The synthesis of a distillation system including no-sharp separations was studied with emphasis on the coding and flowsheet multiformity caused by no-sharp separation.The same streams composed of the same components appeared in the flowsheet

and had three kinds of relationships

i.e.

independent

united

and thermally-coupled.In the genetic programming coding

an integer array was used to denote the relationships for these same streams so as to describe the distillation flowsheet with no-sharp separations.There was an equivalent simple column flowsheet for a complex flowsheet and the maximum number of simple columns (MNSC) in one flowsheet was used to describe the scale of problem.The relationship between MNSC and middle component number (MCN) that was between two key components was presented.As MCN was 2

MNSC was 4N-9

and it meant that the best result would be searched in the space that could include 4N-9 columns instead of N-1.The searching scope was enlarged and better results could be obtained in comparison with only considering sharp separations.