Abstract
An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. With this initial starting feasible point, in phase 2, it sequentially jumps to the improved objective feasible points. The last phase reinstates the rest of the non-acute constraints and uses the dual simplex method to find the optimal point. The computation results show that this method is more efficient than the standard simplex method and the artificial-free simplex algorithm based on the non-acute constraint relaxation for 41 netlib problems and 280 simulated linear programs.
Highlights
A linear program (LP) is an optimization problem consisting of a linear objective function, linear equality, or inequality constraints
The maximizing linear programs are randomly generated with the objective vector c, equal to a vector of ones, and the number of constraints is higher than the number of variables, which exhibits the worst-case performance of SNAR
This paper proposes a new self-regulating artificial-free method for solving a linear program, namely SAJS
Summary
A linear program (LP) is an optimization problem consisting of a linear objective function (maximizing or minimizing), linear equality, or inequality constraints. For a small-sized linear programming model with a number of constraints and variables of less than 50, Junior et al assert that their method starts close to the optimal point This method cannot start when the initial matrix is singular. An artificial-free simplex algorithm based on the non-acute constraint relaxation (SNAR) was proposed by Boonperm and Sinapiromsaran [18] in 2014, starting with a relaxation model consisting of a group of acute constraints formed from the objective gradient vector. For this reason, a self-regulating artificial-free linear programming solver using jump and simplex method (SAJS) is proposed. A self-regulating artificial-free linear programming solver using jump and simplex method (SAJS) is proposed It integrates the jump concept on a relaxation model similar to SNAR.
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