Unconstraint Problem Research Articles

Mathematical Treatment of Nonlinear Pine Wilt Disease Model: An Evolutionary Approach

In human life, the forest plays an important role in safeguarding trees against disease infection. The pine wilt disease is one of the big threats for the forest and the environment. Optimum control theory is about discovering a complex system control rule over a period of time. In this paper Evolutionary Pad¶e Approximation (EPA) scheme has been implemented for the treatment of non-linear pine wilt disease model. Evolutionary Pad¶e Approximation scheme transforms the nonlinear pine wilt disease model into optimization problem. Initial conditions are converted into problem constraints and then constraint problem is converted into unconstraint problem by using penalty function. Sufficient parameter settings for EPA have been implemented. The simulations are numerical solutions of the model of pine wilt disease by solving the proven problem of optimization. It is also determined the threshold value for the fundamental reproductive number and the endemic disease balance point of the model. Evolutionary Pad¶e Approximation has provided convergence solution regarding relationship among the different population compartments for diseases equilibrium, it has been observed that the results EPA scheme are more reliable and significant when a comparison is drawn with Non-Standard Finite Difference (NSFD) numerical scheme. Finally, EPA scheme reduces the infected rates very fast. Further, in a strong contrast to NFSD, this technique has eliminated the need to provide step size.

Secure energy efficient power allocation in massive multiple‐input multiple‐output systems with an eavesdropper using cell division technique

SummaryIn this paper, we study energy‐efficient power allocation (PA) to secure the confidential information of massive multiple‐input multiple‐output (MIMO) systems in the presence of an eavesdropper. First a training scheme is presented in the uplink using the MMSE method. Based on the estimated channel state information (CSI), the base station (BS) encrypts the confidential information. Next, the ergodic secret rate is obtained at the downlink. In this paper, in order to maximize the ergodic secrecy rate, the allocation of common power in the uplink and downlink is proposed by considering the constraints such as the transmit power constraint in the uplink, the transmit power constraint in the downlink, and the minimum ergodic secret rate constraint. The objective function in the proposed scenario is a nonconvex problem, which first becomes a convex problem and then, by using the Lagrange dual function method, the problem becomes an unconstraint problem. We also divide the cell into two areas using the cell division method. A practical energy‐efficient PA algorithm is presented which deals with the adverse effect of the eavesdropper. Simulations are carried out to demonstrate the effectiveness of the proposed methods.

Waveform Design in MIMO Radar Using Radial Point Interpolation Method

In this letter, we consider the problem of waveform design in colocated multiple-input multiple-output radars in order to obtain a desired beampattern. In this problem, practical constraints, such as constant envelope (CE) and low peak-to-average power ratio, are very important. Therefore, we propose a simple method to generate some practical waveforms, such as different versions of phase-shift keying and pulse-amplitude modulation. We map a non-CE to the desired finite alphabet by a mapping function (MP). In the proposed method, first, the values of cross-correlation relationship between the input and the output of MP are calculated in a few points, and then, using radial point interpolation method, the mentioned relationship and its first-order derivative are derived in the remaining points. Finally, we use the obtained derivative in order to design the desired waveform in an unconstraint problem by a gradient descend algorithm. Simulation results show that there are many different waveforms on which the proposed method can approximate the desired beampattern with a high accuracy.

Transmit Beamforming for Single-User Large-Scale MISO Systems With Sub-Connected Architecture and Power Constraints

This letter considers optimal transmit beamforming for a sub-connected large-scale MISO system with RF chain and per-antenna power constraints. The system is configured such that each RF chain serves a group of antennas. For the hybrid scheme, necessary and sufficient conditions to design the optimal digital and analog precoders are provided. It is shown that, in the optimum, the optimal phase shift at each antenna has to match the channel coefficient and the phase of the digital precoder. In addition, an iterative algorithm is provided to find the optimal power allocation. We study the case where the power constraint on each RF chain is smaller than the sum of the corresponding per-antenna power constraints. Then, the optimal power is allocated based on two properties: each RF chain uses full power and if the optimal power allocation of the unconstraint problem violates a per-antenna power constraint then it is optimal to allocate the maximal power for that antenna.

Vibro-acoustic topology optimization of sandwich panels partially treated with MR fluid and silicone rubber core layer

This study aims to investigate the topology optimization of sandwich panels partially treated with magnetorheological (MR) fluid and silicone rubber core layer. The finite element (FE) model of the partially treated sandwich panel has been developed using circular and 4-node quadrilateral elements. The FE model is then utilized to solve the free and forced vibration equations of motion to obtain the natural frequencies, loss factors and sound transmission loss (STL), respectively. Systematic parametric studies on the effect of the position of the MR fluid and silicone rubber on the first axisymmetric natural frequency, the corresponding loss factor and also the STL are presented. It has been shown that the vibrational and acoustical behavior of the sandwich panel changes considerably as the location of the MR treatment changes. To conduct optimization problems efficiently without using the full FE model, linear meta-models have been derived using random and D-optimal design points. The developed meta-models are then utilized to solve the topology optimization problems using the genetic algorithm and integer programing methods. The suitability of the identified optimal candidates are further evaluated using the developed FE model to determine the optimized topology for the constraint and unconstraint problems.

Constrained Target Clustering for Military Targeting Process

<p>Constrained target clustering (CTC) is proposed to support the targeting decision-making in the network centric warfare environment. When area targets are detected by sensors, it is required to decide the points at which a missile or bomb is aimed to achieve operational goals. CTC can determine the optimal numbers and positions of aiming points by transforming the targeting problem into clustering-based optimisation problems. The CTC formulations include objective functions and constraints in consideration of area targets, protected objects, target-level background information, lethal radius, and required damage rate. The numerical example shows how to apply the CTC formulation given a sample data set. In order to compare the effects of different constraints, the demonstration explores from an unconstraint problem to constrained problems by adding constraints. The results show that CTC can effectively decide the aiming points with consideration of both targets and capabilities of friendly weapons, and serve as a targeting decision support system in the network centric warfare environment.</p>

Analytical method for optimum non‐negative integer bit allocation

The optimum bit allocation (OBA) problem was first investigated by Huang and Schultheiss in 1963. They solved the problem allowing the bits to be signed real numbers. Later, different algorithms were proposed for OBA problem when the bits were constrained to be integer and non-negative. In 2006, Farber and Zeger proposed new algorithms for solving optimum integer bit allocation (OIBA) and optimum non-negative integer bit allocation (ONIBA). None of the existing algorithms for OIBA and ONIBA problems end with an analytical solution. In this study, a new analytical solution is proposed for OIBA and ONIBA problems based on a novel analytical optimisation approach. At first, a closed form solution is derived for Lagrange unconstraint problem. Then, by removing the Lagrange multiplier, an analytical solution is obtained for OIBA and ONIBA problems. Using the selection and bisection algorithms, a low complexity algorithm is proposed for searching in a group of discrete functions which can reduce the computational complexity of the analytical solution. The complexity of computing the analytical solution is O (k) which is much lower than the complexity of existing ONIBA algorithms.

Seismic facies classification based on the improved transductive support vector machine

In order to solve the problem of seismic facies classification, transductive support vector machine is improved. The improvement of transductive support vector machine model is proposed. Now the research of TSVM is only on the elementary stage, the optimization of TSVM is able to be solved theoretically, but itis quite difficult tofind the exact solution. Therefore, we try to convert the optimization of TSVM into unconstraint problem, then we could able to construct smooth unconstraint prob- lem with kernel, in order to create an optimized model which is easy to be solved by TSVM. The improvement of transductive support vector machine is applied to the seismic facies classification. This is a new method in the seismic facies classification never used. The experimental data show that the proposed algorithm can improve the seismic facies classification, economic benefit. The main positive feature of improved transductive support vector machine such as the less number of support vec- tors,there are the smaller training time and testing time and the higher correctly prediction.It has theoretical value and practical significance.

An Alternative Approach of Dual Response Surface Optimization Based on Penalty Function Method

The dual response surface for simultaneously optimizing the mean and variance models as separate functions suffers some deficiencies in handling the tradeoffs between bias and variance components of mean squared error (MSE). In this paper, the accuracy of the predicted response is given a serious attention in the determination of the optimum setting conditions. We consider four different objective functions for the dual response surface optimization approach. The essence of the proposed method is to reduce the influence of variance of the predicted response by minimizing the variability relative to the quality characteristics of interest and at the same time achieving the specific target output. The basic idea is to convert the constraint optimization function into an unconstraint problem by adding the constraint to the original objective function. Numerical examples and simulations study are carried out to compare performance of the proposed method with some existing procedures. Numerical results show that the performance of the proposed method is encouraging and has exhibited clear improvement over the existing approaches.

New Scaled Three-Term Memoryless vm-Methods for Solving Nonlinear Unconstraint Problems

Four new scaled three-term memoryless VM methods for solving nonlinear unconstrained problems are presented. The basic idea is to deal with Al-Bayati's (1991) and Biggs's (1983) self-scaling VMupdates in the frame of new scaled CG-methods. Birgin-Martinez (2001) and Abbo (2007) positive parameters are used to scale these spectral CG-methods. The new search directions are reset to the standard Steepest Descent (SD) direction when Powell's (1977) restarting criterion holds. Andrei's (2010) acceleration scheme of the step-size parameter has been employed in the new proposed methods to improve the efficiency of such methods. Under common assumptions; the new methods are proved to be globally convergent. Computational results for a set consisting of 100 unconstrained optimization test problems show that the new methods substantially outperforms the scaled memoryless BFGS method.

On a new index theory and non semi-trivial solutions for elliptic systems

Two indices, which are similar to the Krasnoselski's genus on thesphere, are defined on the product of spheres. They are applied toinvestigate the multiple non semi-trivial solutions for ellipticsystems. Both constraint and unconstraint problems are studied.