A novel non-dominated sorting algorithm for evolutionary multi-objective optimization

Evolutionary computation has shown great performance in solving many multi-objective optimization problems; in many such algorithms, non-dominated sorting plays an important role in determining the relative quality of solutions in a population. However, the implementation of non-dominated sorting can be computationally expensive, especially for populations with a large number of solutions and many objectives. The main reason is that most existing non-dominated sorting algorithms need to compare one solution with almost all others to determine its front, and many of these comparisons are redundant or unnecessary. Another reason is that as the number of objectives increases, more and more candidate solutions become non-dominated solutions, and most existing time-saving approaches cannot work effectively. In this paper, we present a novel non-dominated sorting strategy, called Hierarchical Non-Dominated Sorting (HNDS). HNDS first sorts all candidate solutions in ascending order by their first objective. Then it compares the first solution with all others one by one to make a rapid distinction between different quality solutions, thereby avoiding many unnecessary comparisons. Experiments on populations with different numbers of solutions, different numbers of objectives and different problems have been done. The results show that HNDS has better computational efficiency than fast non-dominated sort, Arena's principle and deductive sort.