(1+1) EA on Generalized Dynamic OneMax

Kötzing, Timo; Lissovoi, Andrei; Witt, Carsten

doi:10.1145/2725494.2725502

Cited by 51 publications

(37 citation statements)

References 24 publications

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“…The ability of a very simple EA without a population, the (1 + 1) EA, to track a target bitstring in a OneMax-like function is analysed in [3,18]. The analysis has recently been extended from bitstrings to larger alphabets [8]. The influence of magnitude and frequency of changes on the efficiency of the (1 + 1) EA in optimising a specifically designed function was investigated in [17], showing that some dynamic optimisation problems become easier with higher frequency of change.…”

Section: Introductionmentioning

confidence: 99%

Populations can be Essential in Dynamic Optimisation

Dang

Jansen

Lehre

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Real-world optimisation problems are often dynamic. Previously good solutions must be updated or replaced due to changes in objectives and constraints. It is often claimed that evolutionary algorithms are particularly suitable for dynamic optimisation because a large population can contain different solutions that may be useful in the future. However, rigorous, theoretical demonstrations for how populations in dynamic optimisation can be essential are sparse and restricted to special cases.This paper provides theoretical explanations of how populations can be essential in evolutionary dynamic optimisation. The ability of evolutionary algorithms to track optimal solutions is investigated by considering a Hamming ball of optimal points that moves randomly through the search space. It is shown that algorithms based on a single individual are likely to be unable to track the optimum while non-elitist population-based evolutionary algorithms can be able to do so with overwhelmingly high probability. It is shown that this holds for a range of the most commonly used selection mechanisms even without diversity enhancing mechanisms. Appropriate parameter settings to achieve this behaviour are derived for these selection mechanisms.

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Section: Introductionmentioning

confidence: 99%

Populations can be Essential in Dynamic Optimisation

Dang

Jansen

Lehre

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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“…The runtime analysis of dynamic evolutionary optimization is still in its very infancy, with only few results available (e. g. [9,29,31,32,38,47,48]).…”

Section: How Diversity Benefits Dynamic Optimisationmentioning

confidence: 99%

The Benefits of Population Diversity in Evolutionary Algorithms: A Survey of Rigorous Runtime Analyses

Sudholt

2019

Natural Computing Series

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Population diversity is crucial in evolutionary algorithms to enable global exploration and to avoid poor performance due to premature convergence. This book chapter reviews runtime analyses that have shown benefits of population diversity, either through explicit diversity mechanisms or through naturally emerging diversity. These works show that the benefits of diversity are manifold: diversity is important for global exploration and the ability to find several global optima. Diversity enhances crossover and enables crossover to be more effective than mutation. Diversity can be crucial in dynamic optimization, when the problem landscape changes over time. And, finally, it facilitates search for the whole Pareto front in evolutionary multiobjective optimization.The presented analyses rigorously quantify the performance of evolutionary algorithms in the light of population diversity, laying the foundation for a rigorous understanding of how search dynamics are affected by the presence or absence of population diversity and the introduction of diversity mechanisms.

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“…To the best of our knowledge Branke and Wang (2003) are the only ones to consider the scenario of change during a generation and provide a detailed analysis of a simple (1, 2) evolution strategy, an algorithm that also performs only 2 function evaluations per generation, for this case. Other articles, among them work by Jansen and Schellbach (2005), Kötzing et al (2015), Lissovoi and Witt (2013), Lissovoi and Witt (2014), Oliveto and Zarges (2013), and Oliveto and Zarges (2014), larger population size or offspring population size are taken into account but it is (sometimes implicitly) assumed that the fitness function does not change within a generation. This assumption becomes critical when the effects of the choice of the population size and of the offspring population size are studied.…”

Section: State Of the Art In The Theoretical Analysis Of Dynamic Optimentioning

confidence: 99%

Analysis of Randomised Search Heuristics for Dynamic Optimisation

Jansen

Zarges

2015

Evolutionary Computation

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This is the author accepted manuscript. The final version is available from Massachusetts Institute of Technology Press via http://dx.doi.org/doi:10.1162/EVCO_a_00164Dynamic optimisation is an area of application where randomised search heuristics like evolutionary algorithms and artificial immune systems are often successful. The theoretical foundation of this important topic suffers from a lack of a generally accepted analytical framework as well as a lack of widely accepted example problems. This article tackles both problems by discussing necessary conditions for useful and practically relevant theoretical analysis as well as introducing a concrete family of dynamic example problems that draws inspiration from a well-known static example problem and exhibits a bi-stable dynamic. After the stage has been set this way, the framework is made concrete by presenting the results of thorough theoretical and statistical analysis for mutation-based evolutionary algorithms and artificial immune systems.authorsversionPeer reviewe

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(1+1) EA on Generalized Dynamic OneMax

Cited by 51 publications

References 24 publications

Populations can be Essential in Dynamic Optimisation

Populations can be Essential in Dynamic Optimisation

The Benefits of Population Diversity in Evolutionary Algorithms: A Survey of Rigorous Runtime Analyses

Analysis of Randomised Search Heuristics for Dynamic Optimisation

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