An approach to stopping criteria for multi-objective optimization evolutionary algorithms: The MGBM criterion

In this work we put forward a comprehensive study on the design of global stopping criteria for multi-objective optimization. We describe a novel stopping criterion, denominated MGBM criterion that combines the mutual domination rate (MDR) improvement indicator with a simplified Kalman filter that is used for evidence gathering process. The MDR indicator, which is introduced along, is a special purpose solution meant for the stopping task. It is capable of gauging the progress of the optimization with a low computational cost and therefore suitable for solving complex or many-objective problems. The viability of the proposal is established by comparing it with some other possible alternatives. It should be noted that, although the criteria discussed here are meant for MOPs and MOEAs, they could be easily adapted to other softcomputing or numerical methods by substituting the local improvement metric with a suitable one.