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No Free Lunch Theorems for Search
TLDR
It is shown that all algorithms that search for an extremum of a cost function perform exactly the same, when averaged over all possible cost functions, which allows for mathematical benchmarks for assessing a particular search algorithm's performance.Abstract:
We show that all algorithms that search for an extremum of a cost function perform exactly the same, when averaged over all possible cost functions. In particular, if algorithm A outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions where B outperforms A. Starting from this we analyze a number of the other a priori characteristics of the search problem, like its geometry and its information-theoretic aspects. This analysis allows us to derive mathematical benchmarks for assessing a particular search algorithm's performance. We also investigate minimax aspects of the search problem, the validity of using characteristics of a partial search over a cost function to predict future behavior of the search algorithm on that cost function, and time-varying cost functions. We conclude with some discussion of the justifiablility of biologically-inspired search methods.read more
Citations
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No free lunch theorems for optimization
TL;DR: A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving and a number of "no free lunch" (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class.
Journal ArticleDOI
A global optimisation method for robust affine registration of brain images
Mark Jenkinson,Stephen M. Smith +1 more
TL;DR: It is demonstrated that the use of local optimisation methods together with the standard multi-resolution approach is not sufficient to reliably find the global minimum, so a global optimisation method is proposed that is specifically tailored to this form of registration.
Journal ArticleDOI
Evolutionary programming made faster
Xin Yao,Yong Liu,Guangming Lin +2 more
TL;DR: A "fast EP" (FEP) is proposed which uses a Cauchy instead of Gaussian mutation as the primary search operator and is proposed and tested empirically, showing that IFEP performs better than or as well as the better of FEP and CEP for most benchmark problems tested.
Journal ArticleDOI
The fully informed particle swarm: simpler, maybe better
TL;DR: The canonical particle swarm algorithm is a new approach to optimization, drawing inspiration from group behavior and the establishment of social norms, but each individual is not simply influenced by the best performer among his neighbors.
Journal ArticleDOI
A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm
TL;DR: Simulation results reveal that using CSA may lead to finding promising results compared to the other algorithms, and this paper proposes a novel metaheuristic optimizer, named crow search algorithm (CSA), based on the intelligent behavior of crows.
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