An Improved Simplex-Genetic Method to Solve Hard Linear Programming Problems

Authors:
Juan Frausto-Solís;Alma Nieto-Yáñez
Affiliations:
ITESM Campus Cuernavaca, Reforma 182-A, Col Lomas De Cuernavaca, 62589, Temixco Morelos, México;ITESM Campus Cuernavaca, Reforma 182-A, Col Lomas De Cuernavaca, 62589, Temixco Morelos, México
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
Year:
2007

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Abstract

Linear programming (LP) is an important field of optimization. Even though, interior point methods are polynomial algorithms, many LP practical problems are solved more efficiently by the primal and dual revised simplex methods (RSM); however, RSM has a poor performance in hard LP problems (HLPP) as in the Klee-Minty Cubes problem. Among LP methods, the hybrid method known as Simplex-Genetic (SG) is very robust to solve HLPP. The objective of SG is to obtain the optimal solution of a HLPP, taking advantages from each one of the combined methods -a genetic algorithm (GA) and the classical primal RSM-. In this paper a new SG method named Improved Simplex Genetic Method (ISG) is presented. ISG combines a GA (with special genetic operators) with both primal and dual RSM. Numerical experimentation using some instances of the Klee-Minty cubes problem shows that ISG has a better performance than both RSM and SG.