Abstract: In this paper the rules ot matches between hot and cold streams in the synthesis of optimized HEN are given. On the basis of the rules and engineering practice, a set of artificial intelligence graphes were developed to be used in the synthesis of optimized HEN. The procedures of synthesise were given as completely analytical algorithm, escaping iterative and evolutionary computations. Nine HEN as examples were synthesised by this method and compared with optimized results in the literature. In synthesising HEN with this method, the streams can be with no splitting, no phase change and no constraint as well as with splitting, phase change and constraints. The method is not limited by the number of streams.