Randomized algorithms
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Introduction to Algorithms
Theoretical Computer Science - Natural computing
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Towards an analytic framework for analysing the computation time of evolutionary algorithms
Artificial Intelligence
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Subthreshold-seeking local search
Theoretical Computer Science - Foundations of genetic algorithms
Randomized local search, evolutionary algorithms, and the minimum spanning tree problem
Theoretical Computer Science
Algorithmic analysis of a basic evolutionary algorithm for continuous optimization
Theoretical Computer Science
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Theoretical Computer Science
On the futility of blind search: An algorithmic view of “no free lunch”
Evolutionary Computation
Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
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
Adaptive Memetic Differential Evolution with Global and Local neighborhood-based mutation operators
Information Sciences: an International Journal
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The No-Free-Lunch theorem states that there does not exist a genuine general-purpose optimizer because all algorithms have the identical performance on average over all functions. However, such a result does not imply that search heuristics or optimization algorithms are futile if we are more cautious with the applicability of these methods and the search space. In this paper, within the No-Free-Lunch framework, we firstly introduce the discrete Lipschitz class by transferring the Lipschitz functions, i.e., functions with bounded slope, as a measure to fulfill the notion of continuity in discrete functions. We then investigate the properties of the discrete Lipschitz class, generalize an algorithm called subthreshold-seeker for optimization, and show that the generalized subthreshold-seeker outperforms random search on this class. Finally, we propose a tractable sampling-test scheme to empirically demonstrate the superiority of the generalized subthreshold-seeker under practical configurations. This study concludes that there exist algorithms outperforming random search on the discrete Lipschitz class in both theoretical and practical aspects and indicates that the effectiveness of search heuristics may not be universal but still general in some broad sense.