scholarly journals On a Dual Direct Cosine Simplex Type Algorithm and Its Computational Behavior

2019 ◽  
Author(s):  
Elsayed Badr ◽  
khalid Aloufi
Keyword(s):  
Simplex Algorithm ◽  
Phase Method ◽  
Test Problems ◽  
Computational Results ◽  
Two Phase ◽  
Dual Version ◽  
Type Algorithm ◽  
Linear Problems ◽  
Computational Behavior ◽  
Number Of Iterations

The goal of this paper is to propose a dual version of the direct cosine simplex algorithm (DDCA) for general linear problems. Unlike the two-phase and the big-M methods, our technique does not involve artificial variables. Our technique solves the dual Klee-Minty problem in two iterations and solves the dual Clausen’s problem in four iterations. The utility of the proposed method is evident from the extensive computational results on test problems adapted from NETLIB. Preliminary results indicate that this dual direct cosine simplex algorithm (DDCA) reduces the number of iterations of two-phase method.

scholarly journals On a Dual Direct Cosine Simplex Type Algorithm and Its Computational Behavior

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Elsayed Badr ◽  
Sultan Almotairi
Keyword(s):  
Simplex Algorithm ◽  
Benchmark Problems ◽  
Phase Method ◽  
Two Phase ◽  
Preliminary Results ◽  
Dual Version ◽  
Type Algorithm ◽  
Linear Problems ◽  
Computational Behavior ◽  
Number Of Iterations

The goal of this paper is to propose a dual version of the direct cosine simplex algorithm (DDCA) for general linear problems. The proposed method has not artificial variables, so it is different from both the two-phase method and big-M method. Our technique solves the dual Klee–Minty problem via two iterations and solves the dual Clausen problem via four iterations. The power of the proposed algorithm is evident from the extensive experimental results on benchmark problems adapted from NETLIB. Preliminary results indicate that this dual direct cosine simplex algorithm (DDCA) reduces the number of iterations of the two-phase method.

scholarly journals On the Simplex Algorithm Initializing

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Nebojša V. Stojković ◽  
Predrag S. Stanimirović ◽  
Marko D. Petković ◽  
Danka S. Milojković
Keyword(s):  
Feasible Solution ◽  
Numerical Test ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
Initial Solution ◽  
Test Problems ◽  
Basic Feasible Solution ◽  
Cpu Time ◽  
Starting Point ◽  
Number Of Iterations

This paper discusses the importance of starting point in the simplex algorithm. Three different methods for finding a basic feasible solution are compared throughout performed numerical test examples. We show that our two methods on theNetlibtest problems have better performances than the classical algorithm for finding initial solution. The comparison of the introduced optimization softwares is based on the number of iterative steps and on the required CPU time. It is pointed out that on average it takes more iterations to determine the starting point than the number of iterations required by the simplex algorithm to find the optimal solution.

scholarly journals A Two-Phase Support Method for Solving Linear Programs: Numerical Experiments

2012 ◽  
Vol 2012 ◽  
pp. 1-28 ◽  
Author(s):  
Mohand Bentobache ◽  
Mohand Ouamer Bibi
Keyword(s):  
Real Life ◽  
Simplex Algorithm ◽  
Oil Refinery ◽  
Test Problems ◽  
Large Set ◽  
Linear Programs ◽  
Two Phase ◽  
Life Problems ◽  
Bounded Variables ◽  
Matlab Programming

We develop a single artificial variable technique to initialize the primal support method for solving linear programs with bounded variables. We first recall the full artificial basis technique, then we will present the proposed algorithm. In order to study the performances of the suggested algorithm, an implementation under the MATLAB programming language has been developed. Finally, we carry out an experimental study about CPU time and iterations number on a large set of the NETLIB test problems. These test problems are practical linear programs modelling various real-life problems arising from several fields such as oil refinery, audit staff scheduling, airline scheduling, industrial production and allocation, image restoration, multisector economic planning, and data fitting. It has been shown that our approach is competitive with our implementation of the primal simplex method and the primal simplex algorithm implemented in the known open-source LP solver LP_SOLVE.

Solving Neutrosophic Linear Programming Problems With Two-Phase Approach

2020 ◽  
pp. 391-412
Author(s):  
Elsayed Metwalli Badr ◽  
Mustafa Abdul Salam ◽  
Florentin Smarandache
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Feasible Solution ◽  
Simplex Algorithm ◽  
Phase Method ◽  
Basic Feasible Solution ◽  
Two Phase ◽  
Linear Programming Problems

The neutrosophic primal simplex algorithm starts from a neutrosophic basic feasible solution. If there is no such a solution, we cannot apply the neutrosophic primal simplex method for solving the neutrosophic linear programming problem. In this chapter, the authors propose a neutrosophic two-phase method involving neutrosophic artificial variables to obtain an initial neutrosophic basic feasible solution to a slightly modified set of constraints. Then the neutrosophic primal simplex method is used to eliminate the neutrosophic artificial variables and to solve the original problem.

Peristaltic Carreau-Yasuda nanofluid flow and mixed heat transfer analysis in an asymmetric vertical and tapered wavy wall channel

2020 ◽  
Vol 1 (1) ◽  
pp. 128-140 ◽  
Author(s):  
Mohammad Hatami ◽  
◽  
D Jing ◽  
Keyword(s):  
Heat Transfer ◽  
Least Square Method ◽  
Weissenberg Number ◽  
Least Square ◽  
Heat Transfer Analysis ◽  
Phase Method ◽  
Nanofluid Flow ◽  
Two Phase ◽  
Nanoparticles Concentration ◽  
The Right

In this study, two-phase asymmetric peristaltic Carreau-Yasuda nanofluid flow in a vertical and tapered wavy channel is demonstrated and the mixed heat transfer analysis is considered for it. For the modeling, two-phase method is considered to be able to study the nanoparticles concentration as a separate phase. Also it is assumed that peristaltic waves travel along X-axis at a constant speed, c. Furthermore, constant temperatures and constant nanoparticle concentrations are considered for both, left and right walls. This study aims at an analytical solution of the problem by means of least square method (LSM) using the Maple 15.0 mathematical software. Numerical outcomes will be compared. Finally, the effects of most important parameters (Weissenberg number, Prandtl number, Brownian motion parameter, thermophoresis parameter, local temperature and nanoparticle Grashof numbers) on the velocities, temperature and nanoparticles concentration functions are presented. As an important outcome, on the left side of the channel, increasing the Grashof numbers leads to a reduction in velocity profiles, while on the right side, it is the other way around.

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

The Method of Dynamic Reserves Prediction for a Constant Volume Gas Reservoir

2013 ◽  
Vol 275-277 ◽  
pp. 456-461
Author(s):  
Lei Zhang ◽  
Lai Bing Zhang ◽  
Bin Quan Jiang ◽  
Huan Liu
Keyword(s):  
Pressure Drop ◽  
Material Balance ◽  
Production Method ◽  
Gas Production ◽  
Constant Volume ◽  
Phase Method ◽  
Gas Reservoirs ◽  
Two Phase ◽  
Material Balance Method ◽  
Unit Pressure

The accurate prediction of the dynamic reserves of gas reservoirs is the important research content of the development of dynamic analysis of gas reservoirs. It is of great significance to the stable and safe production and the formulation of scientific and rational development programs of gas reservoirs. The production methods of dynamic reserves of gas reservoirs mainly include material balance method, unit pressure drop of gas production method and elastic two-phase method. To clarify the characteristics of these methods better, in this paper, we took two typeⅠwells of a constant volume gas reservoir as an example, the dynamic reserves of single well controlled were respectively calculated, and the results show that the order of the calculated volume of the dynamic reserves by using different methods is material balance method> unit pressure drop of gas production method >elastic two-phase method. Because the material balance method is a static method, unit pressure drop of gas production method and elastic two-phase method are dynamic methods, therefore, for typeⅠwells of constant volume gas reservoirs, when the gas wells reached the quasi-steady state, the elastic two-phase method is used to calculate the dynamic reserves, and when the gas wells didn’t reach the quasi-steady state, unit pressure drop of gas production method is used to calculate the dynamic reserves. The conclusion has some certain theoretical value for the prediction of dynamic reserves for constant volume gas reservoirs.

Sign in / Sign up

Export Citation Format

Share Document