Ensemble dominance for solving interval programming problems

Interval programming problems are ubiquitous in real-world situations. There exist a variety of theories and methods for handling them; the existing methods, however, have adopted various dominance criteria to distinguish solutions, and these criteria are always subjective. Different dominance criteria will produce different optimal solution(s), and subjective criteria make users, especially for those who are not familiar with interval arithmetic, difficult to choose, which restricts their widespread applications. In this study, the idea of ensemble dominance on intervals for tackling these problems is proposed. Dominance criteria on intervals are first defined, and their correlations are depicted by equivalent, inclusive and non-included relations; then, a reduction scheme is derived by investigating the influence of different criteria on the ordering of solutions, and a novel ensemble dominance relation on intervals is defined to rationally and equally evaluate the quality of a solution; furthermore, the complexity of the proposed method is analyzed; finally, empirical results indicate the effectiveness of the proposed method.