LightAdam: Towards a Fast and Accurate Adaptive Momentum Online Algorithm

Author(s):  
Yangfan Zhou ◽  
Kaizhu Huang ◽  
Cheng Cheng ◽  
Xuguang Wang ◽  
Xin Liu
Algorithmica ◽  
2021 ◽  
Author(s):  
Matthias Englert ◽  
David Mezlaf ◽  
Matthias Westermann

AbstractIn the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to change the assignment of up to k jobs at the end for some limited number k. For m identical machines, Albers and Hellwig (Algorithmica 79(2):598–623, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and $$\approx 1.4659$$ ≈ 1.4659 . They show that $$k = O(m)$$ k = O ( m ) is sufficient to achieve this bound and no $$k = o(n)$$ k = o ( n ) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a $$\delta = \varTheta (1)$$ δ = Θ ( 1 ) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than $$1.4659 + \delta $$ 1.4659 + δ with $$k = o(n)$$ k = o ( n ) . We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and $$\approx 1.7992$$ ≈ 1.7992 with $$k = O(m)$$ k = O ( m ) . We also show that $$k = \varOmega (m)$$ k = Ω ( m ) is necessary to achieve a competitive ratio below 2. Our algorithm is based on maintaining a specific imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.


2012 ◽  
Vol 241-244 ◽  
pp. 1602-1607
Author(s):  
Guang Hai Han ◽  
Xin Jun Ma

It usually need different ways to process different objects in the manufacturing, Therefore, firstly we need to distinguish the categories of objects to be processed, then the machine will know how to deal with the objects. In order to automatically recognize the category of the irregular object, this paper extracted the improved Hu's moments of each object as the feature by the way of processing images of the working platform that the irregular objects are putting on. This paper adopts the variable step BP neural network with adaptive momentum factor as the classifier. The experiment shows that this method can effectively distinguish different irregular objects, and during the training of the neural network, it has faster convergence speed and better approximation compared with the traditional BP neural network


1992 ◽  
Vol 28 (4) ◽  
pp. 377 ◽  
Author(s):  
G. Qiu ◽  
M.R. Varley ◽  
T.J. Terrell
Keyword(s):  

2019 ◽  
Vol 56 (2) ◽  
pp. 517-528 ◽  
Author(s):  
Juan D. Jurado ◽  
Clark C. McGehee

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