Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: PEI-WANG GAO and XING CAI
Pages: [265] - [278]
Received Date: May 26, 2008
Submitted by:
This paper presents an improved stopped simplex algorithm that aims to further decrease the stopped number of the variables. First of all, two special cuts are generated by introducing a linear transformation to cut the intersection of the objective function hyperplane and the feasible region of the linear programming relaxation problem. So, the cuts lead to the more narrow intervals of the variables on the objective function hyperplane. Secondly, the stopped simplex algorithm with the cuts is carried out to do a search on the objective function hyperplane. Finally, a test on some classical numerical examples is made. It shows that the algorithm presented here is more efficient and potential, compared with Thompson\'s algorithm.
linear programming, integer programming, objective function hyperplane, simplex algorithm, stopped simplex algorithm.
