A Steady Performance Stopping Criterion for Pareto-based Evolutionary Algorithms
Olga Roudenko and Marc Schoenauer
Proceedings of the 6th International Multi-Objective Programming and Goal Programming Conference
The most commonly used stopping criterion in Evolutionary Multi-objective
Algorithms is an a priori fixed number of generations (or evaluations). But it is rather difficult to speak about achieving a particular compromise between the quality of the final solutions and the computation time when stopping an algorithm this way. Unfortunately, whereas single-objective Evolutionary Algorithms can stop when the fitness does not improve during a given number of generations, such ``steady-fitness'' stopping criterion does not easily extend to the multi-objective framework.
This paper introduces a stability measure based on the density of the non-dominated solutions and proposes to use it to stop the optimization process when no significant improvement is likely to take place on further iterations. This approach is validated by the empirical results obtained applying NSGA-II to the well-known bi-objective ZDT-benchmarks.
In particular, the problem ZDT4 best illustrates the ability of the proposed criterion to avoid useless continuation of a wedged optimization process when a local Pareto-optimal set is reached.