Deductive sort and climbing sort: new methods for non-dominated sorting

In recent years an increasing number of real-world many-dimensional optimisation problems have been identified across the spectrum of research fields. Many popular evolutionary algorithms use non-dominance as a measure for selecting solutions for future generations. The process of sorting populations into non-dominated fronts is usually the controlling order of computational complexity and can be expensive for large populations or for a high number of objectives. This paper presents two novel methods for non-dominated sorting: deductive sort and climbing sort. The two new methods are compared to the fast non-dominated sort of NSGA-II and the non-dominated rank sort of the omni-optimizer. The results demonstrate the improved efficiencies of the deductive sort and the reductions in comparisons that can be made when applying inferred dominance relationships defined in this paper.