An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.

SPEEDING-UP RE-SAMPLED ALGORITHM IN RAY CASTING VOLUME RENDERING OF MEDICAL IMAGES

Ray casting algorithm can obtain a better quality image in volume rendering, however, it exists some problems, such as powerful computing capacity and slow rendering speed. How to improve the re-sampled speed is a key to speed up the ray casting algorithm. An algorithm is introduced to reduce matrix computation by matrix transformation characteristics of re-sampling points in a two coordinate system. The projection of 3-D datasets on image plane is adopted to reduce the number of rays. Utilizing boundary box technique avoids the sampling in empty voxel. By extending the Bresenham algorithm to three dimensions, each re-sampling point is calculated. Experimental results show that a two to three-fold improvement in rendering speed using the optimized algorithm, and the similar image quality to traditional algorithm can be achieved. The optimized algorithm can produce the required quality images, thus reducing the total operations and speeding up the volume rendering.

Bi-extrapolated subgradient projection algorithm for solving multiple-sets split feasibility problem

This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.

A new accelerating algorithm for multi-agent reinforcement learning

In multi-agent systems, joint-action must be employed to achieve cooperation because the evaluation of the behavior of an agent often depends on the other agents’ behaviors. However, joint-action reinforcement learning algorithms suffer the slow convergence rate because of the enormous learning space produced by joint-action. In this article, a prediction-based reinforcement learning algorithm is presented for multi-agent cooperation tasks, which demands all agents to learn predicting the probabilities of actions that other agents may execute. A multi-robot cooperation experiment is run to test the efficacy of the new algorithm, and the experiment results show that the new algorithm can achieve the cooperation policy much faster than the primitive reinforcement learning algorithm.

APPLICATION OF INTEGER CODING ACCELERATING GENETIC ALGORITHM IN RECTANGULAR CUTTING STOCK PROBLEM

An improved genetic algorithm and its application to resolve cutting stock problem arc presented. It is common to apply simple genetic algorithm （SGA） to cutting stock problem, but the huge amount of computing of SGA is a serious problem in practical application. Accelerating genetic algorithm （AGA） based on integer coding and AGA＇s detailed steps are developed to reduce the amount of computation, and a new kind of rectangular parts blank layout algorithm is designed for rectangular cutting stock problem. SGA is adopted to produce individuals within given evolution process, and the variation interval of these individuals is taken as initial domain of the next optimization process, thus shrinks searching range intensively and accelerates the evaluation process of SGA. To enhance the diversity of population and to avoid the algorithm stagnates at local optimization result, fixed number of individuals are produced randomly and replace the same number of parents in every evaluation process. According to the computational experiment, it is observed that this improved GA converges much sooner than SGA, and is able to get the balance of good result and high efficiency in the process of optimization for rectangular cutting stock problem.

The application of projection pursuit classification in the process of strategy selection and evaluation based on the real coded accelerating genetic algorithm

During the process of enterprises＇ strategy evaluation and selection, there are many evaluating indicators, and among them there are some potential correlations and conflicts. Thus it poses the problems to the decision-makers how to conduct correct evaluation on a business and how to make strategy adjustment and selection according to the evaluation. Based on the qualitative and quantitative method, the paper introduces the Projection Pursuit Classification （PPC） model based on the Real-coded Accelerating Genetic Algorithm （RAGA） into the process of enterprises＇ strategy evaluation and selection. The characteristic of PPC model is that it ultimately overcomes the influence of the proportion of subjectivity and avoids precocious convergence, thus providing a new objective method for strategy evaluation and selection by pursuing the most objective strategy evaluation to make the relatively sensible strategy portfolio and action.

Research on three-step accelerated gradient algorithm in deep learning

Gradient descent(GD)algorithm is the widely used optimisation method in training machine learning and deep learning models.In this paper,based on GD,Polyak’s momentum(PM),and Nesterov accelerated gradient(NAG),we give the convergence of the algorithms from an ini-tial value to the optimal value of an objective function in simple quadratic form.Based on the convergence property of the quadratic function,two sister sequences of NAG’s iteration and par-allel tangent methods in neural networks,the three-step accelerated gradient(TAG)algorithm is proposed,which has three sequences other than two sister sequences.To illustrate the perfor-mance of this algorithm,we compare the proposed algorithm with the three other algorithms in quadratic function,high-dimensional quadratic functions,and nonquadratic function.Then we consider to combine the TAG algorithm to the backpropagation algorithm and the stochastic gradient descent algorithm in deep learning.For conveniently facilitate the proposed algorithms,we rewite the R package‘neuralnet’and extend it to‘supneuralnet’.All kinds of deep learning algorithms in this paper are included in‘supneuralnet’package.Finally,we show our algorithms are superior to other algorithms in four case studies.

Dynamic finite element model updating of prestressed concrete continuous box-girder bridge

The dynamic finite element model （FEM） of a prestressed concrete continuous box-girder bridge, called the Tongyang Canal Bridge, is built and updated based on the results of ambient vibration testing （AVT） using a real-coded accelerating genetic algorithm （RAGA）. The objective functions are defined based on natural frequency and modal assurance criterion （MAC） metrics to evaluate the updated FEM. Two objective functions are defined to fully account for the relative errors and standard deviations of the natural frequencies and MAC between the AVT results and the updated FEM predictions. The dynamically updated FEM of the bridge can better represent its structural dynamics and serve as a baseline in long-term health monitoring, condition assessment and damage identification over the service life of the bridge .

Distributed accelerated optimization algorithms:Insights from an ODE

In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over undirected connected graphs. Several distributed accelerated algorithms have been proposed for solving such a problem in the existing literature. In this paper, we provide insights for understanding these existing distributed algorithms from an ordinary differential equation(ODE) point of view. More specifically, we first derive an equivalent second-order ODE, which is the exact limit of these existing algorithms by taking the small step-size. Moreover, focusing on the quadratic objective functions, we show that the solution of the resulting ODE exponentially converges to the unique global optimal solution. The theoretical results are validated and illustrated by numerical simulations.

Research on cubic polynomial acceleration and deceleration control model for high speed NC machining

To satisfy the need of high speed NC (numerical control) machining, an acceleration and deceleration (acc/dec) control model is proposed, and the speed curve is also constructed by the cubic polynomial. The proposed control model provides continuity of acceleration, which avoids the intense vibration in high speed NC machining. Based on the discrete characteristic of the data sampling interpolation, the acc/dec control discrete mathematical model is also set up and the discrete expression of the theoretical deceleration length is obtained furthermore. Aiming at the question of hardly predetermining the deceleration point in acc/dec control before interpolation, the adaptive acc/dec control algorithm is deduced from the expressions of the theoretical deceleration length. The experimental result proves that the acc/dec control model has the characteristic of easy implementation, stable movement and low impact. The model has been applied in multi-axes high speed micro fabrication machining successfully.

On grey relation projection model based on projection pursuit

Multidimensional grey relation projection value can be synthesized as one-dimensional projection value by using projection pursuit model. The larger the projection value is,the better the model. Thus,according to the projection value,the best one can be chosen from the model aggregation. Because projection pursuit modeling based on accelerating genetic algorithm can simplify the implementation procedure of the projection pursuit technique and overcome its complex calculation as well as the difficulty in implementing its program,a new method can be obtained for choosing the best grey relation projection model based on the projection pursuit technique.

Optimization Design of Multi-hole and Varied Diameter Pipe Based on RAGA

Combining real accelerating genetic algorithm(RAGA) with the optimization design of multi-hole and varied diameter pipe, the authors solved the problem of optimizing multi-dimensional parameters at the same time. In which the advanced convergence and easily to run into partial optimization were avoid. Applied the RAGA to solving the problem in the optimization design of fixed piping sprinkler irrigation system. The optimized parameters, such as diameters and the length of pipe were calculated and the result was reasonable, which provides as a reference to readers who work at related research.

Alleviating limit cycling in training GANs with an optimization technique

In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCAA).Specifically,we first derive the upper and lower complexity bounds of PCAA for a general bilinear game,with the last-iterate convergence rate notably improving upon previous results.Then,we combine PCAA with the adaptive moment estimation algorithm(Adam)to propose PCAA-Adam,for practical training of GANs to enhance their generalization capability.Finally,we validate the effectiveness of the proposed algorithm through experiments conducted on bilinear games,multivariate Gaussian distributions,and the CelebA dataset,respectively.

Coupled modified Kd V equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property

In this paper, we show that the coupled modified Kd V equations possess rich mathematical structures and some remarkable properties. The connections between the system and skew orthogonal polynomials,convergence acceleration algorithms and Laurent property are discussed in detail.

A Numerical Algorithm for Arbitrary Real-Order Hankel Transform

The Hankel transform is widely used to solve various engineering and physics problems,such as the representation of electromagnetic field components in the medium,the representation of dynamic stress intensity factors,vibration of axisymmetric infinite membrane and displacement intensity factors which all involve this type of integration.However,traditional numerical integration algorithms cannot be used due to the high oscillation characteristics of the Bessel function,so it is particularly important to propose a high precision and efficient numerical algorithm for calculating the integral of high oscillation.In this paper,the improved Gaver-Stehfest(G-S)inverse Laplace transform method for arbitrary real-order Bessel function integration is presented by using the asymptotic characteristics of the Bessel function and the accumulation of integration,and the optimized G-S coefficients are given.The effectiveness of the algorithm is verified by numerical examples.Compared with the linear transformation accelerated convergence algorithm,it shows that the G-S inverse Laplace transform method is suitable for arbitrary real order Hankel transform,and the time consumption is relatively stable and short,which provides a reliable calculation method for the study of electromagnetic mechanics,wave propagation,and fracture dynamics.

A Data-driven Variable Reduction Approach for Transmission-constrained Unit Commitment of Large-scale Systems

This paper presents a data-driven variable reduction approach to accelerate the computation of large-scale transmission-constrained unit commitment(TCUC).Lagrangian relaxation(LR)and mixed-integer linear programming(MILP)are popular approaches to solving TCUC.However,with many binary unit commitment variables,LR suffers from slow convergence and MILP presents heavy computation burden.The proposed data-driven variable reduction approach consists of offline and online calculations to accelerate computational performance of the MILP-based large-scale TCUC problems.A database including multiple nodal net load intervals and the corresponding TCUC solutions is first built offline via the data-driven and all-scenario-feasible(ASF)approaches,which is then leveraged to efficiently solve new TCUC instances online.On/off statuses of considerable units can be fixed in the online calculation according to the database,which would reduce the computation burden while guaranteeing good solution quality for new TCUC instances.A feasibility proposition is proposed to promptly check the feasibility of the new TCUC instances with fixed binary variables,which can be used to dynamically tune parameters of binary variable fixing strategies and guarantee the existence of feasible UC solutions even when system structure changes.Numerical tests illustrate the efficiency of the proposed approach.

An Accelerated Method for Simulating Population Dynamics

We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations.To benchmark accuracy and performance,we compare simulation results with those generated from a previously validated population dynamics algorithm.The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions.Considering the increasing complexity of cell population models,the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient,coarse-grained exploration of parameter space.

Estimation of crowd density from UAVs images based on corner detection procedures and clustering analysis

With rapid developments in platforms and sensors technology in terms of digital cameras and video recordings,crowd monitoring has taken a considerable attentions in many disciplines such as psychology,sociology,engineering,and computer vision.This is due to the fact that,monitoring of the crowd is necessary to enhance safety and controllable movements to minimize the risk particularly in highly crowded incidents(e.g.sports).One of the platforms that have been extensively employed in crowd monitoring is unmanned aerial vehicles(UAVs),because UAVs have the capability to acquiring fast,low costs,high-resolution and real-time images over crowd areas.In addition,geo-referenced images can also be provided through integration of on-board positioning sensors(e.g.GPS/IMU)with vision sensors(digital cameras and laser scanner).In this paper,a new testing procedure based on feature from accelerated segment test(FAST)algorithms is introduced to detect the crowd features from UAV images taken from different camera orientations and positions.The proposed test started with converting a circle of 16 pixels surrounding the center pixel into a vector and sorting it in ascending/descending order.A single pixel which takes the ranking number 9(for FAST-9)or 12(for FAST-12)was then compared with the center pixel.Accuracy assessment in terms of completeness and correctness was used to assess the performance of the new testing procedure before and after filtering the crowd features.The results show that the proposed algorithms are able to extract crowd features from different UAV images.Overall,the values of Completeness range from 55 to 70%whereas the range of correctness values was 91 to 94%.