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Index

• Royal Road
• Hierarchical If-and-only-if
• NK
  • NKp
  • NKq
• Hyperplane defined functions (hdf)
• Hierarchically defined functions (HDF)
• Hopfield network energy function

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Royal Road

This function (RR) is described in:

• Mitchell, M., Holland, J. H., & Forrest, S. (1994). When will a genetic algorithm outperform hill climbing? In Advances in Neural Information Processing Systems 6, 51-58, MIT Press.

RR is defined for 4, 8 and 16 dimensions with all levels of the hierarchy (schemata at every level of the hierarchy).

Hierarchical If-and-only-if

This function (HIFF) is described in:

• Watson, R. A., Hornby, G. S., & Pollack, J. B., (1998). Modeling building-block interdependency. In A. E. Eiben, T. Bäck, H.-P. Schwefel, & M. Schoenaur, Parallel Problem Solving from Nature: Proceedings of the Fifth International Conference, 97-106, Springer.

HIFF is defined for 4, 8 and 16 dimensions with all levels of the hierarchy (schemata at every level of the hierarchy).

NK

Kauffman's NK family of functions. This family is described in

• Kauffman, S. (1993), The Origins of Order, Oxford University Press:NY.

Defined here for values of N up to 32. Gene epistasticity may be either systematic or randomised. Some quantised variations are also provided. The differences between these quantised versions is discussed in

• Geard, N., Wiles, J., Hallinan, J., & Tonkes, B. (2002). A comparison of neutral landscapes - NK, NKp and Nkq. To appear: Proceedings of CEC 2002.

NKp

In this quantised variant of NK, the fitness contribution of a particular gene sequence is set to 0 with probability p.

NKq

In this variant version of NK, the fitness contribution of gene sequences are quantised to q distinct levels.

Hyperplane-Defined Functions

Holland's hdf family of functions. Described in:

• Holland, J. H. (2000). Building blocks, cohort genetic algorithms, and hyperplane-defined functions. In Evolutionary Computation, 8:4, 373-391.

Hierarchical Decomposable Functions

Golderberg's HDF function. Described in:

• Pelikan, M., & Goldberg, D. E. (2000). Hierarchical problem solving by the bayesian optimization algorithm. IlliGAL Report No. 200002, Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL.

Hopfield network energy function

The energy function defined over states of a Hopfield network. Each point in the graph represents a particular state of the Hopfield network (where -1 values are assumed to be `0' values for the purposes of positioning on the graph). Initially, the weights of the network are all 0, so consequently all states have 0 energy. New vectors can be added to the Hopfield network memory by shift+left-clicking on the desired vector.

The weights of the network can be reset by choosing "Reset network" from the context menu.