A society of hill-climbers

The paper is concerned with function optimisation in binary search spaces. It focuses on how hill climbers can work together and/or use their past trials in order to speed up the search. A hill climber is viewed as a set of mutations. The challenge is twofold: one must determine how many bits should be mutated, and which bits should preferably be mutated, or in other words, which climbing directions are to be preferred. The latter question is addressed by recording the last worst trials of the hill climbers within an individual, called repoussoir. The hill climbers further explore the neighborhood of their current point so as to get away from the repoussoir. As to the former question, no definite answer is proposed. Nevertheless, we experimentally show that hill climbers behave quite differently depending on whether one sets a mutation rate p_m per bit, or sets the exact number M of bits to mutate per individual. Two algorithms describing societies of hill climbers, with or without memory of the past trials, are described. These are experimented on several 900-bit problems, and significantly outperform standard genetic algorithms and evolution strategies