Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

Zheng, Weijie; Doerr, Benjamin

doi:10.1109/tevc.2024.3402996

Cited by 2 publications

(8 citation statements)

References 47 publications

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“…Noting that the maximal function value of f 1 (P t ) and f 2 (P t ) cannot decrease (there always is one individual witnessing this value and having infinite truthful crowding distance), we easily obtain that in expected O(n log n) iterations both extreme points 0 n and 1 n are reached for the first time, and also for all future iterations. This can be shown with a proof analogous to the one of [ZD24a,Lemma 15]. Therefore, we have the following main result on approximation ability and runtime of the NSGA-II-T. Theorem 14.…”

Section: Approximation Ability and Runtimementioning

confidence: 81%

“…Besides, together with this original crowding distance, the survival selection in the original NSGA-II also has possible difficulty (for some examples) for approximation [ZD24a]. Also in [ZD24a], they prove that the NSGA-II with the sequential survival selection, that is, updating the crowding distance after each removal, and the steady-state NSGA-II is proven to have a nice approximation for bi-objective OneMinMax. This paper will also consider such a fact for survival selection in the NSGA-II variant equipped with the designed crowding distance variant.…”

Section: Original Crowding Distance In the Nsga-iimentioning

confidence: 89%

“…In this section, we will consider the approximation ability of the NSGA-II when the population size is too small to cover the full Pareto front. We will prove that the NSGA-II-T has a slightly better approximation performance than the NSGA-II with sequential crowding distance and the steady-state NSGA-II for OneMinMax [ZD24a].…”

Section: Approximation Ability and Runtimementioning

confidence: 94%

“…where OneMax(z) = n ′ i=1 z i for z ∈ {0, 1} n ′ . Also mentioned before, the theoretical approximation ability of the NSGA-II with sequential survival selection is proven for the OneMinMax benchmark [ZD24a]. Here, we note OneMinMax from Definition 1 with k = 0, m = 2, and f 1 and f 2 exchanged, which will be used for the discussion of the runtime for good approximation ability of the proposed NSGA-II variant.…”

Section: Problems To Analyzementioning

confidence: 99%

“…such objective, the truthful one regards the smallest normalized "overall" distance between the current point and all points that are better than it in the considered objective. Noticing the possible difficulty of the original NSGA-II for approximation and the efficiency of the sequential survival selection for two objectives [ZD24a], we call the following variant of the NSGA-II, NSGA-II-T, that replaces the crowding distance calculation in the original NSGA-II by the truthful crowding distance, and updates the truthful crowding distance after each removal.…”

Section: Introductionmentioning

confidence: 99%

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Better approximation guarantees for the NSGA-II by using the current crowding distance

Zheng

Doerr

2022

Proceedings of the Genetic and Evolutionary Computation Conference

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A recent runtime analysis (Zheng, Liu, Doerr (2022)) has shown that a variant of the NSGA-II algorithm can efficiently compute the full Pareto front of the OneMinMax problem when the population size is by a constant factor larger than the Pareto front, but that this is not possible when the population size is only equal to the Pareto front size. In this work, we analyze how well the NSGA-II approximates the Pareto front when it cannot compute the whole front. We observe experimentally and by mathematical means that already when the population size is half the Pareto front size, relatively large gaps in the Pareto front remain. The reason for this phenomenon is that the NSGA-II in the selection stage computes the crowding distance once and then repeatedly removes individuals with smallest crowding distance without updating the crowding distance after each removal. We propose an efficient way to implement the NSGA-II using the momentary crowding distance. In our experiments, this algorithm approximates the Pareto front much better than the previous version. We also prove that the gaps in the Pareto front are at most a constant factor larger than the theoretical minimum.

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Section: Approximation Ability and Runtimementioning

confidence: 81%

Section: Original Crowding Distance In the Nsga-iimentioning

confidence: 89%

Section: Approximation Ability and Runtimementioning

confidence: 94%

Section: Problems To Analyzementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Better approximation guarantees for the NSGA-II by using the current crowding distance

Zheng

Doerr

2022

Proceedings of the Genetic and Evolutionary Computation Conference

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Exploring the Impact of Pre-Mechanical Activation of Nickel Powder on the Structure of Deposited Metal: A Deep Neural Network Perspective

Malashin,

Kobernik,

Pankratov

et al. 2024

Metals

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This study explores the potential application of the mechanical activation (MA) of nickel powder for incorporation into the composition of powder wire blends for the deposition of wear-resistant coatings. Nickel powder of PNE-1 grade was processed in a vibrational mill for various durations (4 to 16 min) with different combinations of grinding media. The influence of MA parameters on the bulk density and apparent particle size of nickel powder was investigated. The greatest effect was observed at the maximum processing time of 16 min, where electron microscopy revealed significant deformation and an increase in discoid particles, leading to enhanced energy accumulation. Nickel powder processed with a combination of 6 balls that are 20 mm in diameter and 8 balls that are 10 mm in diameter showed significant changes, though no major alteration in chemical composition was noted. XRMA indicated that the powder’s surface was partially covered with oxides, with a composition of 96.8–98.4% Ni and 0.8–1.7% O2. Additionally, the effect of nickel powders after the treatment on the structure of deposited metal was determined, demonstrating alterations in the morphology and a slight increase in hardness. Furthermore, a convolutional neural network (CNN)-based approach was proposed to discern fragments within images depicting surface microstructures, both with and without MA.

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Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

Cited by 2 publications

References 47 publications

Better approximation guarantees for the NSGA-II by using the current crowding distance

Better approximation guarantees for the NSGA-II by using the current crowding distance

Exploring the Impact of Pre-Mechanical Activation of Nickel Powder on the Structure of Deposited Metal: A Deep Neural Network Perspective

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