Speeding up evolutionary multi-objective optimisation through diversity-based parent selection

Osuna, Edgar Covantes; Gao, Wanru; Neumann, Franz‐Josef; Sudholt, Dirk

doi:10.1145/3071178.3080294

Cited by 8 publications

(8 citation statements)

References 13 publications

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“…The results for OneMinMax also hold for Global SEMO (GSEMO) which uses standard bit mutations where every bit in the mutation step is flipped with probability 1/n. This article extends its conference version [6] in various ways. In [6] for LOTZ only SEMO was analysed as the analysis of GSEMO was too challenging.…”

Section: Introductionmentioning

confidence: 91%

“…This article extends its conference version [6] in various ways. In [6] for LOTZ only SEMO was analysed as the analysis of GSEMO was too challenging. Here we address this challenge by providing investigations for a variant of GSEMO on LOTZ.…”

Section: Introductionmentioning

confidence: 91%

“…It seems that the selection mechanism performs better compared with the other selection approaches. Nevertheless, as an observant reviewer for [6] pointed out, it is possible to find populations where the probability of selecting a good parent is 0, and the analytical framework used in Sections 5 and 6 breaks down.…”

Section: Nmuar Is Fast But Brittlementioning

confidence: 99%

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Design and analysis of diversity-based parent selection schemes for speeding up evolutionary multi-objective optimisation

Osuna

Gao

Neumann

et al. 2020

Theoretical Computer Science

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Parent selection in evolutionary algorithms for multi-objective optimisation is usually performed by dominance mechanisms or indicator functions that prefer non-dominated points. We propose to refine the parent selection on evolutionary multi-objective optimisation with diversity-based metrics. The aim is to focus on individuals with a high diversity contribution located in poorly explored areas of the search space, so the chances of creating new non-dominated individuals are better than in highly populated areas. We show by means of rigorous runtime analysis that the use of diversity-based parent selection mechanisms in the Simple Evolutionary Multi-objective Optimiser (SEMO) and Global SEMO for the well known bi-objective functions OneMinMax and LOTZ can significantly improve their performance. Our theoretical results are accompanied by experimental studies that show a correspondence between theory and empirical results and motivate further theoretical investigations in terms of stagnation. We show that stagnation might occur when favouring individuals with a high diversity contribution in the parent selection step and provide a discussion on which scheme to use for more complex problems based on our theoretical and experimental results.

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 91%

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Design and analysis of diversity-based parent selection schemes for speeding up evolutionary multi-objective optimisation

Osuna

Gao

Neumann

et al. 2020

Theoretical Computer Science

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“…All results surveyed so far use diversity mechanisms in the environmental selection, i. e. to decide which search points are allowed to survive to the next generation. Here we present recent work by Covantes Osuna et al [5], who suggested to use diversity mechanisms in the parent selection in the context of evolutionary multiobjective optimization.…”

Section: Diversity-based Parent Selectionmentioning

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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“…Problems with similar features are found in combinatorial optimisation, for instances as worst-case examples for finding shortest paths [50]. Multiobjective variants like LOTZ are popular example functions in the theory of evolutionary multiobjective optimisation [7,21,28,34,41].…”

Section: Introductionmentioning

confidence: 99%

Analysing the Robustness of Evolutionary Algorithms to Noise: Refined Runtime Bounds and an Example Where Noise is Beneficial

Sudholt

2020

Algorithmica

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We analyse the performance of well-known evolutionary algorithms (1+1) EA and (1+λ) EA in the prior noise model, where in each fitness evaluation the search point is altered before evaluation with probability p. We present refined results for the expected optimisation time of the (1+1) EA and the (1+λ) EA on the function LeadingOnes, where bits have to be optimised in sequence. Previous work showed that the (1+1) EA on LeadingOnes runs in polynomial expected time if p = O((log n)/n 2 ) and needs superpolynomial expected time if p = ω((log n)/n), leaving a huge gap for which no results were known. We close this gap by showing that the expected optimisation time is Θ(n 2 ) · exp(Θ(min{pn 2 , n})) for all p ≤ 1/2, allowing for the first time to locate the threshold between polynomial and superpolynomial expected times at p = Θ((log n)/n 2 ). Hence the (1+1) EA on LeadingOnes is much more sensitive to noise than previously thought. We also show that offspring populations of size λ ≥ 3.42 log n can effectively deal with much higher noise than known before.Finally, we present an example of a rugged landscape where prior noise can help to escape from local optima by blurring the landscape and allowing a hill climber to see the underlying gradient. We prove that in this particular setting noise can have a highly beneficial effect on performance.

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Speeding up evolutionary multi-objective optimisation through diversity-based parent selection

Cited by 8 publications

References 13 publications

Design and analysis of diversity-based parent selection schemes for speeding up evolutionary multi-objective optimisation

Design and analysis of diversity-based parent selection schemes for speeding up evolutionary multi-objective optimisation

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

Analysing the Robustness of Evolutionary Algorithms to Noise: Refined Runtime Bounds and an Example Where Noise is Beneficial

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