When a genetic algorithm outperforms hill-climbing

A toy optimisation problem is introduced which consists of a ÿtness gradient broken up by a series of hurdles. The performance of a hill-climber and a stochastic hill-climber are computed. These are compared with the empirically observed performance of a genetic algorithm (GA) with and without. The hill-climber with a suuciently large neighbourhood outperforms the stochastic hill-climber, but is outperformed by a GA both with and without crossover. The GA with crossover substantially outperforms all the other heuristics considered here. The relevance of this result to real world problems is discussed.