A note on the first hitting time of (1 + λ) evolutionary algorithm for linear functions with boolean inputs

Linear functions, as a canonical model of unimodal problems, have been widely used in the theoretical study of evolutionary algorithms (EAs). However in most of cases, only the simplest linear function, i.e. One-Max function, is taken in the theoretical study. A question arises naturally: whether can the results for One-Max function be generalized to linear functions? The main contribution of this paper is to generalize a result about the first hitting time of (1 + λ) EA from One-Max function [1] to linear functions. A new proof is proposed based on drift analysis. This work is a direct extension of the previous analysis of (1 + 1) EA for linear functions [2].