Chemical processes frequently include multicomponent separation sequences which produce more than two products. Such separation systems are used for feed preparation, product separation, product finishing and waste treatment. The separation process of a chemical plant has a large effect on the total capital investment and the annual operating cost - in some cases it might be the major cost contributor. Therefore efforts to develop systematic automated approaches that will produce near-optimum separation sequences are of great interest to industry. The goal of this research is to use mathematical programming techniques to obtain a better understanding of the general problem of separating several multicomponent sources into several multicomponent products. Specifically, the work is directed toward solving the general problem: synthesize such separation sequences with "non-sharp" (meaning neither overhead, bottoms, or side exit streams contains any one pure product), complex, and thermally coupled units. The work plan includes: (a) Performing a systematic study on the synthesis of separation systems that involve "non-sharp" units, using mathematical programming approaches. (b) Investigating the synthesis of "complex" columns that may involve several feed streams, several side streams and pump- around systems. (c) Developing systematic approaches for coupling goals (a) and that is, the synthesis of thermally coupled systems that involve "non-sharp" prefractionators associated with several "complex" columns. (d) Investigating the simultaneous consideration of heat integration and optimization of the systems that invlove "non-sharp" and "complex" columns. (e) Developing software for the automation of the approaches described in the above goals. In addition to generating column design criteria, this work should also provide information on whether separator units are required at all for the generation of the desired multicomponent products. Other alternatives may result in substantial savings.