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In this paper we study cellular automata (CAs) that perform the computationalMajority task. This task is a good example of what the phenomenon of emergencein complex systems is. We take an interest in the reasons that make thisparticular fitness landscape a difficult one. The first goal is to study thelandscape as such, and thus it is ideally independent from the actualheuristics used to search the space. However, a second goal is to understandthe features a good search technique for this particular problem space shouldpossess. We statistically quantify in various ways the degree of difficulty ofsearching this landscape. Due to neutrality, investigations based on samplingtechniques on the whole landscape are difficult to conduct. So, we go exploringthe landscape from the top. Although it has been proved that no CA can performthe task perfectly, several efficient CAs for this task have been found.Exploiting similarities between these CAs and symmetries in the landscape, wedefine the Olympus landscape which is regarded as the ''heavenly home'' of thebest local optima known (blok). Then we measure several properties of thissubspace. Although it is easier to find relevant CAs in this subspace than inthe overall landscape, there are structural reasons that prevent a searcherfrom finding overfitted CAs in the Olympus. Finally, we study dynamics andperformance of genetic algorithms on the Olympus in order to confirm ouranalysis and to find efficient CAs for the Majority problem with lowcomputational cost.

Fitness landscape of the cellular automata majority problem: View from the Olympus