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Analyses of Evolution Strategy Behaviour

Evolution strategies are nature inspired algorithms for black box optimisation. Mathematical analyses of their behaviour yield scaling laws that aid practitioners in the choice of strategy variants, the setting of their parameters, and the design of better algorithms. Adaptive variants can be compared with each other as well as with hypothetical optimal behaviour. An ongoing challenge is to extend the boundaries of the analyses to include both strategies and test function classes of increasing complexity. Our recent work considers a range of step size adaptation mechanisms as well as several convex-quadratic and ridge functions and noisy, time varying, and constrained problems.

Publications

D. V. Arnold, H.-G. Beyer, and A. Melkozerov
On the behaviour of weighted multi-recombination evolution strategies optimising noisy cigar functions
Genetic and Evolutionary Computation Conference, Montreal, 2009.

D. V. Arnold and D. Brauer
On the behaviour of the (1+1)-ES for a simple constrained problem
Parallel Problem Solving from Nature — PPSN X, Dortmund, 2008.

D. V. Arnold and A. MacLeod
Step length adaptation on ridge functions
Evolutionary Computation, 16(2):151-184, 2008.

D. V. Arnold
On the use of evolution strategies for optimising certain positive definite quadratic forms
Genetic and Evolutionary Computation Conference, London, 2007.

D. V. Arnold and H.-G. Beyer
Optimum tracking with evolution strategies
Evolutionary Computation, 14(3):291-308, 2006.

D. V. Arnold and H.-G. Beyer
A general noise model and its effects on evolution strategy performance
IEEE Transactions on Evolutionary Computation, 10(4):380-391, 2006.

D. V. Arnold and H.-G. Beyer
Performance analysis of evolutionary optimization with cumulative step length adaptation
IEEE Transactions on Automatic Control, 49(4):617-622, 2004.

D. V. Arnold
Noisy Optimization with Evolution Strategies
Kluwer Academic Publishers, 2002.

Support

This research is supported through grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Foundation for Innovation (CFI).