Modern production process is accompanied with new challenges in reducing the environmental impacts related to machining processes. The turning process is a manufacturing process widely used with numerous applications for creating engineering components. Accordingly, many studies have been conducted in order to optimize the machining parameters and facilitate the decision-making process. This work aims to optimize the quality of the machined products (surface finish) and the productivity rate of the turning manufacturing process. To do so, we use Aluminum as the material test to perform the turning process with cutting speed, feed rate, depth of cut, and nose radius of the cutting tool as our design factors. Product quality is quantified using surface roughness (R_a) and the productivity rate based on material removal rate (MRR). We develop a predictive and optimization model by coupling Artificial Neural Networks (ANN) and the Particle Swarm Optimization (PSO) multi-function optimization technique, as an alternative to predict the model response (R_a) first and then search for the optimal value of turning parameters to minimize the surface roughness (R_a) and maximize the material removal rate (MRR). The results obtained by the proposed models indicate good match between the predicted and experimental values proving that the proposed ANN model is capable to predict the surface roughness accurately. The optimization model PSO has provided a Pareto Front for the optimal solution determining the best machining parameters for minimum R_a and maximum MRR. The results from this study offer application in the real industry where the selection of optimal machining parameters helps to manage two conflicting objectives, which eventually facilitate the decision-making process of machined products.