Simple max-min ant systems and the optimization of linear pseudo-boolean functions

Kötzing, Timo; Neumann, Franz‐Josef; Sudholt, Dirk; Wagner, Markus

doi:10.1145/1967654.1967673

Cited by 22 publications

(12 citation statements)

References 26 publications

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“…For the lower bounds presented in Table 1, we assume that the number of search points with the optimal function value f k is bounded from above by a polynomial in the problem size n. Note that the function LeadingOnes(x) := n i=1 i j=1 xi is n-unimodal. The fitness partitions that are used in the proof of Theorem 11 are similar to those employed in previous applications of the fitness-level technique [8,9,14]. Proof.…”

Section: Upper Boundsmentioning

confidence: 96%

Fitness-levels for non-elitist populations

Lehre

2011

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

100

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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.

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Section: Upper Boundsmentioning

confidence: 96%

Fitness-levels for non-elitist populations

Lehre

2011

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

100

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“…While a well-developed theory of evolutionary algorithms exists for many years, it was not before the year 2000 that convergence results were proven [11,12] and it took until 2007 for the first theoretical run-time analyses for ACO systems to appear [15,16,7,17]. These results clearly show that analyzing even very simple ACO algorithms is much more difficult than analyzing simple evolutionary algorithms, and even more recent papers like [24] seemingly found no simple analysis method.…”

Section: Ant Colony Optimizationmentioning

confidence: 99%

Ants easily solve stochastic shortest path problems

Doerr

Hota

Kötzing

2012

Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation

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The recent theoretical analysis (Horoba, Sudholt (GECCO 2010)) of an ant colony optimizer for the stochastic shortest path problem suggests that ant system experiences significant difficulties when the input data is prone to noise. In this work, we propose a slightly different ant optimizer to deal with noise.We prove that, under mild conditions, it finds the paths with shortest expected length efficiently, despite the fact that we do not have convergence in the classic sense. To prove our results, we introduce a stronger drift theorem that can also deal with the situation that the progress is faster when one is closer to the goal.

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“…We recall those arguments shortly as follows. The fbased partitions and upgrade probabilities are similar to the ones in [21,22,33]. For a Linear function f , without loss of generality we assume the weights c 1 ≥ c 2 ≥ · · · ≥ c n ≥ 0, then set m := n and choose the partition…”

Section: Tighter Upper Boundsmentioning

confidence: 99%

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

Dang

Lehre

2016

Algorithmica

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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.

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Simple max-min ant systems and the optimization of linear pseudo-boolean functions

Cited by 22 publications

References 26 publications

Fitness-levels for non-elitist populations

Fitness-levels for non-elitist populations

Ants easily solve stochastic shortest path problems

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

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