# Sustainable Optimization of the Injection Molding Process Using Particle Swarm Optimization (PSO)
## 3 Materials and Methods
### Taguchi Method  
The Taguchi method emphasizes the concept of quality loss, uses the signal-to-noise ratio (S/N) to evaluate the stability and performance of experimental results, and uses orthogonal tables to efficiently arrange experiments, reduce the number of experiments, and improve experimental efficiency. This method is particularly popular in the industry. It is widely used in manufacturing to optimize design and process parameters, improve product consistency and reliability, and reduce production costs. Recent advances in machine learning have revolutionized parameter optimization for plastic injection molding, with backpropagation neural networks (BPNNs) and particle swarm optimization (PSO) emerging as particularly effective tools. BPNN's multi-layered architecture excels at modeling the complex nonlinear relationships between process parameters and part quality. In injection molding applications, studies by [6,10] have demonstrated BPNN's ability to predict warpage and shrinkage with >90% accuracy, even with limited training data--a critical advantage for small manufacturers. The network's learning mechanism, which propagates errors backward to adjust synaptic weights, enables precise mapping of how parameter interactions (e.g., melt temperature vs. holding pressure) affect final part dimensions [12,13]. In Figure 2, this visual clarifies the BPNN's architecture and training process for injection molding optimization. The network receives six key process parameters as inputs, processes them through two ReLU-activated hidden layers (10 neurons each), and outputs weight and thickness predictions via linear activation. Training uses Taguchi-optimized experimental data (200 samples), with 70% allocated for model development. The Mean Squared Error (MSE) loss function directly minimizes prediction errors, optimized through Stochastic Gradient Descent (SGD) at a 0.1 learning rate. Early stopping prevents overfitting during the average 143 training epochs. These industry-standard choices (ReLU, MSE, and SGD) balance accuracy with computational efficiency for SME implementation, as evidenced by the model's strong real-world performance. PSO complements BPNNs by providing an efficient metaheuristic search capability. Inspired by swarm intelligence, PSO iteratively refines parameter combinations by balancing global exploration and local exploitation [22; 23]. This proves invaluable for injection molding, where the high-dimensional parameter space (often 6-10 interacting variables) makes gradient-based methods prone to local optima. Recent applications by [15; 18] show PSO reducing optimization time by 40-60% compared with genetic algorithms while maintaining solution quality, particularly for multi-criteria problems like simultaneous weight and thickness control. The synergy of these algorithms addresses key industry challenges. BPNN's predictive accuracy combined with PSO's search efficiency creates a robust framework for parameter optimization, as evidenced by [5]'s 35% reduction in energy use for automotive components and [7]'s success in minimizing warpage in thin-walled connectors. For SMEs, this hybrid approach offers particular value by achieving CAE-level optimization without requiring expensive software licenses or high-performance computing resources [9; 20]. Our work  
Figure 1: Research framework. builds on these foundations by incorporating Taguchi-designed neural architectures and sustainability-focused objective functions, advancing accessible precision manufacturing. The application scope of the Taguchi method includes product development, engineering design, and quality control, providing a scientific method for achieving efficient and economical process optimization. This study optimizes three factors: the number of neurons in two hidden layers and the learning rate. A double hidden-layer structure is adopted to capture complex nonlinear relationships efficiently while maintaining computational feasibility.