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 Comprehensive Method for Arriving at Initial Feasible Solution for Optimization Problems in Engineering with Illustrative Examples

2021 ◽  
Vol 12 (5) ◽  
pp. 1189-1205
Author(s):  
Chandrasekhar Putcha, Et. al.
Keyword(s):  
Feasible Solution ◽  
Optimization Problems ◽  
Computer Software ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
The Other ◽  
Basic Feasible Solution ◽  
Adequate Number ◽  
Comprehensive Method ◽  
Initial Feasible Solution

Two methods have been used extensively for arriving at initial basic feasible solution (IBF). One of them is Northwest corner rule and the other on is Russell method (Hillier & Lieberman, 2005.) Both methods have drawbacks. The IBF obtained is either far from optimal solution or does not have adequate number of entries to initiate transportation simplex algorithm. The Northwest Corner rule gives an initial feasible solution that is far from optimal while the IBF solution obtained using Russell method doesn’t give enough number of entries to start the transportation simplex algorithm. Hence, there is a need for developing a method for arriving at initial basic feasible solution with adequate number of entries needed to initiate transportation simplex algorithm, which can then be used to get an optimal solution. A computer software has been developed based on the new proposed method for this purpose. The proposed new method has been validated through four simple but illustrative examples.

scholarly journals A metaheuristic penalty approach for the starting point in nonlinear programming

2020 ◽  
Vol 54 (2) ◽  
pp. 451-469
Author(s):  
David R. Penas ◽  
Marcos Raydan
Keyword(s):  
Nonlinear Programming ◽  
Feasible Solution ◽  
Packing Problem ◽  
Merit Function ◽  
Test Problems ◽  
Huge Amount ◽  
Novel Approach ◽  
Starting Point ◽  
Metaheuristic Techniques ◽  
Optimization Schemes

Solving nonlinear programming problems usually involve difficulties to obtain a starting point that produces convergence to a local feasible solution, for which the objective function value is sufficiently good. A novel approach is proposed, combining metaheuristic techniques with modern deterministic optimization schemes, with the aim to solve a sequence of penalized related problems to generate convenient starting points. The metaheuristic ideas are used to choose the penalty parameters associated with the constraints, and for each set of penalty parameters a deterministic scheme is used to evaluate a properly chosen metaheuristic merit function. Based on this starting-point approach, we describe two different strategies for solving the nonlinear programming problem. We illustrate the properties of the combined schemes on three nonlinear programming benchmark-test problems, and also on the well-known and hard-to-solve disk-packing problem, that possesses a huge amount of local-nonglobal solutions, obtaining encouraging results both in terms of optimality and feasibility.

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.

A Primal-Dual Interior-Point QP Method and its Extension for Engineering Optimization

1996 ◽  
Author(s):  
Xiong Zhang ◽  
Ji Zhou ◽  
Jun Yu ◽  
Ju Cao
Keyword(s):  
Interior Point ◽  
Structural Design ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Test Problems ◽  
Engineering Optimization ◽  
Design Problems ◽  
Primal Dual ◽  
And Function ◽  
Approximate Optimal Solution

Abstract Presented in this paper is a primal-dual infeasible-interior-point quadratic programming (QP) algorithm and its extension for nonlinear programming that is suited for engineering design and structural optimization, where the number of variables are very large and function evaluations are computationally expensive. The computational experience in solving both test problems and optimal structural design problems using the algorithm demonstrated that the algorithm finds an approximate optimal solution in fewer iterations and function evaluations, the obtained solution usually is an interior feasible solution, and so the resulting method is very efficient and effective.

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.

scholarly journals Fundamentals of Transportation Problem

2021 ◽  
Vol 10 (5) ◽  
pp. 90-103
Author(s):  
Bhabani Mallia ◽  
Manjula Das ◽  
C. Das
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method

Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem.

scholarly journals Optimization of Fuzzy Species Pythagorean Transportation Problem under Preserved Uncertainties

2021 ◽  
Vol 6 (6) ◽  
pp. 1629-1645
Author(s):  
Priyanka Nagar ◽  
Pankaj Kumar Srivastava ◽  
Amit Srivastava
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Uncertain Parameters ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method ◽  
New Approach ◽  
Work Done ◽  
Cost Of Transportation

The transportation of big species is essential to rescue or relocate them and it requires the optimized cost of transportation. The present study brings out an optimized way to handle a special class of transportation problem called the Pythagorean fuzzy species transportation problem. To deal effectively with uncertain parameters, a new method for finding the initial fuzzy basic feasible solution (IFBFS) has been developed and applied. To test the optimality of the solutions obtained, a new approach named the Pythagorean fuzzy modified distribution method is developed. After reviewing the literature, it has been observed that till now the work done on Pythagorean fuzzy transportation problems is solely based on defuzzification techniques and so the optimal solutions obtained are in crisp form only. However, the proposed study is focused to get the optimal solution in its fuzzy form only. Getting results in the fuzzy form will lead to avoid any kind of loss of information during the defuzzification process. A comparative study with other defuzzification-based methods has been done to validate the proposed approach and it confirms the utility of the proposed methodology.

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.

scholarly journals Sequentially Updated Weighted Cost Opportunity Based Algorithm in Transportation Problem

2019 ◽  
Vol 38 ◽  
pp. 47-55
Author(s):  
ARM Jalal Uddin Jamali ◽  
Pushpa Akhtar
Keyword(s):  
Opportunity Cost ◽  
Feasible Solution ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Basic Feasible Solution ◽  
New Approach ◽  
Cost Matrix ◽  
Transportation Problems ◽  
The Cost ◽  
First Time

Transportation models are of multidisciplinary fields of interest. In classical transportation approaches, the flow of allocation is controlled by the cost entries and/or manipulation of cost entries – so called Distribution Indicator (DI) or Total Opportunity Cost (TOC). But these DI or TOC tables are formulated by the manipulation of cost entries only. None of them considers demand and/or supply entry to formulate the DI/ TOC table. Recently authors have developed weighted opportunity cost (WOC) matrix where this weighted opportunity cost matrix is formulated by the manipulation of supply and demand entries along with cost entries as well. In this WOC matrix, the supply and demand entries act as weight factors. Moreover by incorporating this WOC matrix in Least Cost Matrix, authors have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems. But in that approach, WOC matrix was invariant in every step of allocation procedures. That is, after the first time formulation of the weighted opportunity cost matrix, the WOC matrix was invariant throughout all allocation procedures. On the other hand in VAM method, the flow of allocation is controlled by the DI table and this table is updated after each allocation step. Motivated by this idea, we have reformed the WOC matrix as Sequentially Updated Weighted Opportunity Cost (SUWOC) matrix. The significance difference of these two matrices is that, WOC matrix is invariant through all over the allocation procedures whereas SUWOC   matrix is updated in each step of allocation procedures. Note that here update (/invariant) means changed (/unchanged) the weighted opportunity cost of the cells. Finally by incorporating this SUWOC matrix in Least Cost Matrix, we have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems.  Some experiments have been carried out to justify the validity and the effectiveness of the proposed SUWOC-LCM approach. Experimental results reveal that the SUWOC-LCM approach outperforms to find out IBFS. Moreover sometime this approach is able to find out optimal solution too. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 47-55

scholarly journals An algorithm for solving a capacitated indefinite quadratic transportation problem with enhanced flow

2014 ◽  
Vol 24 (2) ◽  
pp. 217-236 ◽  
Author(s):  
Kavita Gupta ◽  
S.R. Arora
Keyword(s):  
Special Class ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Flow Problem ◽  
Optimal Solution ◽  
Total Flow ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Indefinite Quadratic

The present paper discusses enhanced flow in a capacitated indefinite quadratic transportation problem. Sometimes, situations arise where either reserve stocks have to be kept at the supply points say, for emergencies, or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied, where the total transportation flow is enhanced to a known specified level. A related indefinite quadratic transportation problem is formulated, and it is shown that to each basic feasible solution called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this enhanced flow problem. The optimal solution to enhanced flow problem may be obtained from the optimal solution to the related transportation problem. An algorithm is presented to solve a capacitated indefinite quadratic transportation problem with enhanced flow. Numerical illustrations are also included in support of the theory. Computational software GAMS is also used.

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