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Conclusions

 

Even when given appropriate building blocks the Boolean parity problems are still difficult. The fitness landscapes are a ``needles-in-haystacks'' with the chance of random search finding a solution falling exponentially with number of inputs. We conclude solving such problems efficiently also requires consideration of how the inputs are structured. Work is continuing to understand the role of different function sets and search operators on the Boolean problems.

In two very different classes of problems (the Ant and Boolean problems) we have now shown that the fitness space is in a gross manner independent of program length. In general the number of programs of a given length grows approximately exponentially with that length. Thus the number of programs with a particular fitness score or level of performance also grows exponentially, in particular the number of solutions also grows exponentially.



William B Langdon
Mon Jul 13 15:53:27 BST 1998