On the equality constraints tolerance of Constrained Optimization Problems

The tolerance value plays an important role when converting equality constraints into inequality constraints in solving Constrained Optimization Problems. Many researchers use a fixed or dynamic setting directly based on trial or experiments without systematic study. As a well-known constraint handling technique, Deb's feasibility-based rule is widely adopted, but it has one drawback as the ranking is not consistent with the actual ranking after introducing the tolerance value. After carefully analyzing how the tolerance value influences the ranking difference, a novel strategy named Ranking Adjustment Strategy (RAS) is proposed, which can be considered as a complement of Deb's feasibility-based rule. The experiment has verified the effectiveness of the proposed strategy. This is the first time to analyze the inner mechanism of the tolerance value for equality constraints systematically, which can give some guide for future research.