Abstract The ethylene cracking furnace system is crucial for an olefin plant. Multiple cracking furnaces are used to convert various hydrocarbon feedstocks to smaller hydrocarbon molecules, and the operational conditions of these furnaces significantly influence product yields and fuel consumption. This paper develops a multiobjective operational model for an industrial cracking furnace system that describes the operation of each furnace based on current feedstock allocations, and uses this model to optimize two important and conflicting objectives: maximization of key products yield, and minimization of the fuel consumed per unit ethylene. The model incorporates constraints related to material balance and the outlet temperature of transfer line exchanger. The self-adaptive multiobjective teaching-learning-based optimization algorithm is improved and used to solve the designed multiobjective optimization problem, obtaining a Pareto front with a diverse range of solutions. A real industrial case is investigated to illustrate the performance of the proposed model: the set of solutions returned offers a diverse range of options for possible implementation, including several solutions with both significant improvement in product yields and lower fuel consumption, compared with typical operational conditions.