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

Rujira Visuthirattanamanee, Krung Sinapiromsaran and Aua-aree Boonperm
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Rujira Visuthirattanamanee: Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 13300, Thailand
Krung Sinapiromsaran: Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 13300, Thailand
Aua-aree Boonperm: Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathumthani 12121, Thailand

Mathematics, 2020, vol. 8, issue 3, 1-15

Abstract: 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.

Keywords: artificial-free linear programming method; simplex method; jump technique; non-acute constraint; relaxation model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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