Runtime Analysis of the (1+1) EA on Weighted Sums of Transformed Linear Functions
Abstract
Linear functions play a key role in the runtime analysis of evolutionary algorithms and studies have provided a wide range of new insights and techniques for analyzing evolutionary computation methods. Motivated by studies on separable functions and the optimization behaviour of evolutionary algorithms as well as objective functions from the area of chance constrained optimization, we study the class of objective functions that are weighted sums of two transformed linear functions. Our results show that the (1+1) EA, with a mutation rate depending on the number of overlapping bits of the functions, obtains an optimal solution for these functions in expected time O(n log n), thereby generalizing a well-known result for linear functions to a much wider range of problems.
Keywords
Cite
@article{arxiv.2208.05670,
title = {Runtime Analysis of the (1+1) EA on Weighted Sums of Transformed Linear Functions},
author = {Frank Neumann and Carsten Witt},
journal= {arXiv preprint arXiv:2208.05670},
year = {2022}
}
Comments
To appear at PPSN 2022. arXiv admin note: text overlap with arXiv:2109.05799