Analysis on the alternative designs on top of the optimal network has proven valuable and meaningful for the decision-makers in determining the most suitable options which fulfill a wide range of objective functions. On the basis of an extension of the P-graph framework, a procedure was developed previously for multiple-solution heat exchanger network (HEN) synthesis. This procedure is capable of generating the n-best HENs depending on predefined structural constraints, for example, the maximum number of heat exchangers used for the entire system, the maximum number of sequential heat exchangers on each stream, the maximum number of stream splittings per stream. Since the choice of a parameter influences the effect of other parameters on the result, it is difficult to find the proper set of parameters for the solver that result in all plausible solutions to the original problem. Naturally, this issue emerges in any HEN synthesis problem, its systematic treatment is essential. The purpose of the current work was to develop a heuristic framework for determining the most reasonable parameters of the HEN generation algorithm and guiding the designer through the optimization process. The outcome of this study not only benefits the researchers and industrial practitioners of this field but may also be extended for educational purposes.