The benefits and limitations of voting mechanisms in evolutionary optimisation.

We study the use of voting mechanisms in populations, and introduce a new Voting algorithm which can solve ONEMAX and JUMP in O(n log n), even for gaps as large as O(n). More significantly, the algorithm solves ONEMAX with added posterior noise in O(n log n), when the variance of the noise distribution is σ2 = O(n) and in O(σ2 log n) when the noise variance is greater than this. We assume only that the noise distribution has finite mean and variance and (for the larger noise case) that it is unimodal. We also examine the performance on arbitrary linear and monotonic functions. The Voting algorithm fails on LEADINGSONES but we give a variant which can solve the problem in O(n log n). We empirically study the use of voting in population based algorithms (UMDA, PCEA and cGA) and show that this can be effective for large population sizes.