ABSTRACT
For the past 25 years, NK landscapes have been the classic benchmarks for modeling combinatorial fitness landscapes with epistatic interactions between up to K+1 of N binary features. However, the ruggedness of NK landscapes grows in large discrete jumps as K increases, and computing the global optimum of unrestricted NK landscapes is an NP-complete problem. Walsh polynomials are a superset of NK landscapes that solve some of the problems. In this paper, we propose a new class of benchmarks called NM landscapes, where M refers to the Maximum order of epistatic interactions between N features. NM landscapes are much more smoothly tunable in ruggedness than NK landscapes and the location and value of the global optima are trivially known. For a subset of NM landscapes the location and magnitude of global minima are also easily computed, enabling proper normalization of fitnesses. NM landscapes are simpler than Walsh polynomials and can be used with alphabets of any arity, from binary to real-valued. We discuss several advantages of NM landscapes over NK landscapes and Walsh polynomials as benchmark problems for evaluating search strategies.
- J. Buzas and J. Dinitz. An analysis of NK landscapes: Interaction structure, statistical properties and expected number of local optima. IEEE Transactions on Evolutionary Computation, in press, DOI 10.1109/TEVC.2013.2286352, 2014.Google Scholar
- S. Kauffman. The origins of order: Self organization and selection in evolution. Oxford University Press, 1993.Google Scholar
- S. A. Kauffman and E. D. Weinberger. The NK model of rugged fitness landscapes and its application to maturation of the immune response. Journal of theoretical biology, 141(2):211--245, 1989.Google ScholarCross Ref
- R. Tanese. Distributed genetic algorithms for Function Optimization. PhD thesis, The University of Michigan, Ann Arbor, MI, 1989. Google ScholarDigital Library
- A. H. Wright, R. K. Thompson, and J. Zhang. The computational complexity of NK fitness functions. IEEE Transactions on Evolutionary Computation, 4(4):373--379, 2000. Google ScholarDigital Library
Index Terms
- NM landscapes: beyond NK
Recommendations
Fitness landscapes and graphs: multimodularity, ruggedness and neutrality
GECCO '12: Proceedings of the 14th annual conference companion on Genetic and evolutionary computationOne of the most commonly-used metaphors to describe the process of heuristic search methods in solving combinatorial optimization problems is that of a fitness landscape. The landscape metaphor appears most commonly in work related to evolutionary ...
Fitness landscapes and graphs: multimodularity, ruggedness and neutrality
GECCO '09: Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking PapersThe performances of evolutionary algorithms (genetics algorithms, genetic programming, etc.) or local search algotihms (Simulated annealing, tabu search, etc.) depends on the properties of seach space structure. One concept to analyse the search space ...
Fitness landscapes and graphs: multimodularity, ruggedness and neutrality
GECCO '13 Companion: Proceedings of the 15th annual conference companion on Genetic and evolutionary computationOne of the most commonly-used metaphors to describe the process of heuristic search methods in solving combinatorial optimization problems is that of a fitness landscape. The landscape metaphor appears most commonly in work related to evolutionary ...
Comments