Accession Number : ADA193084

Title :   Making Progress during a Stall in the Simplex Algorithm.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB

Personal Author(s) : Dantzig, George B

PDF Url : ADA193084

Report Date : Feb 1988

Pagination or Media Count : 11

Abstract : All the standard methods for avoiding cycling in the simplex algorithm set up a subprogram related to the blocking rows in the canonical form and look for an improving homogeneous solution. The method proposed in this paper does not. Instead, the Gass-Saaty parametric method applied to the objective (cost) form is used to choose the incoming column. The pivot-row choice among blocking rows, i.e., those tied for pivot, is arbitrary. A simple anti-cycling device is used which avoids dual degeneracy of the parameterized objective with probability one. Tests were run on nine highly degenerate practical test problems ranging in size from small to large. Using MINOS software, the standard simplex method required 31,195 iterations of which 20,504 (or 66%) were blocked pivots. Using the parametric scheme required 14,379 iterations, of which 9,481 or 66% were also blocked. The reduction in the number of iterations for this set of highly degenerate test problems is over 50%. CPU time reduction under the current way of implementation is 40%.

Descriptors :   *SIMPLEX METHOD, *ALGORITHMS, BLOCKING, COMPUTER PROGRAMS, COSTS, HOMOGENEITY, ITERATIONS, PARAMETRIC ANALYSIS, REDUCTION, SOLUTIONS(GENERAL), STANDARDIZATION, TIME, LINEAR PROGRAMMING, STALLING

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE