Facing the current energy structure urgently needs to be transformed, heat exchanger network (HEN) can implement heat recovery and cost reduction by the arrangement for heat exchanges between cold and hot streams. The plenty of integer and continuous variables involved in HEN synthesis cause the results to be easily trapped in local optima. To avoid this situation, the mechanism of accepting imperfect solutions is added in a novel algorithm called Random Walk Algorithm with Compulsive Evolution. However, several potential solutions maybe abandoned by accepting imperfect solutions. To maintain the global searching ability, and at the same time, protecting the potential solutions during the optimization process, the limitations of accepting imperfect solutions are investigated in this work, then a back substitution strategy and elite optimization strategy based on algorithm are proposed. The former is to identify and adjust the inferior individuals in long-term stagnation while the latter is to keep and perform a fine search for the better solutions. Furthermore, a modified stage-wised superstructure is also developed to implement the flexible placement of utilities, which efficiently enlarges the solution domain. The validation of strategies and model is implemented by three cases, the results are lower, with 2219 $/year, 1280 $/year, and 2M $/year than the best published result, revealing the strong abilities of the proposed method in designing more economical HENs.