The non-structural model of a heat exchanger network randomly selects a position of a node on hot and cold streams to generate a heat exchanger and an existing heat exchanger to participate in the evolution. Despite the model being more random and flexible, this selection method cannot easily find a good solution. In addition, the heat exchangers participating in the evolution might not be involved in all streams in each evolutionary process. A stream that does not participate in the evolution will have no significance to the current iteration. Therefore, many iterations are required to make each stream participate in the evolution, which limits the evolution efficiency of the optimization algorithm. In view of this shortcoming, this study proposes a participatory evolutionary strategy for streams based on hot streams. The proposed strategy reorders the existing heat exchangers on hot and cold streams and takes the corresponding measures to ensure that a heat exchanger is selected for each stream to participate in the evolution in every cycle. The proposed participatory evolutionary strategy for streams improves the global optimal solution for designs based on non-structural models. The effectiveness of the proposed strategy is demonstrated in two cases.