For a competitive design of a distillation system, heat integration is currently a necessary component in the chemical industry. In distillation systems with heat integration, the complex interaction among the column design variables and heat integration calls for a systematic optimization method. In this study, the development of a simultaneous optimization framework for distillation systems and heat integration is described. To achieve an accurate and reliable design, rigorous distillation column, heat exchanger and compressor models were used for the optimization. These models were reformulated using a pseudo transient continuation (PTC) approach to improve their robustness. Because the framework is based on the equation-oriented environment, the automatic or symbolic differentiation is accessible for highly efficient gradient-based optimization algorithms. The results of two optimization cases of distillation systems with heat integration validated the proposed framework. In addition, the application of a bypass efficiency method while optimizing the number of stages is further discussed. (C) 2017 Elsevier Ltd. All rights reserved.