Design theory
Non-trivial t-designs without repeated blocks exist for all t
Discrete Mathematics
Locally trivial t-designs and t-designs without repeated blocks
Discrete Mathematics - Combinatorial designs: a tribute to Haim Hanani
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Theoretical Computer Science - Natural computing
On classes of functions for which No Free Lunch results hold
Information Processing Letters
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
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
Evolutionary Computation
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We study the precise conditions under which all optimization strategies for a given family of finite functions yield the same expected maximization performance, when averaged over a uniform distribution of the functions. In the case of bounded-length searches in a family of Boolean functions, we provide tight connections between such ''No Free Lunch'' conditions and the structure of t-designs and t-wise balanced designs for arbitrary values t. As a corollary, we obtain a nontrivial family of n-variate Boolean functions that satisfies the ''No Free Lunch'' condition with respect to searches of length @W(n^1^/^2/log^1^/^2n). Modifying the construction, we also obtain nontrivial ''No Free Lunch'' families of functions with large ranges.