Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

Accelerating Factor Xa inhibitor discovery with a de novo drug design pipeline

Small-molecule drugs are essential for maintaining human health. The objective of this study is to identify a molecule that can inhibit the Factor Xa protein and be easily procured. An optimization-based de novo drug design framework, Drug CAMD, that integrates a deep learning model with a mixed-integer nonlinear programming model is used for designing drug candidates. Within this framework, a virtual chemical library is specifically tailored to inhibit Factor Xa. To further filter and narrow down the lead compounds from the designed compounds, comprehensive approaches involving molecular docking,binding pose metadynamics(BPMD), binding free energy calculations, and enzyme activity inhibition analysis are utilized. To maximize efficiency in terms of time and resources, molecules for in vitro activity testing are initially selected from commercially available portions of customized virtual chemical libraries. In vitro studies assessing inhibitor activities have confirmed that the compound EN300-331859shows potential Factor Xa inhibition, with an IC_(50)value of 34.57 μmol·L^(-1). Through in silico molecular docking and BPMD, the most plausible binding pose for the EN300-331859-Factor Xa complex are identified. The estimated binding free energy values correlate well with the results obtained from biological assays. Consequently, EN300-331859 is identified as a novel and effective sub-micromolar inhibitor of Factor Xa.

A COMBINED PARAMETRIC QUADRATIC PROGRAMMING AND PRECISE INTEGRATION METHOD BASED DYNAMIC ANALYSIS OF ELASTIC-PLASTIC HARDENING/SOFTENING PROBLEMS

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.

Motor relearning program and Bobath method improve motor function of the upper extremities in patients with stroke

BACKGROUND: In the natural evolution of cerebrovascular disease, unconscious use of affected extremity during drug treatment and daily life can improve the function of affected upper extremity partially, but it is very slow and also accompanied by the formation of abnormal mode. Therefore, functional training should be emphasized in recovering the motor function of extremity. OBJECTIVE: To observe the effects of combination of motor relearning program and Bobath method on motor function of upper extremity of patients with stroke. DESIGN: Comparison of therapeutic effects taking stroke patients as observation subjects. SETTING: Department of Neurology, General Hospital of Beijing Jingmei Group. PARTICIPANTS: Totally 120 stroke patients, including 60 males and 60 females, averaged (59±3) years, who hospitalized in the Department of Neurology, General Hospital of Beijing Jingmei Group between January 2005 and June 2006 were recruited. The involved patients met the following criteria: Stroke attack within 2 weeks; diagnosis criteria of cerebral hemorrhage or infarction made in the 4th National Cerebrovascular Disease Conference; confirmed by skull CT or MRI; Informed consents of therapeutic regimen were obtained. The patients were assigned into 2 groups according to their wills: rehabilitation group and control group, with 30 males and 30 females in each group. Patients in rehabilitation group averaged (59±2)years old, and those in the control group averaged (58±2)years old. METHODS: ① Patients in two groups received routine treatment in the Department of Neurology. When the vital signs of patients in the rehabilitation group were stable, individualized treatment was conducted by combined application of motor relearning program and Bobath method. Meanwhile, training of activity of daily living was performed according to the disease condition changes of patients at different phases, including the nursing and instruction of body posture, the maintenance of good extremity position, bed exercise, bedside sit up and sitting position balance, sit up exercise, dynamic and static balance exercise, walking exercise, active training and passive training. The strength, time and speed of training were increased gradually according to their physical abilities. Patients were trained 45 to 60 minutes once, 5 times a week, within 2 weeks. ② Evaluation criteria of therapeutic effect: The motor function of upper extremity was evaluated by Fugl-Meyer method on the day of beginning and end of treatment. Higher points indicated better function of upper extremity. ③ t test and paired t test were used for comparing the difference of intergroup and intragroup measurement data, respectively. MAIN OUTCOME MEASURES: Changes in Fugl-Meyer scoring of two groups before and after treatment. RESULTS: Totally 120 stroke patients participated in the final analysis. Before treatment, Fugl-Meyer scoring was close between rehabilitation group and control group [(14.47±2.38),(14.16±2.39) points, P > 0.05]; Fugl-Meyer scoring of rehabilitation group after treatment was significantly higher than that before treatment and that of control group[(37.93±2.67),(18.36±2.43) points, t =11.053, 5.408, P < 0.01]; There were no significant differences in Fugl-Meyer scoring between before treatment in the control group and control group (P > 0.05). CONCLUSION: Combined application of motor relearning program and Bobath method can significantly improve the motor function of upper extremity of patients with stroke.

BLOCK PIVOT METHODS FOR SOLVING FRICTIONAL CONTACT PROBLEMS

Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.

A NEW METHOD FOR SOLUTION OF 3D ELASTIC-PLASTIC FRICTIONAL CONTACT PROBLEMS

The solution of 3 D elastic-plastic frictional contact problems belongs to the un specified boundary problems where the interaction between two kinds of nonlinearities should occur. Considering the difficulties for the solution of 3 D frictional contact problems, the key part is the determination of the tangential slip states at the contact points, and a great amount of computing work is needed for a high accuracy result. A new method based on a combination of programming and iteration methods, which are respectively known as two main kinds of methods for contact analysis, was put forward to deal with 3 D elastic-plastic contact problems. Numerical results demonstrate the efficiency of the algorithm illustrated here.

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF HETEROGENEOUS MATERIALS WITH VORONOI FINITE ELEMENT METHOD

The Voronoi cell finite element method （VCFEM） is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.

Set Programming Method and Performance Improvement of Phase Change Random Access Memory Arrays

A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by different set programming strategies based on this new set pulse. The amplitude difference （I1 - I2） of the set pulse is proved to be a crucial parameter for set programming. We observe and analyze the cell characteristics with different I1 - I2 by means of thermal simulations and high-resolution transmission electron microscopy, which reveal that an incomplete set programming will occur when the proposed slow-down pulse is set with an improperly high I1 - I2. This will lead to an amorphous residue in the active region. We also discuss the programming method to avoid the set performance degradations.

Modified Exact Jacobian Semidefinite Programming Relaxation for Celis-Dennis-Tapia Problem

A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.

Proportional Fairness-Based Energy-Efficient Power Allocation in Downlink MIMO-NOMA Systems with Statistical CSI

In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel state information(CSI) is utilized for perfect CSI is impossible to achieve in practice. PF is used to balance the transmission efficiency and user fairness. Energy efficiency(EE) is formulated under basic data rate requirements and maximum transmitting power constraints. Due to the non-convex nature of EE, a two-step algorithm is proposed to obtain sub-optimal solution with a low complexity. Firstly, power allocation is determined by golden section search for fixed power. Secondly total transmitting power is determined by fractional programming method in the feasible regions. Compared to the performance of MIMO-NOMA without PF constraint, fairness is obtained at expense of decreasing of EE.

Construction of improved rigid blocks failure mechanism for ultimate bearing capacity calculation based on slip-line field theory

Based on the slip-line field theory, a two-dimensional slip failure mechanism with mesh-like rigid block system was constructed to analyze the ultimate bearing capacity problems of rough foundation within the framework of the upper bound limit analysis theorem. In the velocity discontinuities in transition area, the velocity changes in radial and tangent directions are allowed. The objective functions of the stability problems of geotechnical structures are obtained by equating the work rate of external force to internal dissipation along the velocity discontinuities, and then the objective functions are transformed as an upper-bound mathematic optimization model. The upper bound solutions for the objective functions are obtained by use of the nonlinear sequential quadratic programming and interior point method. From the numerical results and comparative analysis, it can be seen that the method presented in this work gives better calculation results than existing upper bound methods and can be used to establish the more accurate plastic collapse load for the ultimate bearing capacity of rough foundation.

Dynamic Positioning Capability Analysis for Marine Vessels Based on A DPCap Polar Plot Program

Dynamic positioning capability(DPCap) analysis is essential in the selection of thrusters, in their configuration, and during preliminary investigation of the positioning ability of a newly designed vessel dynamic positioning system.DPCap analysis can help determine the maximum environmental forces, in which the DP system can counteract in given headings. The accuracy of the DPCap analysis is determined by the precise estimation of the environmental forces as well as the effectiveness of the thrust allocation logic. This paper is dedicated to developing an effective and efficient software program for the DPCap analysis for marine vessels. Estimation of the environmental forces can be obtained by model tests, hydrodynamic computation and empirical formulas. A quadratic programming method is adopted to allocate the total thrust on every thruster of the vessel. A detailed description of the thrust allocation logic of the software program is given. The effectiveness of the new program DPCap Polar Plot(DPCPP)was validated by a DPCap analysis for a supply vessel. The present study indicates that the developed program can be used in the DPCap analysis for marine vessels. Moreover, DPCap analysis considering the thruster failure mode might give guidance to the designers of vessels whose thrusters need to be safer.

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF COSSERAT CONTINUUM

A new algorithm is developed based on the parametric variational principle for elastic-plastic analysis of Cosserat continuum. The governing equations of the classic elastic-plastic problem are regularized by adding rotational degrees of freedom to the conventional translational degrees of freedom in conventional continuum mechanics. The parametric potential energy princi- ple of the Cosserat theory is developed, from which the finite element formulation of the Cosserat theory and the corresponding parametric quadratic programming model are constructed. Strain localization problems are computed and the mesh independent results are obtained.

Penalty model for delay of bidding section construction period in South-to-North Water Diversion Eastern Route Project from perspective of programs

According to the multi-project and program management theory, this paper analyzes the program generation principle and establishes a program based on progress goals. On the basis of the present situation of calculation of penalty for delay of the bidding section construction period with the critical path method, we studied the effects of contractor-induced delay of the bidding section construction period in detail, including the effects on the construction period of the bidding section itself, the earliest start times of the next bidding section and other subsequent bidding sections, and the construction period of the program, and then constructed a penalty model for delay of the bidding section construction period from the perspective of programs. Using the penalty model, we conducted a practical analysis of penalty for delay of the construction period of the Baoying station program in the South-to-North Water Diversion Project. The model can help determine the amount of penalty for delay of the construction period in bidding sections scientifically and reasonably,

Discrete differential evolution algorithm for integer linear bilevel programming problems

A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.

A Study on the Reasonable Distribution of Total Funds

How to distribute total sum of funds among different investment priorities？ It is not only a theoretical problem in Management Accounting, but also a realistic problem in the investment decision of an enterprise. In this paper, the author queries the method of ＂use linear programming to find out optimum combination＂, which put forward in management accounting, and gives a convenient and reasonable method---effective gradient method.

A BRANCH BOUND METHOD FOR SUBSET SUM PROBLEM

This paper indicates the possible difficulties for applying the interior point method to NPcomplete problems,transforms an NP-complete problem into a nonconvex quadratic program and then develops some convexity theories for it. Lastly it proposes an algorithm which uses Karmarkar's algorithm as a subroutine. The finite convergence of this algorithm is also proved.

SEQUENTIAL CONVEX PROGRAMMING METHODS FOR SOLVING LARGE TOPOLOGY OPTIMIZATION PROBLEMS： IMPLEMENTATION AND COMPUTATIONAL RESULTS

In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.

A Unified Approach for Developing EfficientAlgorithmic Programs

A unified approach called partition-and-recur for developing efficient and correct algorithmic programs is presented. An algorithm (represented by recurrence and initiation) is separated from program, and special attention is paid to algorithm manipulation rather than program calculus. An algorithm is exactly a set of mathematical formulae. It is easier for formal derivation and proof. After getting efficient and correct algorithm, a trivial transformation is used to get a final program. The approach covers several known algorithm design techniques, e.g. dynamic programming, greedy, divide-and-conquer and enumeration, etc. The techniques of partition and recurrence are not new. Partition is a general approach for dealing with complicated objects and is typically used in divide-and-conquer approach. Recurrence is used in algorithm analysis, in developing loop invariants and dynamic programming approach. The main contribution is combining two techniques used in typical algorithm development into a unified and systematic approach to develop general efficient algorithmic programs and presenting a new representation of algorithm that is easier for understanding and demonstrating the correctness and ingenuity of algorithmic programs.