A New Dynamic Basis Algorithm for Solving Linear Programming Problems for Engineering Design

Abstract

A new linear programming algorithm is proposed which has significant advantages compared to a traditional simplex method. A search direction is generated along a common edge of the active constraint set. This direction is followed in order to identify candidate constraints and to modify the current basis. The dimension of the basis matrix begins with a single element and dynamically increases but remains less than or equal to the number of design variables. This is true regardless of the number of inequality constraints present including upper and lower bounds. The proposed method can operate equally well from a feasible or infeasible point. The pivot operation and artificial variable strategy of the simplex method are not used. Examples are presented and results are compared to those generated by a traditional revised simplex algorithm. Extensions are presented for both exterior and interior versions of the approach.