Exploration and Exploitation Without Mutation: Solving the Jump Function in $$\varTheta (n)$$ Time

A number of modern hybrid genetic algorithms do not use mutation. Instead, these algorithms use local search to improve intermediate solutions. This same strategy of combining local search and crossover is also used by stochastic local algorithms, such the LKH heuristic for the Traveling Salesman Problem. We prove that a simple hybrid genetic algorithm that uses only local search and a form of deterministic “voting crossover” can solve the well known Jump Function in \(\varTheta (n)\) time where the jump distance is log(n).