Combining interior and exterior simplex type algorithms
Pages 174 - 179
Abstract
Linear Programming (LP) is a significant research area in the field of operations research. The simplex algorithm is the most widely used and well-studied method for solving Linear Programming problems (LPs). Many algorithms have been proposed for the solution of LPs. The vast majority of these algorithms belong to three main categories: (i) Simplex-type or pivoting algorithms, (ii) interior-point methods (IPMs) and (iii) exterior point simplex type algorithms (EPSA). The aim of this paper is to present an implementation of a hybrid simplex algorithm that begins to solve the LP using an IPM and after a number of iterations continues with a primal-dual EPSA algorithm. This hybrid approach aims to take advantage of: (i) IPM strengths, which is the fast convergence in the first iterations, and (ii) EPSA strengths, i.e. the fast convergence when making steps in directions that are linear combinations of attractive directions. The idea of combining different types of linear programming algorithms is not new; to the best of our knowledge, this is the first time that interior point methods and exterior point algorithms are combined. The interior point that is calculated by IPM after a number of iterations can lead to such attractive directions. In order to gain an insight into the practical behavior of the proposed algorithm, we have performed some computational experiments over sparse randomly generated optimal LPs. Finally, in the computational study that we have conducted, we investigate the adequate number of iterations that IPM should run in order to decrease the CPU time and the iterations of the proposed algorithm.
References
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Index Terms
- Combining interior and exterior simplex type algorithms
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Published In
September 2013
359 pages
ISBN:9781450319690
DOI:10.1145/2491845
- General Chairs:
- Panayiotis H. Ketikidis,
- Kostas Margaritis,
- Ioannis Vlahavas,
- Program Chairs:
- Alexandros Chatzigeorgiou,
- George Eleftherakis,
- Ioannis Stamelos
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- The University of Sheffield: The University of Sheffield
- Alexander TEI of Thessaloniki
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Published: 19 September 2013
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PCI 2013
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- The University of Sheffield
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