Title: Improving the efficiency of the simplex algorithm based on a geometric explanation of phase 1

Authors: Daniel Solow, Hans Halim

Addresses: Department of Operations, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH 44106, USA. ' Department of Operations, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH 44106, USA

Abstract: An open question pertaining to the simplex algorithm is where phase 1 terminates on the feasible region. Here, computer simulations support the conjecture that phase 1 terminates at a feasible point geometrically close to the starting point. This observation leads to a coordinate transformation for bounded Linear Programs (LP) that requires fewer iterations in phase 2. This is confirmed by computational experiments on random LPs and Netlib problems and shows generally increasing benefits as the number of negative coefficients in the minimisation objective function increases. Though not winning on all Netlib problems, the coordinate transformation saves 2–11% of the CPU time.

Keywords: linear programming; simplex algorithm; phase 1; phase 2; coordinate transformations.

DOI: 10.1504/IJOR.2009.025701

International Journal of Operational Research, 2009 Vol.5 No.4, pp.408 - 428

Available online: 23 May 2009 *

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