Spin-Flip Symmetry and Synchronization

In the context of optimization by evolutionary algorithms (EAs), epistasis, deception, and scaling are well-known examples of problem difficulty characteristics. The presence of one such characteristic in the representation of a search problem indicates a certain type of difficulty the EA is to encounter during its search for globally optimal configurations. In this paper, we claim that the occurrence of symmetry in the representation is another problem difficulty characteristic and discuss one particular form, spin-flip symmetry, characterized by fitness invariant permutations on the alphabet. Its usual effect on unspecialized EAs, premature convergence due to synchronization problems, is discussed in detail. We discuss five different ways to specialize EAs to cope with the symmetry: adapting the genetic operators, changing the fitness function, using a niching technique, using a distributed EA, and attaching a highly redundant genotype-phenotype mapping.

[1]  E. Ising.  Beitrag zur Theorie des Ferromagnetismus , 1925 .

[2]  David E. Goldberg,et al.  Alleles, loci and the traveling salesman problem , 1985 .

[3]  T. Liggett.  Interacting Particle Systems , 1985 .

[4]  David E. Goldberg,et al.  AllelesLociand the Traveling Salesman Problem , 1985, ICGA.

[5]  D. E. Goldberg,et al.  Simple Genetic Algorithms and the Minimal, Deceptive Problem , 1987 .

[6]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[7]  Dana S. Richards,et al.  Punctuated Equilibria: A Parallel Genetic Algorithm , 1987, ICGA.

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

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

[10]  Reiko Tanese,et al.  Distributed Genetic Algorithms , 1989, ICGA.

[11]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[12]  Yuval Davidor,et al.  Epistasis Variance: A Viewpoint on GA-Hardness , 1990, FOGA.

[13]  Kalyanmoy Deb,et al.  Messy Genetic Algorithms Revisited: Studies in Mixed Size and Scale , 1990, Complex Syst..

[14]  Gunar E. Liepins,et al.  Deceptiveness and Genetic Algorithm Dynamics , 1990, FOGA.

[15]  G. Syswerda,et al.  Schedule Optimization Using Genetic Algorithms , 1991 .

[16]  Kalyanmoy Deb,et al.  Massive Multimodality, Deception, and Genetic Algorithms , 1992, PPSN.

[17]  Philippe Collard,et al.  DGA: An Efficient Genetic Algorithm , 1994, ECAI.

[18]  Terry Jones,et al.  Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms , 1995, ICGA.

[19]  Peter Ross,et al.  The Phase-Transition Niche for Evolutionary Algorithms in Timetabling , 1995, PATAT.

[20]  Philippe Collard,et al.  'Royal-Road' Landscapes for a Dual Genetic Algorithm , 1996, ECAI.

[21]  A. E. Eiben,et al.  Adaptive Penalties for Evolutionary Graph Coloring , 1997, Artificial Evolution.

[22]  Brad L. Miller,et al.  Noise, sampling, and efficient genetic algorthms , 1997 .

[23]  Alessio Gaspar,et al.  Folding Genetic Algorithms : the Royal Road toward an OptimalChromosome ' s , 1997 .

[24]  Peter Ross,et al.  Some Observations about GA-Based Exam Timetabling , 1997, PATAT.

[25]  Jordan B. Pollack,et al.  Modeling Building-Block Interdependency , 1998, PPSN.

[26]  Jan Naudts,et al.  The Effect of Spin-Flip Symmetry on the Performance of the Simple GA , 1998, PPSN.

[27]  B. Naudts,et al.  SAWing on symmetry , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[28]  Ian P. Gent,et al.  Well out of reach: Why hard problems are hard , 1999 .

[29]  C. Stephens.  Effect of mutation and recombination on the genotype-phenotype map , 1999, nlin/0006051.

[30]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[31]  Rémi Monasson,et al.  2+p-SAT: Relation of typical-case complexity to the nature of the phase transition , 1999, Random Struct. Algorithms.

[32]  Bart Naudts,et al.  A comparison of predictive measures of problem difficulty in evolutionary algorithms , 2000, IEEE Trans. Evol. Comput..

[33]  C. Van Hoyweghen,et al.  Symmetry in the search space , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[34]  M. Shackleton,et al.  An investigation of redundant genotype-phenotype mappings and their role in evolutionary search , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[35]  Julian Francis Miller,et al.  Information Characteristics and the Structure of Landscapes , 2000, Evolutionary Computation.

[36]  D. Goldberg,et al.  Building block superiority, multimodality and synchronization problems , 2001 .

[37]  Christian M. Reidys,et al.  Neutrality in fitness landscapes , 2001, Appl. Math. Comput..

[38]  David E. Goldberg,et al.  From Twomax To The Ising Model: Easy And Hard Symmetrical Problems , 2002, GECCO.

[39]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .