scholarly journals On pivot rules for simplex method of interior points, and their investigation on Klee-Minty cube

2002 ◽  
Vol 15 (2) ◽  
pp. 281-294
Author(s):  
Knarik Tunyan
Keyword(s):  
Simplex Method ◽  
Method Development ◽  
Feasible Solution ◽  
Convex Combination ◽  
Optimal Point ◽  
Elimination Method ◽  
Positive Vector ◽  
Pivot Rules ◽  
Interior Points ◽  
Gauss Transformation

In [25] it was proposed a parametric linear transformation, which is a "convex" combination of the Gauss transformation of elimination method and the Gram-Schmidt transformation of modified orthogonalization process. Using this transformation, in particular, elimination methods were generalized, Dantzig's optimality criterion and simplex method were developed [26]. The essence of the simplex method development is the following. At each sth step the pivot (positive) vector of length Ks is selected, that allows us to move to improved feasible solution after the step of the generalized Gauss-Jordan complete elimination method. In this method the movement to the optimal point takes place over pseudobases, i.e., over interior points. This method is parametric and finite. Since the method is parametric there are various variants to choose the pivot vectors (rules), in the sense of their lengths and indices. In this article we propose three rules, which are the development of Dantzig's first rule. These rules are investigated on the Klee-Minty cube (problem) [14, 31]. It is shown that for two rules the number of steps necessary equals to 2n, and for third rule we obtain the standard simplex method with the largest coefficient rule, i.e., the number of steps for solving this problem is 2n - 1.

An Extended Simplex Algorithm for Linear Programming

2012 ◽  
Vol 532-533 ◽  
pp. 1626-1630
Author(s):  
Guo Guang Zhang
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Feasible Solution ◽  
Simplex Algorithm ◽  
Linear Program ◽  
Problem Solution ◽  
Test Number ◽  
The Times ◽  
Definition Of

Simplex method is one of the most useful methods to solve linear program. However, before using the simplex method, it is required to have a base feasible solution of linear program and the linear program is changed to thetypical form. Although there are some methods to gain the base feasible solution of linear program, artificial variablesare added and the times of calculating are increased with these calculations. In this paper, an extended algorithm of the simplex algorithm is established, the definition of feasible solution in the new algorithm is expended, the test number is not the same sign in the process of finding problem solution. Explained the principle of the new algorithm and showed results of LP problems calculated by the new algorithm.

scholarly journals Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 356
Author(s):  
Rujira Visuthirattanamanee ◽  
Krung Sinapiromsaran ◽  
Aua-aree Boonperm
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Phase 1 ◽  
Simplex Algorithm ◽  
Linear Programs ◽  
Feasible Point ◽  
Optimal Point ◽  
Dual Simplex Method ◽  
Feasible Points ◽  
Initial Starting

An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. With this initial starting feasible point, in phase 2, it sequentially jumps to the improved objective feasible points. The last phase reinstates the rest of the non-acute constraints and uses the dual simplex method to find the optimal point. The computation results show that this method is more efficient than the standard simplex method and the artificial-free simplex algorithm based on the non-acute constraint relaxation for 41 netlib problems and 280 simulated linear programs.

scholarly journals PENERAPAN PROGRAM LINIER MENGGUNAKAN METODE DUAL SIMPLEKS DAN METODE QUICK SIMPLEKS UNTUK MEMINIMUMKAN BIAYA (STUDI KASUS: KELOMPOK WANITA TANI (KWT) SENTOSA SANTUL)

2021 ◽  
Vol 4 (1) ◽  
pp. 117-132
Author(s):  
Elfira - Safitri ◽  
Sri Basriati ◽  
Elvina Andiani
Keyword(s):  
Simplex Method ◽  
Feasible Solution ◽  
Research Result ◽  
Optimal Solution ◽  
Women Farmers ◽  
Food Crops ◽  
Dual Simplex Method ◽  
Dual Simplex ◽  
Number Of Iterations ◽  
Minimum Costs

The Sentosa  Santul Women Farmers Group (KWT) is a group of women farmers in Dusun Santul, Kampar Utara District an is engaged in the field of food crops is chili. The Sentosa Santul Women Farmers group (KWT) uses 4 types of fertilizers for chili plant fertilization, namely hydro complex fertilizer, phonska, NPK Zamrud and goat manure.The KWT wants the minimum fertilizer cost but the nutrients in the plants are met. The method used in this research is the dual simplex method and the quick simplex method. The purpose of this study is to determine the minimum costs that must be incurred by the Womens Farmer Group (KWT) for fertilization using the dual simplex method and the quick simplex method to obtain an optimum and feasible solution. For the dual simplex method, the optimum and feasible solution were obtained using the Gauss Jordanelimination. While the quick simplex method, the solution is illustrated using a matrix to reduce the number of iterations needed to achieve the optimal solution. Based on the research result, it is found that the quick simplex method is more efficient than the dual simplex method. This can be seen from the number of iterations carried out. Dual simplex method iteration there are two iterations and quick simplex one iteration. The dual simplex method and the quick simplex method produce the same value.

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.

Simplex Optimization as a Step in Method Development

1976 ◽  
Vol 59 (6) ◽  
pp. 1204-1207 ◽  
Author(s):  
Thomas J Dols ◽  
Bernard H Armbrecht
Keyword(s):  
Analysis Of Variance ◽  
Simplex Method ◽  
Method Development ◽  
Optimization Procedure ◽  
Performance Characteristics ◽  
Feedback Strategy ◽  
Simplex Optimization

Abstract In the course of method development, an optimization procedure should be performed before critical performance characteristics are measured. Interaction among the operational steps should be assumed to exist. The analysis of variance or the simplex procedures are designed to determine defined optimal responses. Other things being equal, the simplex method is more efficient in terms of the number of experiments required. This is due, in part, to the sequentially operated feedback strategy employed. Decisions are made according to 5 defined rules.

scholarly journals إيجاد الحل المقبول (الممكن) والأمثل لأنموذج البرمجة الخطية في ظل عدم تحقق شرطّي الإمكانية والأمثلية

2008 ◽  
Vol 14 (52) ◽  
pp. 257
Author(s):  
سرمد علوان صالح
Keyword(s):  
Linear Programming ◽  
Decision Maker ◽  
Simplex Method ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Dual Simplex Method ◽  
Effective Factor ◽  
Dual Simplex

Consider the Linear Programming (LP) active & effective factor in decision maker & taker process . So that given certain goals , the Significance of (LP) in solving & evaluation the activity during one tools (General Simplex Mehtod)that the solution is Feasible &no optimal then called (Primal Simplex Method) or vice-versa then called(Dual Simplex Method).Same of cases the solution is infeasible & no optimal then using the two methods alternatively once to find the feasible solution and other to find optimal solution              

SHORTEST PATH SIMPLEX ALGORITHM WITH A MULTIPLE PIVOT RULE: A COMPARATIVE STUDY

2010 ◽  
Vol 27 (06) ◽  
pp. 677-691 ◽  
Author(s):  
A. SEDEÑO-NODA ◽  
C. GONZÁLEZ-MARTÍN
Keyword(s):  
Comparative Study ◽  
Shortest Path ◽  
Simplex Method ◽  
Computational Study ◽  
Simplex Algorithm ◽  
Running Time ◽  
Pivot Rules

This paper introduces a new multiple pivot shortest path simplex method by choosing a subset of non-basic arcs to simultaneously enter into the basis. It is shown that the proposed shortest path simplex method requires O (n) multiple pivots and its running time is O (nm). Results from a computational study comparing the proposed method from previously known methods are reported. The experimental show that the proposed rule is more efficient than the considered shortest path simplex pivot rules.

scholarly journals Feasibility Achievement without the Hassle of Artificial Variables: A Computational Study

2019 ◽  
pp. 1-14
Author(s):  
Syed Inayatullah ◽  
Nasir Touheed ◽  
Muhammad Imtiaz ◽  
Tanveer Ahmed Siddiqi ◽  
Saba Naz ◽  
...  
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Feasible Solution ◽  
Simple Technique ◽  
Computational Study ◽  
Phase 1 ◽  
Primary Result ◽  
Underlying Geometry ◽  
Better Than

The purpose of this article is to encourage students and teachers to use a simple technique for finding feasible solution of an LP. This technique is very simple but unfortunately not much practiced in the textbook literature yet. This article discusses an overview, advantages, computational experience of the method. This method provides some pronounced benefits over Dantzig’s simplex method phase 1. For instance, it does not require any kind of artificial variables or artificial constraints; it could directly start with any infeasible basis of an LP. Throughout the procedure it works in original variables space hence revealing the true underlying geometry of the problem. Last but not the least; it is a handy tool for students to quickly solve a linear programming problem without indulging with artificial variables. It is also beneficial for the teachers who want to teach feasibility achievement as a separate topic before teaching optimality achievement. Our primary result shows that this method is much better than simplex phase 1 for practical Net-lib problems as well as for general random LPs.

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