Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization

@article{Droste2004UpperAL,
  title={Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization},
  author={Stefan Droste and T. Jansen and Ingo Wegener},
  journal={Theory of Computing Systems},
  year={2004},
  volume={39},
  pages={525-544}
}
Abstract Randomized search heuristics like local search, tabu search, simulated annealing, or all kinds of evolutionary algorithms have many applications. However, for most problems the best worst-case expected run times are achieved by more problem-specific algorithms. This raises the question about the limits of general randomized search heuristics. Here a framework called black-box optimization is developed. The essential issue is that the problem but not the problem instance is knownto the… Expand
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References

SHOWING 1-10 OF 30 REFERENCES
A New Framework for the Valuation of Algorithms for Black-Box Optimization
TLDR
It can be concluded that randomized search heuristics whose (worst-case) expected optimization time for some problem is close to the black-box complexity of the problem are provably efficient (in theblack-box scenario). Expand
Evolutionary Algorithms and the Maximum Matching Problem
TLDR
It is proven that the evolutionary algorithm is a polynomial-time randomized approximation scheme (PRAS) for this optimization problem, although the algorithm does not employ the idea of augmenting paths. Expand
On the Optimization of Monotone Polynomials by Simple Randomized Search Heuristics
  • I. Wegener, C. Witt
  • Mathematics, Computer Science
  • Combinatorics, Probability and Computing
  • 2005
TLDR
An analysis of howRandomized search heuristics work on classes of functions, including the class of monotone pseudo-Boolean polynomials, results depending on the degree and the number of terms of the polynomial are obtained. Expand
The time complexity of maximum matching by simulated annealing
TLDR
It is shown for arbitrary graphs that a degenerate form of the basic annealing algorithm (obtained by letting “temperature” be a suitably chosen constant) produces matchings with nearly maximum cardinality in polynomial average time. Expand
Theoretical Aspects of Evolutionary Algorithms
TLDR
Some fundamental results on evolutionary algorithms are presented in order to show how theoretical results on randomized search heuristics can be proved and how they contribute to the understanding of evolutionary algorithms. Expand
Fitness Landscapes Based on Sorting and Shortest Paths Problems
TLDR
Fitness landscapes based on important computer science problems as sorting and shortest paths problems are investigated here and it cannot be expected that evolutionary algorithms outperform the well-known problem specific algorithms on these simple problems. Expand
On the complexity of local search
TLDR
The main results are these: Finding a local optimum under the Lin-Kernighan heuristic for the traveling salesman problem is PLS-complete, and a host of simple unweighted local optimality problems are P-complete. Expand
Long Path Problems
TLDR
It is demonstrated that simple paths to the global optimum can be so long that climbing the path is intractable, which means that a unimodal search space, which consists of a single hill, can be difficult for a hillclimber to optimize. Expand
Local optimization on graphs
TLDR
This work shows how to derive close lower and upper bounds on the minimum number of function evaluations needed to find a local optimum in an arbitrary graph and applies these techniques to the hypercube to give insights into the class PLS and the gap between the average and worst-case behavior of local search. Expand
Search problems in the decision tree model
TLDR
It is shown that the CNF search problem is complete for all the variants of decision trees and that the gaps between the nondeterministic, the randomized, and the deterministic complexities can be arbitrarily large for search problems. Expand
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