On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Measuring, enabling and comparing modularity, regularity and hierarchy in evolutionary design
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
The Cooperative Coevolutionary (1+1) EA
Evolutionary Computation
Analyzing the effects of module encapsulation on search space bias
Proceedings of the 9th annual conference on Genetic and evolutionary computation
A building-block royal road where crossover is provably essential
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Generative encoding for multiagent learning
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Analyzing the effects of modularity on search spaces
Analyzing the effects of modularity on search spaces
Compact genetic codes as a search strategy of evolutionary processes
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Tag-based modules in genetic programming
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Constraining connectivity to encourage modularity in HyperNEAT
Proceedings of the 13th annual conference on Genetic and evolutionary computation
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A recent theoretical investigation of modular representations shows that certain modularizations can introduce a distance bias into a landscape. This was a static analysis, and empirical investigations were used to connect formal results to performance. Here we replace this experimentation with an introductory runtime analysis of performance. We study a base-line, unbiased modularization that makes use of a complete module set (CMS), with special focus on strings that grow logarithmically with the problem size. We learn that even unbiased modularizations can have profound effects on problem performance. Our (1+1) CMS-EA optimizes a generalized OneMax problem in Ω(n2) time, provably worse than a (1+1) EA. More generally, our (1+1) CMS-EA optimizes a particular class of concatenated functions in O(2lm k n) time, where lm is the length of module strings and k is the number of module positions, when the modularization is aligned with the problem separability. We compare our results to known results for traditional EAs, and develop new intuition about modular encapsulation. We observe that search in the CMS-EA is essentially conducted at two levels (intra- and extra-module) and use this observation to construct a module trap, requiring super-polynomial time for our CMS-EA and O(n ln n) for the analogous EA.