Fixed Budget Performance of the (1+1) EA on Linear Functions

Abstract

We present a fixed budget analysis of the (1+1) evolutionary algorithm for general linear functions, considering both the quality of the solution after a predetermined 'budget' of fitness function evaluations (a priori) and the improvement in quality when the algorithm is given additional budget, given the quality of the current solution (a posteriori). Two methods are presented: one based on drift analysis, the other on the differential equation method and Chebyshev's inequality. While the first method is superior for general linear functions, the second can be more precise for specific functions and provides concentration guarantees. As an example, we provide tight a posteriori fixed budget results for the function OneMax.