Computational complexity of the exterior point simplex algorithm

Voulgaropoulou, Sophia; Samaras, Nikolaos; Sifaleras, Angelo

doi:10.1007/s12351-017-0291-z

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…In spite of that, the integration approach was managed to get back in ascending behaviour in the year of 2017 whereby it collects the percentage of usage frequency up to 60.0%. These situations indicate that the researchers were most likely to apply integration as their approach to augment the algorithm as they may find that this approach was very convenient to be worked with and offer more chances to generate new algorithm of Simplex method [2,13,[28][29].…”

Section: Arguments On Diversity Of Augmentation Approachmentioning

confidence: 99%

“…Simplex algorithm is an interesting method solving linear programming (LP) problem which is cited in extensive areas of knowledge and abundance numbers of publications versus years [1]. Plus, the most essential merits are the algorithm that is very useful in multiple dimensional optimization problems, robust technique, firm local optimization and easy to be applied numerically [2]. However, the only drawback of Simplex algorithm is involving its computation pitfall in initialization, iteration calculation and termination stage [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Multiplicity of Approach and Method in Augmentation of Simplex Method: A Review

Azlan

Mohamad

Salleh

et al. 2020

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The purpose of this review paper is to set an augmentation approach and exemplify distribution of augmentation works in Simplex method. The augmentation approach is classified into three forms whereby it comprises addition, substitution and integration. From the diversity study, the result shows that substitution approach appeared to be the highest usage frequency, which is about 45.2% from the total of percentage. This is then followed by addition approach which makes up 32.3% of usage frequency and integration approach for about 22.6% of usage frequency which makes it the least percentage of the overall usage frequency approach. Since it is being the least usage percentage, the paper is then interested to foresee a future study of integration approach that can be performed from the executed distribution of the augmentation works according to Simplex's computation stages. A theme screening is then conducted with a set of criteria and themes to come out with a proposal of new integration approach of augmentation of Simplex method.

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Section: Arguments On Diversity Of Augmentation Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiplicity of Approach and Method in Augmentation of Simplex Method: A Review

Azlan

Mohamad

Salleh

et al. 2020

View full text Add to dashboard Cite

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Predicting the Execution Time of the Primal and Dual Simplex Algorithms Using Artificial Neural Networks

2022

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Selection of the most efficient algorithm for a given set of linear programming problems has been a significant and, at the same time, challenging process for linear programming solvers. The most widely used linear programming algorithms are the primal simplex algorithm, the dual simplex algorithm, and the interior point method. Interested in algorithm selection processes in modern mathematical solvers, we had previously worked on using artificial neural networks to formulate and propose a regression model for the prediction of the execution time of the interior point method on a set of benchmark linear programming problems. Extending our previous work, we are now examining a prediction model using artificial neural networks for the performance of CPLEX’s primal and dual simplex algorithms. Our study shows that, for the examined set of benchmark linear programming problems, a regression model that can accurately predict the execution time of these algorithms could not be formed. Therefore, we are proceeding further with our analysis, treating the problem as a classification one. Instead of attempting to predict exact values for the execution time of primal and dual simplex algorithms, our models estimate classes, expressed as time ranges, under which the execution time of each algorithm is expected to fall. Experimental results show a good performance of the classification models for both primal and dual methods, with the relevant accuracy score reaching 0.83 and 0.84, respectively.

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Computational complexity of the exterior point simplex algorithm

Cited by 2 publications

References 21 publications

Multiplicity of Approach and Method in Augmentation of Simplex Method: A Review

Multiplicity of Approach and Method in Augmentation of Simplex Method: A Review

Predicting the Execution Time of the Primal and Dual Simplex Algorithms Using Artificial Neural Networks

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