One popular method for optimizing systems, referred to as ANN-PSO, uses an artificial neural network (ANN) to approximate the system and an optimization method like particle swarm optimization (PSO) to select inputs. However, with reinforcement learning developments, it is important to compare ANN-PSO to newer algorithms, like Proximal Policy Optimization (PPO). To investigate ANN-PSO’s and PPO’s performance and applicability, we compare their methodologies, apply them on steady-state economic optimization of a chemical process, and compare their results to a conventional first principles modeling with nonlinear programming (FP-NLP). Our results show that ANN-PSO and PPO achieve profits nearly as high as FP-NLP, but PPO achieves slightly higher profits compared to ANN-PSO. We also find PPO has the fastest computational times, 10 and 10,000 times faster than FP-NLP and ANN-PSO, respectively. However, PPO requires more training data than ANN-PSO to converge to an optimal policy. This case study suggests PPO has better performance as it achieves higher profits and faster online computational times. ANN-PSO shows better applicability with its capability to train on historical operational data and higher training efficiency.