How majority-vote crossover and estimation-of-distribution algorithms cope with fitness valleys

The benefits of using crossover in crossing fitness gaps have been studied extensively evolutionary computation. Recent runtime results show that majority-vote is particularly efficient at optimizing the well-known Jump benchmark function includes a gap next to global optimum. Also estimation-of-distribution algorithms (EDAs), which use an implicit crossover, are much more on than typical mutation-based algorithms. However, allowed size for polynomial runtimes with EDAs most logarithmic problem dimension n. In this paper, we investigate variants where shifted and appears middle search trajectory. Such can still be overcome efficiently time O(nlog⁡n) by algorithm, even sizes almost if optimum located instead usual all-ones string, would nevertheless approach string highly inefficient. sharp contrast, EDA find such efficiently. Thanks general property called fair sampling, will high probability sample from every level function, including levels gap, though overall trajectory points towards string. Finally, derive limits allowing EDA.