A steam cracking furnace plays an important role in the naphtha pyrolysis process that produces ethylene and propylene. These two products are the key monomers in the petrochemical industry. This article investigates the multiobjective operation optimization of the naphtha pyrolysis process to maximize the yields of ethylene and propylene. To solve this problem efficiently, multiobjective parallel differential evolution with competitive evolution strategies (MOPDE-CES) is employed. In MOPDE-CES, the population is divided into four parts, each part having its own evolution strategy. During evolution, the four parts of the population compete with each other to survive and evolve. At the same time, they share search information with each other by communicating with an external archive that stores the obtained nondominated solutions. The MOPDE-CES approach is compared to other powerful multiobjective algorithms, and the computational results show that MOPDE-CES is superior based on benchmarking and practical problems. In addition, the computational results of MOPDE-CES indicate that the operation of an ethylene plant can be improved by increasing the yields of ethylene and propylene.