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Algorithmica

, Volume 75, Issue 3, pp 428–461 | Cite as

Runtime Analysis of Non-elitist Populations: From Classical Optimisation to Partial Information

  • Duc-Cuong Dang
  • Per Kristian Lehre
Article

Abstract

Although widely applied in optimisation, relatively little has been proven rigorously about the role and behaviour of populations in randomised search processes. This paper presents a new method to prove upper bounds on the expected optimisation time of population-based randomised search heuristics that use non-elitist selection mechanisms and unary variation operators. Our results follow from a detailed drift analysis of the population dynamics in these heuristics. This analysis shows that the optimisation time depends on the relationship between the strength of the selective pressure and the degree of variation introduced by the variation operator. Given limited variation, a surprisingly weak selective pressure suffices to optimise many functions in expected polynomial time. We derive upper bounds on the expected optimisation time of non-elitist evolutionary algorithms (EA) using various selection mechanisms, including fitness proportionate selection. We show that EAs using fitness proportionate selection can optimise standard benchmark functions in expected polynomial time given a sufficiently low mutation rate. As a second contribution, we consider an optimisation scenario with partial information, where fitness values of solutions are only partially available. We prove that non-elitist EAs under a set of specific conditions can optimise benchmark functions in expected polynomial time, even when vanishingly little information about the fitness values of individual solutions or populations is available. To our knowledge, this is the first runtime analysis of randomised search heuristics under partial information.

Keywords

Runtime Drift analysis Evolutionary algorithms  Non-elitism Fitness-levels Partial evaluation 

Notes

Acknowledgments

The authors are grateful to the anonymous reviewers of the conferences and of the journal for their corrections and constructive comments that improve the quality and the presentation of the paper. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 618091 (SAGE) and from the British Engineering and Physical Science Research Council (EPSRC) Grant No. EP/F033214/1 (LANCS).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of NottinghamNottinghamUK

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