## 2 Materials and Methods
### Computational Model for Photopolymerization Process
#### 2.2.2 Modeling of Photopolymerization in COMSOL Multiphysics
Recently, various population-based optimization algorithms such as genetic algorithm [30] and ant colony optimization [31] have gained attention because of their derivative-free characteristics and efficiency. Particle swarm optimization (PSO) is a meta-heuristic optimization algorithm that mimics the social behavior of birds or fish [32]. Each agent evolves and iteratively searches the global optimizer based on its path as well as its neighbors' paths. Each agent represents a solution of the problem and it will converge to the global optimizer when the iteration ends. PSO has become a useful tool for multiple reasons [33]: (1) since it is not problem specific, it offers a general framework that can be applied to all optimization problems; (2) the algorithm is straightforward and relatively simple to be implemented; (3) it is computationally efficient to find the global optimizer. Multi-objective particle swarm optimization (MOPSO) is a PSO for multiple objective functions [34]. In MOPSO, the result is a set of different solutions instead of a single global optimizer. It is called a Pareto optimal set. There are three main issues that need to be addressed when PSO extends to MOPSO. * Selecting a leader for evolving agents
* Retaining the non-dominant solutions in each iteration
* Maintaining diversity of agents during iterations  
These issues are addressed in detail when the pseudo-code for MOPSO in Figure 4 is explained. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Value** & **Description** \\ \hline w & 12 μm & Gaussian radius * \\ [M]\({}_{0}\) & \(4.46\times 10^{3}\) mol/m\({}^{3}\) & Monomer initial concentration * \\ (PI)\({}_{0}\) & \(48.27\) mol/m\({}^{3}\) & Photoinitiator initial concentration * \\ (PA)\({}_{0}\) & \(4.06\) mol/m\({}^{3}\) & Stabilizer concentration * \\ \(\alpha\) & \(11.9\) m\({}^{2}\)/mol & Molar absorptivity of photoinitiator [21] \\ \(\alpha_{\text{a}}\) & \(4600\) m\({}^{2}\)/mol & Molar absorptivity of stabilizer [21] \\ \(\Phi\) & \(0.59\) & Quantum yield for initiator [27] \\ T\({}_{0}\) & \(303\) K & Environmental temperature * \\ D\({}_{\text{r}}\) & \(3.0\times 10^{-10}\) m\({}^{2}\)/s & Radical diffusion coefficient [28] \\ D\({}_{\text{PI}}\) & \(3.0\times 10^{-10}\) m\({}^{2}\)/s & Initiator diffusion coefficient [28] \\ I\({}_{0}\) & \(24.5\) mW/cm\({}^{2}\) & Incident light intensity * \\ k\({}_{\text{p}0}\) & \(25\) m\({}^{3}\)/mol/s & Propagation rate constant [29] \\ k\({}_{\text{t}0}\) & \(2520\) m\({}^{3}\)/mol/s & Termination rate constant [29] \\ \(\beta\) & \(1/(3.27\times 10^{5})\) mol/J & Amount of energy contained in one photon [23] \\ t\({}_{0}\) & \(5\) s & Time for which light is incident on resin surface * \\ T\({}_{\text{last}}\) & \(0.2\) s & Decay time for the turning the illumination off * \\ k\({}_{0}\) & \(15\) m\({}^{3}\)/mol/s & Oxygen diffusion constant [25; 26] \\ (O)\({}_{0}\) & \(0.9\) mol/m\({}^{3}\) & Initial oxygen concentration in resin [26] \\ (O)\({}_{1}\) & \(8.69\) mol/m\({}^{3}\) & Environmental oxygen concentration * \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of Pt\(\mu\)SL process parameters. * is from experiments. First, the algorithm initializes agents' position and velocity. Population (POP) is the memory where all agents' information in certain iteration is stored. For the initial set, all agents are evaluated based on its randomly distributed positions. Repository (REP) is the external repository where the non-dominated agents in POP are stored. The dominance of each agent is determined by the objective functions. The MOPSO algorithm generates grids that cover all the search space and locate all agents in the grids where the coordinates are its objection function. This controls the density of local agents by determining the local optimizer (leader) that leads neighboring agents. Personal (agent) best position, called PBEST, in the search space keeps the best local optimizer that each agent experiences when it travels through the search space.