A Parallel Implementation of the Revised Simplex Algorithm Using OpenMP: Some Preliminary Results

2012 ◽  
pp. 163-175 ◽  
Author(s):  
Nikolaos Ploskas ◽  
Nikolaos Samaras ◽  
Konstantinos Margaritis
Keyword(s):  
Parallel Implementation ◽  
Simplex Algorithm ◽  
Preliminary Results ◽  
Revised Simplex Algorithm

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.

Revised simplex algorithm for linear programming on GPUs with CUDA

2018 ◽  
Vol 77 (22) ◽  
pp. 30035-30050 ◽  
Author(s):  
Lili He ◽  
Hongtao Bai ◽  
Yu Jiang ◽  
Dantong Ouyang ◽  
Shanshan Jiang
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Revised Simplex Algorithm

A Decision Support System for Solving Linear Programming Problems

2014 ◽  
Vol 6 (2) ◽  
pp. 46-62
Author(s):  
Nikolaos Ploskas ◽  
Nikolaos Samaras ◽  
Jason Papathanasiou
Keyword(s):  
Linear Programming ◽  
Decision Support ◽  
Simplex Algorithm ◽  
Decision Makers ◽  
Web Interface ◽  
Web Based ◽  
Linear Programming Problems ◽  
Revised Simplex Algorithm ◽  
The Given ◽  
Programming Algorithms

Linear programming algorithms have been widely used in Decision Support Systems. These systems have incorporated linear programming algorithms for the solution of the given problems. Yet, the special structure of each linear problem may take advantage of different linear programming algorithms or different techniques used in these algorithms. This paper proposes a web-based DSS that assists decision makers in the solution of linear programming problems with a variety of linear programming algorithms and techniques. Two linear programming algorithms have been included in the DSS: (i) revised simplex algorithm and (ii) exterior primal simplex algorithm. Furthermore, ten scaling techniques, five basis update methods and eight pivoting rules have been incorporated in the DSS. All linear programming algorithms and methods have been implemented using MATLAB and converted to Java classes using MATLAB Builder JA, while the web interface of the DSS has been designed using Java Server Pages.

scholarly journals Pivoting rules for the revised simplex algorithm

2014 ◽  
Vol 24 (3) ◽  
pp. 321-332 ◽  
Author(s):  
Nikolaos Ploskas ◽  
Nikolaos Samaras
Keyword(s):  
Execution Time ◽  
Computational Study ◽  
Simplex Algorithm ◽  
Total Execution Time ◽  
Nonbasic Variable ◽  
Significant Step ◽  
Test Sets ◽  
Revised Simplex Algorithm ◽  
Pricing Rule

Pricing is a significant step in the simplex algorithm where an improving nonbasic variable is selected in order to enter the basis. This step is crucial and can dictate the total execution time. In this paper, we perform a computational study in which the pricing operation is computed with eight different pivoting rules: (i) Bland?s Rule, (ii) Dantzig?s Rule, (iii) Greatest Increment Method, (iv) Least Recently Considered Method, (v) Partial Pricing Rule, (vi) Queue Rule, (vii) Stack Rule, and (viii) Steepest Edge Rule; and incorporate them with the revised simplex algorithm. All pivoting rules have been implemented in MATLAB. The test sets used in the computational study are a set of randomly generated optimal sparse and dense LPs and a set of benchmark LPs (Netliboptimal, Kennington, Netlib-infeasible).

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