Distillation units require huge amounts of energy for the separation of the multicomponent mixtures involved in refineries and petrochemical industries. The overall efficiency of the distillation column system is determined from the trade-offs of the Operating Expenditures (OPEX) and Capital investment cost (CAPEX), as there is a strong interaction between the distillation columns and the Heat Exchanger Network (HEN) of the interconnecting streams. In this paper, a systematic Mixed Integer Non-Linear Programming (MINLP) optimization methodology for process integration of distillation column complex is presented. The highly nonlinear rigorous models of the distillation column and phase change are being substituted with simple surrogate models that generate operating responses with adequate accuracy. The methodology is applied on two case studies of the aromatics separation PARAMAX complex. The results illustrate significant reductions on the Total Annualized Cost. With a scope limited to the benzene and toluene columns, the gain reaches about 15%.