Natural gas (NG) production has significantly increased in the past decade as new unconventional oil and gas wells are being discovered. NG as obtained from the wellhead requires processing before being considered as pipeline grade. The process consists of the removal of acidic gases followed by dehydration. NG processing is associated with toxic emission having substantial environmental and health impact. Difficulty in NG processing arises from varied flow rate and uncertain feed composition that provides a challenge in efficient design as well as finding the optimal operating condition. The present work used a stochastic approach to characterize natural gas composition and its importance on the product and waste emission is studied. Under the uncertain feed composition, optimal operating condition of the controllable variables was attained by a reliability-based robust multi-objective optimization (RBRMOO) technique that mitigates BTEX emission while fulfilling NG pipeline specification. Chemical process simulator is used to find the impact of the control process settings and variation of uncertain feed condition on NG dehydration and BTEX emission. The best prediction models were developed using machine learning algorithm, chosen from a family of metamodels. RBRMOO is performed using metaheuristic algorithm to determine the optimal process condition of the control variables. The impact of uncertain feed composition in process modeling and subsequent optimization demonstrates optimal process condition where the rate of emission is lower by ~83 ton/yr when compared to that from the deterministic model where median value of uncertain feed composition is used for analysis, portraying the limitations of traditional sustainability assessment methods that do not account for uncertainty.