A methane fermentation system can be considered as a multi‐objective optimization problem characterized by conflicting objectives such as investment cost, net biogas production and chemical oxygen demand (COD) removal. To this end, a k‐objective ‐constraint method was used to determine the optimal design and operation parameters of a continuously stirred anaerobic digester. This equipment treats leachates from the controlled solid urban wastes landfill at Garraf (Barcelona, Spain), which receives 5–6 × 105 tonnes of wastes per year. The optimal solutions were generated for two design criteria: (a) reduction of cost to a minimum and (b) maximization of net energy production with at least 75% removal of COD. The preferred solution was obtained by using the non‐inferior solution set.