We show that given a k-bounded pseudo-Boolean function f, one can always compute the cth moment of f over regions of arbitrary radius in Hamming space in polynomial time using algebraic information from the adjacency structure (where k and c are constants). This result has implications for evolutionary algorithms and local search algorithms because information about promising regions of the search space can be efficiently retrieved, even if the cardinality of the region is exponential in the problem size. Finally, we use our results to introduce a method of efficiently calculating the expected fitness of mutations for evolutionary algorithms.
Bibliographical noteFunding Information:
This research was sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-08-1-0422. The US Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The authors would like to thank Schloß Dagstuhl - Leibniz Center for Informatics where some of the ideas contained in this paper were developed during the Dagstuhl seminar on the Theory of Evolutionary Algorithms. The authors would also like to thank the anonymous referees for their useful comments and suggestions.
- Elementary landscapes
- Fitness landscape analysis
- Local search
- Pseudo-Boolean functions
- Walsh analysis