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Runtime analysis of non-elitist populations: from classical optimisation to partial information

Dang, Duc-Cuong; Lehre, Per Kristian


Duc-Cuong Dang

Per Kristian Lehre


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.


Dang, D., & Lehre, P. K. (2016). Runtime analysis of non-elitist populations: from classical optimisation to partial information. Algorithmica, 75(3),

Journal Article Type Article
Acceptance Date Dec 18, 2015
Publication Date Feb 9, 2016
Deposit Date Dec 21, 2015
Publicly Available Date Feb 9, 2016
Journal Algorithmica
Print ISSN 0178-4617
Electronic ISSN 1432-0541
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 75
Issue 3
Keywords Runtime, Drift analysis, Evolutionary Algorithms, Non-elitism, Fitness-levels, Partial evaluation
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