Despite recognised potential of complex distillation schemes in energy savings, their industrial applications are rather slow due to the difficulties on the design and synthesis fronts. These difficulties can be attributed to the large number of design options and the complicated trade-offs associated with them. The mathematical programming approaches embrace to highly interconnected superstructures and disregard available conceptual information in developing the general purpose formulations. That has overloaded the synthesis efforts and restricted their applications to simple and academic problems. In practice, engineers study some basic parameters and apply engineering knowledge to arrive at good designs. So, the challenge is to develop efficient synthesis representation and absorb the process knowledge to screen and target complex design options. This work first presents a new synthesis framework based on tasks and hybrids to effectively represent and address complex distillation systems. It conceptualises each complex design option as an aggregate of simple tasks by defining hybrids and introduces transformations to account for different complex column configurations. It postulates the supertask representation that can develop different non-conventional and novel designs featuring fully integrated columns, parallel sequences and multiple-effect columns. Due to discrete representation of options, the supertask offers distinctive advantage on the modelling and optimisation fronts. The conceptual model for the analysis of complex separation systems that exploits thermodynamics insights and engineering knowledge of the distributed sequence and the primary separation is developed. The design drives of competing options are systematically assessed with the prepositions of general terms "conceptual losses" that enable trade-offs to become clear in the optimal solution. This conceptual information is embedded in the mathematical model to allow efficient screening. In all cases, the approach guarantees simple model that upon formulation results in the mixed integer linear programming (MILP) problem and ensures the global optimum. Furthermore, the approach provides venues to interpret the results and explain the layouts selected by the optimisation. The approach is used to solve several examples of non-azeotropic separation systems that involve complications of industrial problems. The results of these examples show that the approach outperforms conventional techniques in time and effort and allow the optimisation to launch ahead and independent of simulation experiments. The distinguishing aspect of the new approach is that it can systematically translate optimisation solutions and muster support for the favourite designs by reviewing the values of conceptual terms. This provides a confidence in the quality of the solution and reveals dominant trade-offs. Also, due to the speed and the efficiency of the approach, it is used to analyse the effect of process parameters on the structure and performance targets of the designs.