A non-nominating sorting method distributes a population’s solutions into different fronts according to dominance relation. In this paper, we proposed a non-nominating sorting method called solution best-ordered sorting (SBOS) induced by topological gradient, in which we especially manage the duplicate solutions to reduce the time complexity. Many recently proposed popular methods, including bounded best order sort (BBOS) and efficient non-dominated sort (ENS), cost several objective comparisons during the front assignment process. Even generalized best order sort (GBOS), with an objective comparison reduction scheme, fails in constant duplicate checking operations. Our proposed method effectively reduces many unrelated solution comparisons by managing duplicates in priority. Moreover, the time complexity of SBOS is analyzed, and the correctness of the front assignment is proved. Finally, we propose a new sample data algorithm for fixed front sets that can be used as benchmark test data.