On Non-Elitist Evolutionary Algorithms Optimizing Fitness Functions with a Plateau
This work addresses runtime analysis for evolutionary algorithms in optimization problems with plateaus, which is incremental as it builds on existing level-based theorems.
The paper analyzes the expected runtime of non-elitist evolutionary algorithms on fitness functions with a plateau near the optimum, showing polynomial upper bounds for some algorithms but inefficiency for fitness proportionate selection with standard mutation settings.
We consider the expected runtime of non-elitist evolutionary algorithms (EAs), when they are applied to a family of fitness functions with a plateau of second-best fitness in a Hamming ball of radius r around a unique global optimum. On one hand, using the level-based theorems, we obtain polynomial upper bounds on the expected runtime for some modes of non-elitist EA based on unbiased mutation and the bitwise mutation in particular. On the other hand, we show that the EA with fitness proportionate selection is inefficient if the bitwise mutation is used with the standard settings of mutation probability.