Quadratic Algorithm Research Articles

On the string consensus problem and the Manhattan sequence consensus problem

We study the Manhattan Sequence Consensus problem (MSC problem) in which we are given k integer sequences, each of length ℓ, and we are to find an integer sequence x of length ℓ (called a consensus sequence) such that the maximum Manhattan distance of x from each of the input sequences is minimized. A related problem, with Hamming distance instead of Manhattan distance, is called Hamming String Consensus (HSC), also known under the names of string center problem or closest string problem. For binary sequences Manhattan distance coincides with Hamming distance, hence in this case HSC is a special case of MSC. We design a practically efficient O(ℓ)-time algorithm solving MSC for k≤5 sequences. It improves upon the quadratic algorithm by Amir et al. (2012) [1] for HSC for k=5 binary strings. Similarly as in the algorithm of Amir et al., we use a column-based framework. We replace the implied general integer linear programming by its easy special cases due to combinatorial properties of MSC for k≤5. Practicality of our algorithms has been verified experimentally. We also show that for a general parameter k any instance can be reduced in linear time to a kernel of size k!, so the problem is fixed-parameter tractable. Nevertheless, for k≥4 this is still too large for any naive solution to be feasible in practice.This is a full version of an article published at SPIRE 2014 [15].

Design of Buildings with Seismic Isolation Using Linear Quadratic Algorithm

Seismic isolation is a widely accepted control strategy to protect building against earthquakes. The seismic isolation control is a technique that employs a flexible element at the base of a building and allows the resonant frequency of this building being shifted away from the dominant frequency in earthquake excitations. However, large base displacements resulting from the increased flexibility of the seismic isolation system can potentially exceed the design limit of the building subjected to severe earthquake loading. Thus, design codes recommend equipping additive damping devices along with the seismic isolation bearings to lower the base displacements. In this study, a new design method of seismic isolation is developed using the linear quadratic algorithm that concurrently provides the terms of stiffness and damping coefficient. This design method facilitates the linear quadratic regulator control algorithm with output feedback. For a multiple-degree-of-freedom structure, the shear force provided by seismic isolation can be separated from the superstructure and formed as a control input. This control input is a function of the relative displacement and velocity at the isolation layer with a constant stiffness quantity and damping coefficient. This control algorithm provides the opportunity of deriving these two constants. Moreover, the derivation of isolation stiffness and damping coefficient depends on the user-defined weightings that allow adjusting performance of the isolated building in this control algorithm. One example is provided with eight-story buildings as the superstructures. As seen in the result, the root-mean-square responses are quite compatible between isolated buildings with linearly and nonlinearly isolated bearings. Therefore, the proposed method is useful for designing seismic isolation based on a multiple-degree-of-freedom building.

Linear Quadratic Regulation and Tracking using Output Feedback with Direct Feedthrough

This paper presents the development of linear quadratic regulation and output tracking algorithms using output feedback when both the measurement and performance output equations contain direct feedthrough terms. Although all physical systems can be modeled without direct feedthrough, there are still many situations where system models with direct feedthrough are important. For this situation, we modify previous work on the same topic for systems without direct feedthrough. It is shown that for the regulation problem, the optimal output feedback gain for a direct feedthrough case can be directly obtained, via a transformation, from the approach used for systems without direct feedthrough. However, for the tracking problem, a new set of coupled matrix equations for determining the optimal output feedback gain is derived from the necessary conditions for minimizing the cost function. The effectiveness of the developed algorithms is demonstrated using numerical examples.

Green Environment Monitoring System (Gems) for Industries using Li-Fi Technology

Objective: This work assures to design a green environment monitoring system for industries using Li-Fi technology to provide secured communication, high data rate transfer and pollution free environment. Methods: The LPC 2148 microcontroller with ARM 7 core is chosen for implementation. Light-emitting diodes are used as the source for data transmission and they are preferred as they have a longer life-time. Different sensors are deployed to monitor various parameters namely temperature, Gas and light intensity in an industrial environment and these sensors transmit the sensed information using Li-Fi technology in terms of flickering of LEDs. Linear quadratic estimation algorithm is implemented to improve the accuracy of sensor values. Findings: The proposed system is implemented in ARM 7 Core (LPC2148) that consumes less power. The designed system provides communication at the rate of 1.5 Mb/s over a distance of 5 meters and they are free from electromagnetic interference. They are not affected by artificial or natural light sources. Improvement/Applications: The implementation of Linear Quadratic estimator improved the accuracy of sensor output values. This technology is eco-friendly and the working atmosphere is conserved thereby ensuring a green environment. The sensors used in industrial applications communicate with low cost and also in a secured manner.

Bandwidth Allocation Under Multi-Level Service Guarantees of Downlink in the VLC-OFDM System

In this paper, we explore a low-complex bandwidth allocation (BA) scheme with multi-level service guarantees in VLC-OFDM systems. Effective capacity theory, which evaluates wireless channel capacity from a novel view, is utilized to model the system capacity under delay QoS constraints of the link layer. Since intensity modulation of light is used in the system, problems caused by frequency selectivity can be neglected. Then, the BA problem can be formulated as an integer programming problem and it is further relaxed and transformed into a concave one. Lagrangian formulation is used to reformulate the concave problem. Considering the inefficiency of traditional gradient-based schemes and the demand for distributed implementation in local area networks, we localize the global parameters and propose a quasi-distributed quadratic allocation algorithm to provide two-level service guarantees, the first level is QoS oriented, and the second level is QoE oriented. Simulations have shown the efficient performance of the proposed algorithm. The users with more stringent QoS requirements require more subcarriers to guarantee their statistical delay QoS requirements. We also analyze the effect of subcarrier granularity on the aggregate effective capacity via simulations.

Counterparty Risk Minimization by the Optimal Netting of OTC Derivative Trades

The OTC derivatives market has always suffered from the fact that there are generally many contracts among market intermediaries where neither counterparty is an end-user. Active OTC market makers may have thousands of very similar contracts with one another. To the extent that each one needs to be monitored and margined, substantial improvements in efficiency may be possible through “compression” trades in which sets of existing contracts are replaced by a smaller number of essentially equivalent new ones among the same counterparties. But how best to minimize counterparty risk exposures without mismatching terms? In this article, O’Kane explains how compression is currently done for interest rate swaps and reviews both linear and quadratic programming approaches. Using simulation, he explores how the possible degree of compression is affected by the number of trades and the number of counterparties involved. The linear compression algorithm appears to allow more full unwinds of existing contracts than the quadratic algorithm, which is a feature highly desired by the firms in the industry.

Feature Selection with Multi-Cost Constraint

Cost-sensitive learning extends classical machine learning and data mining by considering various types of costs, of the data. Due to money limited, we also have a constraint on the cost for selecting feature and tradeoff between the test costs and misclassification costs. However, the precious works seldom involve the tradeoff problem under the multi-cost constraint. In this paper, we introduce the misclassification costs into the cost constraint problem firstly, and propose a quadratic heuristic algorithm to deal with the minimal feature selection with multi-cost constraint problem. The goal is to obtain a feature subset with minimal average total cost, which includes test costs and misclassification costs. Experimental results indicate the proposed algorithm is effective and efficient.

Multi-phase classification by a least-squares support vector machine approach in tomography images of geological samples

Abstract. Image processing of X-ray-computed polychromatic cone-beam micro-tomography (μXCT) data of geological samples mainly involves artefact reduction and phase segmentation. For the former, the main beam-hardening (BH) artefact is removed by applying a best-fit quadratic surface algorithm to a given image data set (reconstructed slice), which minimizes the BH offsets of the attenuation data points from that surface. A Matlab code for this approach is provided in the Appendix. The final BH-corrected image is extracted from the residual data or from the difference between the surface elevation values and the original grey-scale values. For the segmentation, we propose a novel least-squares support vector machine (LS-SVM, an algorithm for pixel-based multi-phase classification) approach. A receiver operating characteristic (ROC) analysis was performed on BH-corrected and uncorrected samples to show that BH correction is in fact an important prerequisite for accurate multi-phase classification. The combination of the two approaches was thus used to classify successfully three different more or less complex multi-phase rock core samples.

Obstacle Avoidance for Redundant Manipulators Utilizing a Backward Quadratic Search Algorithm

Obstacle avoidance can be achieved as a secondary task by appropriate inverse kinematics (IK) resolution of redundant manipulators. Most prior literature requires the time-consuming determination of the closest point to the obstacle for every calculation step. Aiming at the relief of computational burden, this paper develops what is termed a backward quadratic search algorithm (BQSA) as another option for solving IK problems in obstacle avoidance. The BQSA detects possible collisions based on the root property of a category of quadratic functions, which are derived from ellipse-enveloped obstacles and the positions of each link's end-points. The algorithm executes a backward search for possible obstacle collisions, from the end-effector to the base, and avoids obstacles by utilizing a hybrid IK scheme, incorporating the damped least-squares method, the weighted least-norm method and the gradient projection method. Some details of the hybrid IK scheme, such as values of the damped factor, weights and the clamping velocity, are discussed, along with a comparison of computational load between previous methods and BQSA. Simulations of a planar seven-link manipulator and a PUMA 560 robot verify the effectiveness of BQSA.

An O(m log m)-Time Algorithm for Detecting Superbubbles.

In genome assembly graphs, motifs such as tips, bubbles, and cross links are studied in order to find sequencing errors and to understand the nature of the genome. Superbubble, a complex generalization of bubbles, was recently proposed as an important subgraph class for analyzing assembly graphs. At present, a quadratic time algorithm is known. This paper gives an O(m log m)-time algorithm to solve this problem for a graph with m edges.

Maximizing the sum of a generalized Rayleigh quotient and another Rayleigh quotient on the unit sphere via semidefinite programming

The problem is a type of "sum-of-ratios" fractional programming and is known to be NP-hard. Due to many local maxima, finding the global maximizer is in general difficult. The best attempt so far is a critical point approach based on a necessary optimality condition. The problem therefore has not been completely solved. Our novel idea is to replace the generalized Rayleigh quotient by a parameter $$\mu $$μ and generate a family of quadratic subproblems $$(\hbox {P}_{\mu })'s$$(Pμ)?s subject to two quadratic constraints. Each $$(\hbox {P}_{\mu })$$(Pμ), if the problem dimension $$n\ge 3$$n?3, can be solved in polynomial time by incorporating a version of S-lemma; a tight SDP relaxation; and a matrix rank-one decomposition procedure. Then, the difficulty of the problem is largely reduced to become a one-dimensional maximization problem over an interval of parameters $$[\underline{\mu },\bar{\mu }]$$[μ?,μ¯]. We propose a two-stage scheme incorporating the quadratic fit line search algorithm to find $$\mu ^*$$μ? numerically. Computational experiments show that our method solves the problem correctly and efficiently.

On the variable common due date, minimal tardy jobs bicriteria two-machine flow shop problem with ordered machines

We consider a special case of the ordinary NP-hard two-machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs. In Panwalkar and Koulamas (2012) [5], the authors presented quadratic algorithm for the problem when each job has its smaller processing time on the first machine. In this note, we improve the running time of the algorithm to O(nlog⁡n) by efficient implementation using recently introduced modified binary tree data structure.

Coil Design for Magnetic Particle Imaging: Application for a Preclinical Scanner

A method to design electromagnetic coils for magnetic particle imaging (MPI) scanners is presented. Three different coils for a rabbit sized scanner are designed, namely, a cylindrical drive coil, a biplanar drive coil, and a quadrupole. Based on the inverse boundary elements method, the optimization of all coils used in an MPI scanner is possible. The inverse problem is solved using the Tikhonov regularization and a quadratic programming with quadratic constraints algorithm. Depending on the chosen objectives, the coils can be designed to precisely generate a given field, having a small inductance, resistance, or having a smooth winding pattern. The properties of a cylindrical drive coil are then validated on a prototype. The use of this technique allows the optimization of the scanner design, to enhance the imaging capacity, and to easily gain control over the key properties of the coils in order to scale up scanners to human size.

Design of Composite Control System for an Air-Breathing Hypersonic Vehicle with Wing-Rudder Deflection

The Scramjet performance of air-breathing hypersonic vehicle is highly correlated with flight height, Mach and angle of attack (AOA). The violent disturbance of the AOA can cause the engine power off. Consequently the maneuverability of hypersonic vehicle is strictly limited in the phase of cruise. A composite Control system for an air-breathing hypersonic vehicle is presented. The hypersonic vehicle has a configuration with tail control rudders and a set of deflectable wings installed nearby the center of gravity. During the phase of cruise, the precision of AOA is achieved by deflecting tail rudders, and the maneuverable acceleration command is tracked by deflecting wings. A linear quadratic (LQ) track control algorithm with integrator is used to design the composite control system. Simulation results demonstrate that the composite control system has good performance in tracking AOA and acceleration command by respective deflection in cruise.

Partial discharge localization in power transformers based on the sequential quadratic programming-genetic algorithm adopting acoustic emission techniques

Partial discharge (PD) in power transformers is one of the prime reasons resulting in insulation degradation and power faults. Hence, it is of great importance to study the techniques of the detection and localization of PD in theory and practice. The detection and localization of PD employing acoustic emission (AE) techniques, as a kind of non-destructive testing, plus due to the advantages of powerful capability of locating and high precision, have been paid more and more attention. The localization algorithm is the key factor to decide the localization accuracy in AE localization of PD. Many kinds of localization algorithms exist for the PD source localization adopting AE techniques including intelligent and non-intelligent algorithms. However, the existed algorithms possess some defects such as the premature convergence phenomenon, poor local optimization ability and unsuitability for the field applications. To overcome the poor local optimization ability and easily caused premature convergence phenomenon of the fundamental genetic algorithm (GA), a new kind of improved GA is proposed, namely the sequence quadratic programming-genetic algorithm (SQP-GA). For the hybrid optimization algorithm, SQP-GA, the sequence quadratic programming (SQP) algorithm which is used as a basic operator is integrated into the fundamental GA, so the local searching ability of the fundamental GA is improved effectively and the premature convergence phenomenon is overcome. Experimental results of the numerical simulations of benchmark functions show that the hybrid optimization algorithm, SQP-GA, is better than the fundamental GA in the convergence speed and optimization precision, and the proposed algorithm in this paper has outstanding optimization effect. At the same time, the presented SQP-GA in the paper is applied to solve the ultrasonic localization problem of PD in transformers, then the ultrasonic localization method of PD in transformers based on the SQP-GA is proposed. And localization results based on the SQP-GA are compared with some algorithms such as the GA, some other intelligent and non-intelligent algorithms. The results of calculating examples both stimulated and spot experiments demonstrate that the localization method based on the SQP-GA can effectively prevent the results from getting trapped into the local optimum values, and the localization method is of great feasibility and very suitable for the field applications, and the precision of localization is enhanced, and the effectiveness of localization is ideal and satisfactory.

Passive control of along-wind response of tall building

Most of modern tall buildings using lighter construction materials with high strength and less stiffness are more flexible, which occurs excessive wind-induced vibration, resulting in occupant discomfort and structural unsafety. It is necessary to predict wind-induced vibration response and find out a method to mitigate such an excessive wind-induced vibration at the preliminary design stage. Recently, many studies have been conducted in using actuator control force based on the linear quadratic optimum control algorithm. It was accepted as a common knowledge that the performance of passive tuned mass damper (TMD) could increase by incorporating a feedback active control force in the design of TMD, which is called active tuned mass damper (ATMD). However, the fact that ATMD is superior to TMD to reduce wind-induced vibration of a tall building is still a question. The effectiveness of TMD for mitigating the along-wind vibration of a tall building was investigated. Optimum parameters of tuning frequency and damping ratio for TMD under a random load which has a white noise spectra were used. Fluctuating along-wind load acting on a tall building treated as a stationary Gaussian random process was simulated numerically using the along-wind load spectra. And using this simulated along-wind load, along-wind responses of a tall building with and without TMD were calculated and the effectiveness of TMD in mitigating the along-wind response of a tall building was found out.

An Efficient Hybrid Segmentation Algorithm for Computer Tomography Image Segmentation

Medical Image segmentation plays a major role in medical image processing. During last decades, developing robust and efficient algorithms for medical image segmentation has been a demanding area of growing research interest. Extensive research has been done in creating many different approaches and algorithms for image segmentation, but it is still difficult to assess whether one algorithm produces more accurate segmentations than the other. The proposed method utilizes clustering with distance based segmentation approach for Computer tomography image segmentation. This paper provides new hybrid segmentation method based on K-Means, Medoid shift and Signature Quadratic Form Distance algorithm for computer tomography images. We validate the Hybrid segmentation approach with the parameters in terms of sensitivity, specificity, accuracy and number of fragments. The Real time dataset is used to evaluate the performance of the proposed method. The results obtained from the experimentation show that the proposed approach attains reliable segmentation accuracy and also clear that it is more efficient, robust and more appropriate for organ classification.

The Backbone Coloring Problem for Bipartite Backbones

Let $$G$$G be a simple graph, $$H$$H be its spanning subgraph and $$\lambda \ge 2$$??2 be an integer. By a $$\lambda $$?-backbone coloring of $$G$$G with backbone $$H$$H we mean any function $$c$$c that assigns positive integers to vertices of $$G$$G in such a way that $$|c(u)-c(v)|\ge 1$$|c(u)-c(v)|?1 for each edge $$uv\in E(G)$$uv?E(G) and $$|c(u)-c(v)|\ge \lambda $$|c(u)-c(v)|?? for each edge $$uv\in E(H)$$uv?E(H). The $$\lambda $$?-backbone chromatic number $$BBC_\lambda (G,H)$$BBC?(G,H) is the smallest integer $$k$$k such that there exists a $$\lambda $$?-backbone coloring $$c$$c of $$G$$G with backbone $$H$$H satisfying $$\max c(V(G))=k$$maxc(V(G))=k. A $$\lambda $$?-backbone coloring $$c$$c of $$G$$G with backbone $$H$$H is optimal if and only if $$\max c(V(G))=BBC_\lambda (G,H)$$maxc(V(G))=BBC?(G,H). In the paper we study the problem of finding optimal $$\lambda $$?-backbone colorings of complete graphs with bipartite backbones. We present a linear algorithm that is $$2$$2-approximate in general and $$1.5$$1.5-approximate if backbone is connected. Next we show a quadratic algorithm for backbones being trees that finds optimal $$\lambda $$?-backbone colorings provided $$\lambda $$? is large enough.

Computing optimal rebalance frequency for log-optimal portfolios in linear time

The pure form of log-optimal investment strategies are often considered to be impractical due to the inherent need for continuous rebalancing. It is however possible to improve investor log utility by adopting a discrete-time periodic rebalancing strategy. Under the assumptions of geometric Brownian motion for assets and approximate log-normality for a sum of log-normal random variables, we find that the optimum rebalance frequency is a piecewise continuous function of investment horizon. One can construct this rebalance strategy function, called the optimal rebalance frequency function, up to a specified investment horizon given a limited trajectory of the expected log of portfolio growth when the initial portfolio is never rebalanced. We develop the analytical framework to compute the optimal rebalance strategy in linear time, a significant improvement from the previously proposed search-based quadratic time algorithm.

A Cuckoo Search based WDM Channel Allocation Algorithm

More and more modern metaheuristics nature–inspired algorithms are emerging and they become increasingly popular. This paper formulates an algorithm for solving the channel–allocation problem in optical wavelength division multiplexing (WDM) systems to suppress four–wave mixing crosstalk (FWM) based on a novel nature–inspired algorithm, called Cuckoo Search algorithm by using the concept of Optimal Golomb ruler (OGR) sequences. Simulation results conclude the significance performance improvement, without the requirement of increased total optical channel bandwidth, unlike two existing classical channel–allocation algorithms i.e. Extended Quadratic Congruence (EQC) and Search Algorithm (SA) and one of the existing nature–inspired algorithm i.e. Genetic Algorithm (GA). General Terms Classical computing, Four–wave mixing, Metaheuristics, Optimization.