Linear Optimization Algorithm Research Articles

A wide neighborhood interior-point algorithm based on the trigonometric kernel function

In this paper, a wide neighborhood path-following interior point algorithm for linear optimization (LO) is proposed that uses a trigonometric kernel function to get search directions. The method treats the Newton direction as the sum of two other directions, according to the negative and positive parts of the right-hand-side based on the kernel function. By choosing different and appropriate step sizes for these two directions, the iterates stop in the Ai–Zhang’s wide neighborhood. By an elegant analysis, we show that the method enjoys the low iteration bound of $${\mathcal {O}}(\sqrt{n}\log \frac{(x^0)^Ts^0}{\varepsilon })$$ , where n is the dimension of the problem and $$(x^0, s^0)$$ the initial interior point with $$\varepsilon $$ the required precision. In our knowledge, this result is the first instance of a wide neighborhood interior point method for LO which involving the trigonometric kernel function.

MILP-PSO Combined Optimization Algorithm for an Islanded Microgrid Scheduling with Detailed Battery ESS Efficiency Model and Policy Considerations

This paper presents the optimal scheduling of a diesel generator and an energy storage system (ESS) while using a detailed battery ESS energy efficiency model. Optimal scheduling has been hampered to date by the nonlinearity and complexity of the battery ESS. This is due to the battery ESS efficiency being a multiplication of inverter and battery efficiency and the dependency of an inverter and any associated battery efficiencies on load and charging and discharging. We propose a combined mixed-integer linear programming and particle swarm optimization (MILP-PSO) algorithm as a novel means of addressing these considerations. In the algorithm, MILP is used to find some initial points of PSO, so that it can find better solution. Moreover, some additional algorithms are added into PSO to modify and, hence, improve its ability of dealing with constraint conditions and the local minimum problem. The simulation results show that the proposed algorithm performs better than MILP and PSO alone for the practical microgrid. The results also indicated that simplification or neglect of ESS efficiency when applying MILP to scheduling may cause a constraint violation.

A wide neighborhood predictor-infeasible corrector interior-point algorithm for linear optimization

In this paper, we propose a theoretical framework of a predictor-corrector interior-point method for linear optimization based on the one-norm wide neighborhood of the central path, focusing on infeasible corrector steps. Here, we call the predictor-infeasible corrector algorithm. At each iteration, the proposed algorithm computes an infeasible corrector step in addition to the Ai-Zhang search directions and considers the Newton direction as a linear combination of these directions. We represent the complexity analysis of the algorithm and conclude that its iteration bound is $${\mathcal {O}}(n\log \varepsilon ^{-1})$$ . To our knowledge, this is the best complexity result up to now for infeasible interior-point methods based on these kinds of search directions. The complexity bound obtained here is the same as small neighborhood infeasible interior point algorithms.

Estimation of Petrophysical Parameters from Seismic Inversion by Combining Particle Swarm Optimization and Multilayer Linear Calculator

In heterogeneous reservoir rocks, the accurate characterization of lithology and reservoir parameters is significant to minimize drilling risks and to improve oil and gas recoveries. In this work, a joint inversion strategy based on multilayer linear calculator (MLC) and particle swarm optimization (PSO) algorithm was applied to predict the spatial variations of key petrophysical (porosity, permeability, and saturation) and geomechanical parameters (Young’s modulus, Poisson’s ratio, and brittleness) for inter-well regions. In this method, acoustic impedance (AI) models are computed from post-stack seismic amplitude data by applying the proposed strategy (MLC + PSO) and back propagation neural network-based seismic inversion in the time domain with measured log density and velocity as constraints. The obtained results reveal that the proposed strategy, which combines MLC and PSO, leads to the optimization of lateral and vertical facies heterogeneities and accurate prediction of reservoir parameter distribution, i.e., the low AI is related to sand facies and corresponds to high porosity, permeability, saturation, and mid-range of Young’s modulus. The time slice maps of inverted porosity and permeability at various time intervals indicate a reasonable calibration with the measured core and well log data. The methodology proposed in this study may be considered useful for other basins in Pakistan with similar geological settings and anywhere in the world for reservoir characterization, particularly for intercalated shale and variable depositional environments.

A new approach to non-linear multivariate calibration in laser-induced breakdown spectroscopy analysis of silicate rocks

In this paper a new approach to quantitative Laser-Induced Breakdown Spectroscopy (LIBS) analysis of silicate rocks is presented. The method is adapted from the Franzini and Leoni algorithm, a method widely used in X-Ray Fluorescence analysis for correcting the matrix effects in the determination of the composition of geological materials. To illustrate the features of the new method proposed, nine elements were quantified in 19 geological standards by building linear univariate calibration curves, linear multivariate calibration surfaces (PLS) and using Artificial Neural Networks. The results were then compared with the predictions derived from the application of the algorithm here proposed. It was found that the Franzini and Leoni approach gives results much more precise than linear uni- and multivariate approaches, and comparable with the ones derived from the application of Artificial Neural Networks. A definite advantage of the proposed approach is the possibility of building multivariate non-linear calibration surfaces using linear optimization algorithms, a feature which makes the application of the Franzini and Leoni method in LIBS analysis much simpler (and controllable) with respect to the algorithms based on Artificial Neural Networks.

AN INPUT LIMITED REPETITIVE LEARNING CONTROL OF FLEXIBLE-BASE TWO-FLEXIBLE-LINK AND TWO-FLEXIBLE-JOINT SPACE ROBOT WITH INTEGRATION OF MOTION AND VIBRATION

In order to analyze the dynamic simulation and movement control of space robot under the influence of full flexible of base, links and joints, as well as the active vibration suppression of base, links and joints, an input limited repetitive learning controller with integration of motion and vibration is proposed. The design of the algorithm is not based on the system model information. The flexible base and the flexible joints are regarded as linear spring and torsion springs. The flexible links are analyzed by the Eulerian Bernoulli model, and the dynamic equation is established by the Lagrange equation and the assumed mode method. Based on the singular perturbation theory, the model is decomposed into a slow subsystem including the system rigid variables and the link flexible vibration, and a fast subsystem including the base and joint flexible vibration. The corresponding sub controllers are designed for the slow and fast subsystems to form the general controller with joint flexible compensation. For the slow subsystem, an input limited repetitive learning controller is proposed, which is composed of hyperbolic tangent function, saturation function and repetitive learning term. The hyperbolic tangent function and saturation function realize the requirement of limited input torque. The repetitive learning term compensates the periodic system error to complete the gradual stable tracking of the expected trajectory of base attitude and joint. However, in order to suppress the flexible vibration of the links of the slow subsystem, a hybrid trajectory reflecting the flexible vibration of the links and the rigid motion of the system is constructed by using virtual force conception, and an input limited repetitive learning controller on virtual force conception is proposed to ensure the accurate tracking of the trajectory of the base and joint, while actively suppressing the flexible vibration of the links. For the fast subsystem, the linear quadratic optimal control algorithm is used to suppress the flexible vibration of the base and joints. The simulation results show that the controller is suitable for general flexible nonlinear system, meets the requirements of limited input torque, realizes high-precision tracking of periodic signal, effectively suppresses the flexible vibration of base, links and joints, and verifies the feasibility of the algorithm.

Volumetric Barrier Cutting Plane Algorithms for Stochastic Linear Semi-Infinite Optimization

In this paper, we study the two-stage stochastic linear semi-infinite programming with recourse to handle uncertainty in data defining (deterministic) linear semi-infinite programming. We develop and analyze volumetric barrier cutting plane interior point methods for solving this class of optimization problems, and present a complexity analysis of the proposed algorithms. We establish our convergence analysis by showing that the volumetric barrier associated with the recourse function of stochastic linear semi-infinite programs is a strongly self-concordant barrier and forms a self-concordant family on the first-stage solutions. The dominant terms in the complexity expressions obtained in this paper are given in terms of the problem dimension and the number of realizations. The novelty of our algorithms lies in their ability to kill the effect of the radii of the largest Euclidean balls contained in the feasibility sets on the dominant complexity terms.

The Next 700 Accelerated Layers

Deep learning frameworks automate the deployment, distribution, synchronization, memory allocation, and hardware acceleration of models represented as graphs of computational operators. These operators wrap high-performance libraries such as cuDNN or NNPACK. When the computation does not match any predefined library call, custom operators must be implemented, often at high engineering cost and performance penalty, limiting the pace of innovation. To address this productivity gap, we propose and evaluate: (1) a domain-specific language with a tensor notation close to the mathematics of deep learning; (2) a Just-In-Time optimizing compiler based on the polyhedral framework; (3) carefully coordinated linear optimization and evolutionary algorithms to synthesize high-performance CUDA kernels; (4) the transparent integration of our flow into PyTorch and Caffe2, providing the fully automatic synthesis of high-performance GPU kernels from simple tensor algebra. The performance is comparable to, and often exceeds the performance of, highly tuned libraries.

Experimental Investigation on Semi-Active Control of Base Isolation System Using Magnetorheological Dampers for Concrete Frame Structure

The traditional passive base isolation is the most widely used method in the engineering practice for structural control, however, it has the shortcoming that the optimal control frequency band is significantly limited and narrow. For the seismic isolation system designed specifically for large earthquakes, the structural acceleration response may be enlarged under small earthquakes. If the design requirements under small earthquakes are satisfied, the deformation in the isolation layer may become too large to be accepted. Occasionally, it may be destroyed under large earthquakes. In the isolation control system combined with rubber bearing and magnetorheological (MR) damper, the MR damper can provide instantaneous variable damping force to effectively control the structural response at different input magnitudes. In this paper, the control effect of semi-active control and quasi-passive control for the isolation control system is verified by the shaking table test. In regard to semi-active control, the linear quadratic regulator (LQR) classical linear optimal control algorithm by continuous control and switch control strategies are used to control the structural vibration response. Numerical simulation analysis and shaking table test results indicate that isolation control system can effectively overcome the shortcoming due to narrow optimum control band of the passive isolation system, and thus to provide optimal control for different seismic excitations in a wider frequency range. It shows that, even under super large earthquakes, the structure still exhibits the ability to maintain overall stability performance.

A new wide neighborhood primal-dual second-order corrector algorithm for linear optimization

We propose a new large-step primal-dual second-order corrector interior-point method for linear optimization. At each iteration, our method uses the new wide neighborhood introduced by Darvay and Takacs (Cent Eur J Oper Res 26(3):551–563, 2018. https://doi.org/10.1007/s10100-018-0524-0 ). In this paper we would like to improve the directions proposed by Darvay and Takacs by adding a second-order corrector direction. The corrector step is multiplied by the square of the step length in the expression of the new iterate. To our best knowledge, this is the first primal-dual second-order corrector interior-point algorithm based on Darvay–Takacs’s new wide neighborhood, which has the same complexity as the best short-step algorithms for linear optimization. Finally, numerical experiments show that the proposed algorithm is efficient and reliable.

Active vibration control of rotating beam with moving mass using piezoelectric actuator

The robotic arm carrying a moving end effector can be modeled as a rotating beam with moving mass. Active vibration control of rotating beam with moving mass using piezoelectric actuator is presented. Simply supported beam and cantilevered beam are considered in this studying. The equations of the system are derived by Lagrange’s equation with the assumed mode method. The linear classical optimal control algorithm with displacement-velocity feedback is used to determine the control voltage. The numerical simulations reveal that the transverse displacements of the beam can be effectively reduced by the actuators. The effect of rotational speed and acceleration to the dynamic responses of the beam are also investigated.

Intelligent terminal face spoofing detection algorithm based on deep belief network

In recent years, face recognition has rapidly developed in the field of smartphones and control systems. It has been used to unlock the telephone and face-payment applications. With such rapid development, more and more demands are placed on the security of face recognition. However, face biometric-based recognition technologies are still vulnerable to spoofing attacks. Thus, developing robust and reliable antispoofing attack detection is critical to guarantee the security of facial analysis-based authentication. As deep learning techniques have achieved satisfactory performances in computer vision, they can also be employed to face spoofing detection. We present a multichannel linear local binary pattern optimization algorithm, which combines with Lucas–Kanade optical flow algorithm. The extracted facial features are fused and sent to a deep belief network classifier for classification and learning, and finally tested on the MSU-mobile facial spoofing database. Compared with existing deep leaning-based detection methods, our face spoofing detection algorithm has better scalability and robustness. To evaluate the performance of the proposed algorithm, the experiments are conducted on three crossed standard spoofing databases and excellent performance is also achieved.

Guaranteed -optimal solutions with the linear optimizer ART3+O

The linear optimization algorithm ART3+O introduced by Chen et al (2010 Med. Phys. 37 4938–45) can efficiently solve large scale inverse planning problems encountered in radiation therapy by iterative projection. Its major weakness is that it cannot guarantee -optimality of the final solution due to an arbitrary stopping criterion. We propose an improvement to ART3+O where the stopping criterion is based on Farkas’ lemma. The same theory can be used to detect inconsistency in other projection methods as well. The proposed algorithm guarantees to find an -optimal solution in finite time. The algorithm is demonstrated on numerical examples in radiation therapy.

Position control of a rodless cylinder in pneumatic servo with actuator saturation

In this paper, positioning control of a rodless cylinder in pneumatic servo systems with actuator saturation is investigated via an active disturbance rejection control. A linear extended state observer is designed to estimate and compensate strong friction force and other nonlinearities in the pneumatic rodless cylinder system. An actuator saturation linear feedback control law is developed to further improve the control performance. Furthermore, a linear matrix inequality-based optimization algorithm is employed to estimate a strictly invariance set for the closed-loop system. Experiment results with response time 0.5 s and accuracy 0.005 mm for a 200 mm step signal demonstrate the effectiveness of the proposed control strategy.

Finite-time decentralized non-fragile dissipative control for large-scale systems against actuator saturation

This paper employs linear matrix inequality-based optimization algorithm to establish finite-time boundedness and dissipativeness for a class of large-scale systems in the presence of actuator faults and actuator saturation. In addition, for the proposed system, a novel time-varying actuator fault model is incorporated in controller design, which is more general than the conventional actuator fault models. Specifically, by constructing a suitable Lyapunov−Krasovskii functional, a new set of sufficient conditions is derived, which ensures the finite-time boundedness with dissipativity of the considered large-scale systems. The main intention of this paper is to design a novel decentralized fault-tolerant controller to compensate simultaneously the actuator faults, actuator saturations and nonlinear interconnections. Finally, an example and its simulation study are presented to verify the effectiveness and potential of the proposed control design technique.

Robust Line-Based Radial Distortion Estimation From a Single Image

The pinhole model utilized in most computer vision algorithms becomes unfeasible because of lens distortion. Thus it is a must to compensate lens distortion to make the pinhole model available. In this paper, we propose a new robust line-based distortion estimation method to correct radial distortion. Our method works from a single image and is able to estimate the distortion center rather than assuming it is at the image center. Distortion parameters are estimated from parameters of circulars arcs, on the basis that straight lines are imaged as circular arcs under one-parameter division model. A new feature selection scheme by refining circular arcs is introduced to make the process of distortion estimation fully automatic and more robust. Moreover, a linear optimization algorithm is applied to calculating parameters in each selection run, making our feature selection scheme more efficient. Experiments on synthetic images and real images show that our method performs well in radial distortion estimation even with severely distorted images.

Integrated hierarchical control strategy of active suspension and differential assisted steering system for electric-wheel vehicle

In order to solve the performance decrease of riding comfort and handling stability caused by the increase of unsprung mass for the electricwheel vehicle, an integrated hierarchical control strategy is proposed based on differential assisted steering system (DASS) and active suspension system (ASS). Here, the upper controller is designed to coordinate the overall control strategy and determine the control weight of the two subsystems by the fuzzy control algorithm. Afterwards, for the lower controllers, the linear quadratic optimal algorithm is taken in the differential steering system to determine the additional yaw moment, and the active disturbance rejection control is used in the active suspension system to suppress body vibration and improve riding comfort. The simulation results show that the proposed hierarchical control can effectively improve the riding comfort and handling stability of the electric-wheel vehicle.

Esquema de control jerárquico para fijación óptima de consignas en un separador trifásico de un tren de tratamiento de crudo

Una de las técnicas para tratar el crudo proveniente de los pozos petroleros es utilizar trenes de tratamiento de crudo para separar las tres fases existentes: gas, petróleo y agua. Uno de los equipos que conforma el tren es el separador trifásico. En este trabajo se demuestra la viabilidad de utilizar un esquema de control jerárquico para la fijación en línea de consignas óptimas de presión y temperatura y así reducir el consumo energético en el tratador térmico. Tal que las variables manipulas y los sets point se encuentren dentro de los límites de la operación segura, con esto se obtienen beneficios económicos y ambientales para esta planta. El logro de esta optimización constituye el aporte principal de este trabajo. Para el desarrollo de este trabajo se diseñó un algoritmo de optimización basado en tres capas jerárquicas en donde la primera capa hace referencia al control directo (PIDs), la segunda capa hace referencia a la optimización de objetivos en estado estacionario (SSTO), la tercera capa hace referencia a la optimización local de objetivos (LSSO). Para la solución a este problema se recurrió a soluciones de optimización lineal y optimización no lineal se relaciona estos algoritmos con el modelo linealizado de la planta, en otros trabajos por lo general se basan en la teoría MPC (Modelo de Control Predictivo). La simulación de los algoritmos se realizó en Matlab y se probaron en una planta simulada en Hysys utilizando el conector Active x server que conecta los dos softwares. En este experimento se logró un ahorro de un 30 % del consumo energético a su vez se encontró que es posible relacionar el modelo de la planta con los algoritmos de optimización lineal y no lineal con lo cual se concluyó que es viable la implementación de estos algoritmos en este tipo de plantas para la optimización de procesos.

A wide neighborhood interior-point algorithm for linear optimization based on a specific kernel function

This paper presents an interior point algorithm for solving linear optimization problems in a wide neighborhood of the central path introduced by Ai and Zhang (SIAM J Optim 16:400–417, 2005). In each iteration, the algorithm computes the new search directions by using a specific kernel function. The convergence of the algorithm is shown and it is proved that the algorithm has the same iteration bound as the best short-step algorithms. We demonstrate the computational efficiency of the proposed algorithm by testing some Netlib problems in standard form. To best our knowledge, this is the first wide neighborhood path-following interior-point method with the same complexity as the best small neighborhood path-following interior-point methods that uses the kernel function.

A modified infeasible interior-point algorithm with full-Newton step for semidefinite optimization

ABSTRACTRecently, Mansouri et al. (J. Optim. Theory Appl. 166: 605-618, 2015) presented an improved infeasible interior-point algorithm for linear optimization. Their algorithm has the shortcoming that the proximity measure may be still large when the duality gap approaches to zero. In this paper, we propose an infeasible interior-point algorithm for semidefinite optimization with a modified search direction. This modification is an attempt to decrease the value of the proximity measure, which is important to determine whether or not to perform centreing steps in the classical infeasible interior-point algorithms. Some preliminary numerical results show the benefit of the proposed algorithm as well.