Operating pressures have a significant impact on the economics of distillation systems, but most works optimizing distillation systems using rigorous models neglected the determination of optimal operating pressures. Thus, in this work, we will show the influence of the pressure on mathematical optimization-based design using rigorous distillation models. For the optimization, the pseudo-transient continuation model is used to guarantee the robustness, and the bypass efficiency method is used to optimize the number of stages efficiently. Furthermore, to obtain accurate integer solutions reliably, an improved successive rounding method is proposed to combine with the steady-state optimization algorithm assisted by PTC models. Finally, the optimization results of several intensified/integrated distillation systems persuasively presented that the operating pressures did have a significant influence on optimization-based designs. Also, the rigorous model-based optimization algorithms got much better designs than both heuristic-based method and short-cut model-based optimization algorithm (with more than 10% decreases in TAC). (C) 2019 Elsevier Ltd. All rights reserved.