This paper explores the idea of neutrality in heuristic optimization algorithms. In particular, the effect of having multiple levels of neutrality in representations is explored. Two experiments using a fitness-adaptive walk algorithm are carried out: the first is concerned with function optimization with Random Boolean Networks, the second with a tunable neutral mapping applied to the hierarchical if-and-only-if function. In both of these cases it is shown that a two-level neutral mapping can be found that performs better than both nonneutral mappings and mappings with a single level of neutrality
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