Test Function Generators as Embedded Landscapes

NK-landscapes and kSAT problems have been proposed as potential test problem domains for Genetic Algorithms. We demonstrate that GAs have diiculty solving both kSAT and NK-landscape problems. The construction of random kSAT and NK-landscape problems are very similar, but the diierences between kSAT and NK-landscape generation result in vastly diierent tness landscapes. In this paper we introduce a parameterized model for the construction of test function generators. This model, called embedded landscapes, can be used to isolate the features of combinatorial optimization problems for more control during experimentation. We also show that common forms of embedded landscapes allow for a polynomial time Walsh analysis. This means we also can compose exact schema averages in polynomial time for schema up to order-K, where K is a constant. Yet, in the general case, this information does not allow one to infer the global optimum of a function unless the complexity classes P and NP are equal.

[1]  David E. Goldberg,et al.  Genetic Algorithms and Walsh Functions: Part I, A Gentle Introduction , 1989, Complex Syst..

[2]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[3]  L. Altenberg.  B2.7.2 NK Fitness Landscapes , 1997 .

[4]  Kenneth A. De Jong,et al.  Using Problem Generators to Explore the Effects of Epistasis , 1997, ICGA.

[5]  L. Darrell Whitley,et al.  A Tractable Walsh Analysis of SAT and its Implications for Genetic Algorithms , 1998, AAAI/IAAI.

[6]  Jeremy Frank,et al.  When Gravity Fails: Local Search Topology , 1997, J. Artif. Intell. Res..

[7]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[8]  Larry J. Eshelman.  The CHC Adaptive Search Algo-rithm , 1991 .

[9]  Colin R. Reeves,et al.  An Experimental Design Perspective on Genetic Algorithms , 1994, FOGA.

[10]  E. Weinberger.  NP Completeness of Kauffman's N-k Model, A Tuneable Rugged Fitness Landscape , 1996 .

[11]  L. Darrell Whitley,et al.  A Walsh Analysis of NK-Landscapes , 1997, ICGA.

[12]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[13]  Bart Selman,et al.  An Empirical Study of Greedy Local Search for Satisfiability Testing , 1993, AAAI.

[14]  Tim Jones.  Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[15]  Lawrence Davis,et al.  Bit-Climbing, Representational Bias, and Test Suite Design , 1991, ICGA.

[16]  Albert Donally Bethke,et al.  Genetic Algorithms as Function Optimizers , 1980 .

[17]  Bart Selman,et al.  Local search strategies for satisfiability testing , 1993, Cliques, Coloring, and Satisfiability.

[18]  Lee Altenberg,et al.  Evolving better representations through selective genome growth , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.