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A new approach to the synthesis of a multistage heat exchange network is proposed based on the principle of fixation of variables. This principle enables one to reduce a discrete-continuous programming problem to a sequence of linear and nonlinear programming problems. For their formalization, a new variant of the superstructure of a heat exchange network is put forward which includes all the possible flow patterns of material and heat streams. A computational experiment has proven that this problem is multiextremal. The vertical decomposition of the superstructure decreases the number of local minima of an economic criterion and reduces the computational difficulty of the synthesis problem, which is useful for modeling large-scale engineering systems. The performance of the proposed algorithm is demonstrated by a number of model examples in comparison with that of the efficient SYNHEAT …