scholarly journals Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yujian Zhou ◽  
Liang Bao ◽  
Yiqin Lin

Tensor subspace analysis (TSA) and discriminant TSA (DTSA) are two effective two-sided projection methods for dimensionality reduction and feature extraction of face image matrices. However, they have two serious drawbacks. Firstly, TSA and DTSA iteratively compute the left and right projection matrices. At each iteration, two generalized eigenvalue problems are required to solve, which makes them inapplicable for high dimensional image data. Secondly, the metric structure of the facial image space cannot be preserved since the left and right projection matrices are not usually orthonormal. In this paper, we propose the orthogonal TSA (OTSA) and orthogonal DTSA (ODTSA). In contrast to TSA and DTSA, two trace ratio optimization problems are required to be solved at each iteration. Thus, OTSA and ODTSA have much less computational cost than their nonorthogonal counterparts since the trace ratio optimization problem can be solved by the inexpensive Newton-Lanczos method. Experimental results show that the proposed methods achieve much higher recognition accuracy and have much lower training cost.




Author(s):  
Tarun Gangwar ◽  
Dominik Schillinger

AbstractWe present a concurrent material and structure optimization framework for multiphase hierarchical systems that relies on homogenization estimates based on continuum micromechanics to account for material behavior across many different length scales. We show that the analytical nature of these estimates enables material optimization via a series of inexpensive “discretization-free” constraint optimization problems whose computational cost is independent of the number of hierarchical scales involved. To illustrate the strength of this unique property, we define new benchmark tests with several material scales that for the first time become computationally feasible via our framework. We also outline its potential in engineering applications by reproducing self-optimizing mechanisms in the natural hierarchical system of bamboo culm tissue.



2014 ◽  
Vol 1 (4) ◽  
pp. 256-265 ◽  
Author(s):  
Hong Seok Park ◽  
Trung Thanh Nguyen

Abstract Energy efficiency is an essential consideration in sustainable manufacturing. This study presents the car fender-based injection molding process optimization that aims to resolve the trade-off between energy consumption and product quality at the same time in which process parameters are optimized variables. The process is specially optimized by applying response surface methodology and using nondominated sorting genetic algorithm II (NSGA II) in order to resolve multi-object optimization problems. To reduce computational cost and time in the problem-solving procedure, the combination of CAE-integration tools is employed. Based on the Pareto diagram, an appropriate solution is derived out to obtain optimal parameters. The optimization results show that the proposed approach can help effectively engineers in identifying optimal process parameters and achieving competitive advantages of energy consumption and product quality. In addition, the engineering analysis that can be employed to conduct holistic optimization of the injection molding process in order to increase energy efficiency and product quality was also mentioned in this paper.



Author(s):  
Weilin Nie ◽  
Cheng Wang

Abstract Online learning is a classical algorithm for optimization problems. Due to its low computational cost, it has been widely used in many aspects of machine learning and statistical learning. Its convergence performance depends heavily on the step size. In this paper, a two-stage step size is proposed for the unregularized online learning algorithm, based on reproducing Kernels. Theoretically, we prove that, such an algorithm can achieve a nearly min–max convergence rate, up to some logarithmic term, without any capacity condition.



Author(s):  
Álinson S. Xavier ◽  
Ricardo Fukasawa ◽  
Laurent Poirrier

When generating multirow intersection cuts for mixed-integer linear optimization problems, an important practical question is deciding which intersection cuts to use. Even when restricted to cuts that are facet defining for the corner relaxation, the number of potential candidates is still very large, especially for instances of large size. In this paper, we introduce a subset of intersection cuts based on the infinity norm that is very small, works for relaxations having arbitrary number of rows and, unlike many subclasses studied in the literature, takes into account the entire data from the simplex tableau. We describe an algorithm for generating these inequalities and run extensive computational experiments in order to evaluate their practical effectiveness in real-world instances. We conclude that this subset of inequalities yields, in terms of gap closure, around 50% of the benefits of using all valid inequalities for the corner relaxation simultaneously, but at a small fraction of the computational cost, and with a very small number of cuts. Summary of Contribution: Cutting planes are one of the most important techniques used by modern mixed-integer linear programming solvers when solving a variety of challenging operations research problems. The paper advances the state of the art on general-purpose multirow intersection cuts by proposing a practical and computationally friendly method to generate them.



Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Lin Bao ◽  
Xiaoyan Sun ◽  
Yang Chen ◽  
Guangyi Man ◽  
Hui Shao

A novel algorithm, called restricted Boltzmann machine-assisted estimation of distribution algorithm, is proposed for solving computationally expensive optimization problems with discrete variables. First, the individuals are evaluated using expensive fitness functions of the complex problems, and some dominant solutions are selected to construct the surrogate model. The restricted Boltzmann machine (RBM) is built and trained with the dominant solutions to implicitly extract the distributed representative information of the decision variables in the promising subset. The visible layer’s probability of the RBM is designed as the sampling probability model of the estimation of distribution algorithm (EDA) and is updated dynamically along with the update of the dominant subsets. Second, according to the energy function of the RBM, a fitness surrogate is developed to approximate the expensive individual fitness evaluations and participates in the evolutionary process to reduce the computational cost. Finally, model management is developed to train and update the RBM model with newly dominant solutions. A comparison of the proposed algorithm with several state-of-the-art surrogate-assisted evolutionary algorithms demonstrates that the proposed algorithm effectively and efficiently solves complex optimization problems with smaller computational cost.



Author(s):  
Jose Carrillo ◽  
Shi Jin ◽  
Lei Li ◽  
Yuhua Zhu

We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183{204, 2017], which is a gradient-free optimization method for general nonconvex functions. We rst replace the isotropic geometric Brownian motion by the component-wise one, thus removing the dimensionality dependence of the drift rate, making the method more competitive for high dimensional optimization problems. Secondly, we utilize the random mini-batch ideas to reduce the computational cost of calculating the weighted average which the individual particles tend to relax toward. For its mean- eld limit{a nonlinear Fokker-Planck equation{we prove, in both time continuous and semi-discrete settings, that the convergence of the method, which is exponential in time, is guaranteed with parameter constraints independent of the dimensionality. We also conduct numerical tests to high dimensional problems to check the success rate of the method.



Author(s):  
Tobias Leibner ◽  
Mario Ohlberger

In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic equations that conserve many of the fundamental physical properties of solutions. However, their practical use is limited by their high computational cost, as an optimization problem has to be solved for every cell in the space-time grid. In addition, implementation of numerical solvers for these models is hampered by the fact that the optimization problems are only well-defined if the moment vectors stay within the realizable set. For the same reason, further reducing these models by, e.g., reduced-basis methods is not a simple task. Our new method overcomes these disadvantages of classical approaches. The transformation is performed on the semi-discretized level which makes them applicable to a wide range of kinetic schemes and replaces the nonlinear optimization problems by inversion of the positive-definite Hessian matrix. As a result, the new scheme gets rid of the realizability-related problems. Moreover, a discrete entropy law can be enforced by modifying the time stepping scheme. Our numerical experiments demonstrate that our new method is often several times faster than the standard optimization-based scheme.



2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.



2021 ◽  
Author(s):  
Zhenzhen Wang ◽  
Jincong He ◽  
Shusei Tanaka ◽  
Xian-Huan Wen

Abstract Drill sequence optimization is a common challenge faced in the oil and gas industry and yet it cannot be solved efficiently by existing optimization methods due to its unique features and constraints. For many fields, the drill queue is currently designed manually based on engineering heuristics. In this paper, a heuristic priority function is combined with traditional optimizers to boost the optimization efficiency at a lower computational cost to speed up the decision-making process. The heuristic priority function is constructed to map the individual well properties such as well index and inter-well distance to the well priority values. As the name indicates, wells with higher priority values will be drilled earlier in the queue. The heuristic priority function is a comprehensive metric of inter-well communication & displacement efficiency. For example, injectors with fast support to producers or producers with a better chance to drain the unswept region tend to have high scores. It contains components that weigh the different properties of a well. These components are then optimized during the optimization process to generate the beneficial drill sequences. Embedded with reservoir engineering heuristics, the priority function helps the optimizer focus on exploring scenarios with promising outcomes. The proposed heuristic priority function, combined with the Genetic Algorithm (GA), has been tested through drill sequence optimization problems for the Brugge field and Olympus field. Optimizations that are directly performed on the drill sequence are employed as reference cases. Different continu- ous/categorical parameterization schemes and various forms of heuristic priority functions are also investigated. Our exploration reveals that the heuristic priority function including well type, constraints, well index, distance to existing wells, and adjacent oil in place yields the best outcome. The proposed approach was able to achieve a better optimization starting point (∼5-18% improvement due to more reasonable drill sequence rather than random guess), a faster convergence rate (results stabilized at 12 vs. 30 iterations), and a lower computational cost (150-250 vs. 1,300 runs to achieve the same NPV) over the reference methods. Similar performance improvement was also observed in another application to a North Sea type reservoir. This demonstrated the general applicability of the proposed method. The employment of the heuristic priority function improves the efficiency and reliability of drill sequence optimization compared to the traditional methods that directly optimize the sequence. It can be easily embedded in either commercial or research simulators as an independent module. In addition, it is also an automatic process that fits well with iterative optimization algorithms.



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