Parallelizing the dual revised simplex method

This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called suboptimization and exploits parallelism across multiple iterations. T...

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Vydáno v:Mathematical programming computation Ročník 10; číslo 1; s. 119 - 142
Hlavní autoři: Huangfu, Q., Hall, J. A. J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018
Springer Nature B.V
Témata:
Computation
Full Length Paper
Iterative methods
Linear programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Parallel processing
Simplex method
Solvers
Theory of Computation
90C06
Linear programming
Parallel computing
Revised simplex method
65K05
90C05
ISSN:1867-2949, 1867-2957
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Shrnutí:This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called suboptimization and exploits parallelism across multiple iterations. The other, called SIP, exploits purely single iteration parallelism by overlapping computational components when possible. Computational results show that the performance of PAMI is superior to that of the leading open-source simplex solver, and that SIP complements PAMI in achieving speedup when PAMI results in slowdown. One of the authors has implemented the techniques underlying PAMI within the FICO Xpress simplex solver and this paper presents computational results demonstrating their value. In developing the first parallel revised simplex solver of general utility, this work represents a significant achievement in computational optimization.
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ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-017-0130-5