Although natural gas can provide energy with minimum greenhouse gas emissions compared to other fossilderived fuels, the sulfur removal is the major challenge associated with its use in various applications. In this work, sulfur recovery unit was simulated using the Aspen HYSYS. The environmental, energy, and economic analyses of the process based on special criteria (profit (PBT), weighted global warming potentials (WGWP), and energy consumption (NQ)) were analyzed. After consideration of the sensitivity analysis of the process, the single and multi-objective optimizations were carried out by integrating the HYSYS simulations with MATLAB codes with the Genetic Algorithm method. Feed temperature, feed molar flow rate, combustion air temperature, and reboiler temperature are decision variables in this work. The results show that with increasing the feed temperature, the energy consumption decreases, so, the cost of energy decreases. Also, with increasing the feed temperature, and reduction of consumed energy, the equivalent CO2 emission (which is calculated based on total energy consumption) reduces, so, WGWP decreases. Maximization of PBT, Minimization of WGWP, and Minimization of NQ were considered as the single objective optimizations, separately. Optimum values of decision variables were found. For multi-objective optimization, three different cases were considered: Case 1 (Max. PBT and Min. WGWP), Case 2 (Max. PBT and Min. NQ), Case 3 (Min. WGWP and Min. NQ). In all these cases, it can be found Pareto optimal frontier. The results show that the feed molar flow rate and air combustion temperature variables have more effect than other variables.