This paper proposes a non‐structural model with stream splits, for heat exchanger network (HEN) synthesis, that allows for submixing of substreams within splits and series connection of exchanger units in a substream. In a submix, one substream totally combines with another non‐isothermally, and by allowing this feature, the designer incurs only piping costs, which are significantly low compared to other HEN costs, and benefits from increased possibility of manipulating substream temperatures. An algorithm employing random walk principles and compulsive evolution is applied for HEN optimization. The method's randomness, which enhances its explorative searching power and efficiency, is an attractive property that matches the proposed model. Four case studies from the literature are solved and annual cost savings of $1800, $7769, and $4771/year are achieved for three of them in comparison with published best solutions, attesting to the effectiveness of the proposed model.