Rigorous analyses of fitness-proportional selection for optimizing linear functions

Happ, Edda; Johannsen, Daniel; Klein, Christian; Neumann, Franz‐Josef

doi:10.1145/1389095.1389277

Cited by 57 publications

(60 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is well-known that fitness proportionate selection without scaling (ν = 1) is inefficient, i. e., it requires exponential optimisation time on simple functions (see [14,24,30]). However, these previous studies often concern the standard mutation rate 1/n, thus it may be possible to optimise OneMax and LeadingOnes in expected polynomial time without scaling but with a different mutation rate.…”

Section: Polynomial Runtime With Standard Fitness Proportionate Selecmentioning

confidence: 99%

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

Dang

Lehre

2016

Algorithmica

View full text Add to dashboard Cite

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 nonelitist 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.

show abstract

Section: Polynomial Runtime With Standard Fitness Proportionate Selecmentioning

confidence: 99%

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

Dang

Lehre

2016

Algorithmica

View full text Add to dashboard Cite

show abstract

“…Happ et al (2008) performed the first runtime analysis of fitness proportional selection (f.p.s.) by considering only one individual and bitwise mutation.…”

Section: Algorithm and Proof Strategymentioning

confidence: 99%

Improved time complexity analysis of the Simple Genetic Algorithm

Oliveto

Witt

2015

Theoretical Computer Science

117

View full text Add to dashboard Cite

A runtime analysis of the Simple Genetic Algorithm (SGA) for the OneMax problem has recently been presented proving that the algorithm with population size µ ≤ n 1/8−ε requires exponential time with overwhelming probability. This paper presents an improved analysis which overcomes some limitations of the previous one. Firstly, the new result holds for population sizes up to µ ≤ n 1/4−ε which is an improvement up to a power of 2 larger. Secondly, we present a technique to bound the diversity of the population that does not require a bound on its bandwidth. Apart from allowing a stronger result, we believe this is a major improvement towards the reusability of the techniques in future systematic analyses of GAs. Finally, we consider the more natural SGA using selection with replacement rather than without replacement although the results hold for both algorithmic versions. Experiments are presented to explore the limits of the new and previous mathematical techniques.

show abstract

“…Happ et al considered variants of the RLS and the (1+1) EA where the plus-selection mechanism is replaced with fitness proportionate selection [5]. They found that changing the algorithms this way makes them highly inefficient on linear functions.…”

Section: Fitness Proportionate Selectionmentioning

confidence: 99%

Fitness-levels for non-elitist populations

Lehre

2011

Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation

100

View full text Add to dashboard Cite

This paper introduces an easy to use technique for deriving upper bounds on the expected runtime of non-elitist population-based evolutionary algorithms (EAs). Applications of the technique show how the efficiency of EAs is critically dependant on having a sufficiently strong selective pressure. Parameter settings that ensure sufficient selective pressure on commonly considered benchmark functions are derived for the most popular selection mechanisms. Together with a recent technique for deriving lower bounds, this paper contributes to a much-needed analytical tool-box for the analysis of evolutionary algorithms with populations.

show abstract

Rigorous analyses of fitness-proportional selection for optimizing linear functions

Cited by 57 publications

References 11 publications

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

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

Improved time complexity analysis of the Simple Genetic Algorithm

Fitness-levels for non-elitist populations

Contact Info

Product

Resources

About