Rigorous optimization is a valuable tool that can support the engineer to tap the full economic potential of a distillation process. Unfortunately, the solution of these large-scale discrete-continuous optimization problems usually suffers from a lack of robustness, long computational times, and a low reliability toward good local optima. In this paper, the rigorous optimization of complex distillation processes for azeotropic multicomponent mixtures is achieved with outstanding robustness, reliability, and efficiency through progress oil two levels. First, the integration within a process synthesis framework allows a reduction of the complexity of the optimization superstructure and provides an excellent initialization by shortcut evaluation with the rectification body method. Second, the reformulation as a purely continuous optimization problem enables a Solution with reliable and efficient NLP solvers. Moreover, the continuous reformulation considers a particular tight column model formulation such that the introduction of special nonlinear constraints to force integer decisions could be largely avoided. A careful initialization phase and a stepwise solution procedure with gradually tightened bounds facilitate a robust and efficient Solution. Different Superstructures for the tray optimization of distillation columns are tested. The methods are illustrated by three demanding case Studies. The first case study considers the conceptual design as well as the rigorous optimization of a Curved boundary process for the complete separation of an azeotropic four-component mixture. The rigorous optimization of a pressure swing process for the separation of a highly nonideal five component mixture is presented in the second case Study. Finally, the third case study covers the rigorous optimization of an extractive separation within a complex column system. All case studies could be robustly solved due to the favorable initialization phase. The continuously reformulated problems required significantly less Computational time and identified local optima of better quality as compared to the mixed-integer nonlinear programming techniques (MINLP) solution.