is still challenging due to surface roughness caused by the inherent layer-wise process of AM. Surface roughness is one of the universal defects that AM products have due to a staircase effect caused by the inherent nature of layer-by-layer AM processes. Not only does rough surface profile induce dimensional inaccuracy, it also results in a significant reduction in mechanical performance of AM parts [10]. Various approaches have been proposed to address the surface roughness issue in AM parts. A predictive model for surface roughness of AM parts using an interpolation equation was introduced by [PERSON] et al. [11]. An interesting study done by [PERSON] et al. [12] used a parameter estimation (PE) method to improve surface quality in stereolithography. Recently, it is also found that the stiffness variations of AM parts is induced by the geometrical differences between computer-aided design (CAD) models and the printed parts [13]. The effect of build direction that controls the directional surface roughness on tensile strength and stiffness of additively manufactured parts was also researched by [PERSON] et al. [14]. The numerical method was also used to optimize printing orientation in order to minimize the effect of surface roughness on mechanical properties [15]. [PERSON] et al. reported the close correlation between the mechanical properties of stereolithography components and the layer thickness and surface roughness [16]. However, a systematic approach to understand and control surface profiles of a 3D printed part while accounting for process throughput has not been reported. This study presents a systematic approach to identify optimal printing process parameters using a computational model for projection micro-stereolithography (P\(\mu\)SL), a digital light processing (DLP) based AM technique shown in Figure 1[17]. Figure 1a shows a schematic diagram of P\(\mu\)SL and a 3D printed part with surface roughness. CAD file is sliced in the printing software and the UV light corresponding to each cross-sectional image is projected on top of the resin vat using DMD. The liner stage moves vertically to successively build polymerized layers. Figure 1b shows microscope images of 3D printed struts with surface roughness. The polymer used is HDDA and the strut diameter is 200 \(\upmu\)m. The three printing angles studied are 90\({}^{\circ}\) (vertical) and 60\({}^{\circ}\). The thickness of each layer is 80 \(\upmu\)m and a curing time per layer of 3 s was used. The surface profile of printed struts clearly demonstrates the geometrical deviations between CAD and the actual printed shape.