Smoothness, ruggedness and neutrality of fitness landscapes: from theory to application

  • Authors:
  • Vesselin K. Vassilev;Terence C. Fogarty;Julian F. Miller

  • Affiliations:
  • School of Computing, Napier University, Edinburgh, EH14 1DJ, UK;School of Computing, Napier University, Edinburgh, EH14 1DJ, UK;School of Computer Science, University of Birmingham, Birmingham, B15 2TT, UK

  • Venue:
  • Advances in evolutionary computing
  • Year:
  • 2003

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Abstract

The theory of fitness landscapes has been developed to provide a suitable mathematical framework for studying the evolvability of a variety of complex systems. In evolutionary computation the notion of evolvability refers to the efficiency of evolutionary search. It has been shown that the structure of a fitness landscape affects the ability of evolutionary algorithms to search. Three characteristics specify the structure of landscapes. These are the landscape smoothness, ruggedness and neutrality. The interplay of these characteristics plays a vital role in evolutionary search. This has motivated the appearance of a variety of techniques for studying the structure of fitness landscapes. An important feature of these techniques is that they characterize the landscapes by their smoothness and ruggedness, ignoring the existence of neutrality. Perhaps, the reason for this is that the role of neutrality in evolutionary search is still poorly understood.In this chapter some recent results on the spectral properties of the algebraic structures of fitness landscapes are summarized to provide a basis for studying the landscape structure. This approach is further employed to introduce an information analysis that characterizes the structure of fitness landscapes in terms of their smoothness, ruggedness and neutrality. The findings are finally applied in a study of the fitness landscapes generated by evolving digital circuits using an idealized model of a field-programmable gate array. The landscapes of this engineering problem are quite different from many recently studied landscapes that tend to be defined over simplified combinatorial and optimization problems. The difference originates from the genotype representation that is a configuration defined over two completely different alphabets. This makes the study of the corresponding landscapes much more involved. It is shown that the circuit evolution landscapes are products of subspaces with different characteristics. They are landscapes with vast neutrality and sharply differentiated plateau.