Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
On classes of functions for which No Free Lunch results hold
Information Processing Letters
Fitness-proportional negative slope coefficient as a hardness measure for genetic algorithms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Two broad classes of functions for which a no free lunch result does not hold
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
No free lunch theorems for optimization
IEEE Transactions on Evolutionary Computation
There Is a Free Lunch for Hyper-Heuristics, Genetic Programming and Computer Scientists
EuroGP '09 Proceedings of the 12th European Conference on Genetic Programming
Optimization speed and fair sets of functions
Proceedings of the 12th annual conference on Genetic and evolutionary computation
A study of search algorithms' optimization speed
Journal of Combinatorial Optimization
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We introduce the concept of "minimal" search algorithm for a set of functions to optimize. We investigate the structure of closed under permutation (c.u.p.) sets and we calculate the performance of an algorithm applied to them. We prove that each set of functions based on the distance to a given optimal solution, among which trap functions, onemax or the recently introduced onemix functions, and the NK-landscapes are not c.u.p. and thus the thesis of the sharpened No Free Lunch Theorem does not hold for them. Thus, it makes sense to look for a specific algorithm for those sets. Finally, we propose a method to build a "good" (although not necessarily minimal) search algorithm for a specific given set of problems. The algorithms produced with this technique show better average performance than a genetic algorithm executed on the same set of problems, which was expected given that those algorithms are problem-specific. Nevertheless, in general they cannot be applied for real-life problems, given their high computational complexity that we have been able to estimate.