ABSTRACTDifferent operating conditions of p-xylene oxidation have different influences on the product, purified terephthalic acid. It is necessary to obtain the optimal combination of reaction conditions to ensure the quality of the products, cut down on consumption and increase revenues. A multi-objective differential evolution (MODE) algorithm co-evolved with the population-based incremental learning (PBIL) algorithm, called PBMODE, is proposed. The PBMODE algorithm was designed as a co-evolutionary system. Each individual has its own parameter individual, which is co-evolved by PBIL. PBIL uses statistical analysis to build a model based on the corresponding symbiotic individuals of the superior original individuals during the main evolutionary process. The results of simulations and statistical analysis indicate that the overall performance of the PBMODE algorithm is better than that of the compared algorithms and it can be used to optimize the operating conditions of the p-xylene oxidation process eff...