On the Optimization of Unimodal Functions with the (1 + 1) Evolutionary Algorithm
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Complexity Theory: Exploring the Limits of Efficient Algorithms
Complexity Theory: Exploring the Limits of Efficient Algorithms
Properties of Gray and Binary Representations
Evolutionary Computation
Algorithmic analysis of a basic evolutionary algorithm for continuous optimization
Theoretical Computer Science
Gray, binary and real valued encodings: quad search and locality proofs
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Evolutionary Computation
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We investigate the effects of precision on the efficiency of various local search algorithms on 1-D unimodal functions. We present a (1+1)-EA with adaptive step size which finds the optimum in O(log n) steps, where n is the number of points used. We then consider binary and Gray representations with single bit mutations. The standard binary method does not guarantee locating the optimum, whereas using Gray code does so in O((log n)2) steps. A (1+1)-EA with a fixed mutation probability distribution is then presented which also runs in O((log n)2). Moreover, a recent result shows that this is optimal (up to some constant scaling factor), in that there exist unimodal functions for which a lower bound of Ω((log n)2) holds regardless of the choice of mutation distribution. Finally, we show that it is not possible for a black box algorithms to efficiently optimise unimodal functions for two or more dimensions (in terms of the precision used).