On the value of operator-induced neighborhoods in fitness landscapes

All of the solutions to a combinatorial optimization problem can be collected into a fitness landscape. Often these landscapes are huge, making an exhaustive search for the best solution impractical. Stochastic search algorithms work best if the search operators are tailored to the fitness landscape structure. Some researchers claim this structure is induced by the search operator itself. In this paper we show structural information obtained from operator-induced neighborhoods can be completely misleading unless specific ordering has prevailed during the mapping process and appropriate isomorphic proofs have been made.