A DVCC-based non-linear analog circuit for solving linear programming problems

Abstract

This paper presents a neural circuit for solving linear programming problem (LPP). The objective is to minimize a first order cost function subject to linear constraints. The dynamic analog circuit, consisting of N identical units for N variable problem, can solve the general LPP and always converges to the optimal solution in constant time, irrespective of the initial conditions, which is of the order of its time constant. The proposed circuit employs non-linear feedback, in the form of Differential Voltage Current Conveyor (DVCC) based unipolar comparators, to introduce transcendental terms in the energy function ensuring fast convergence to the solution. Further, the use of resistors to generate weighted inputs to the neurons is avoided. Instead, DVCCs are utilized to directly generate the required scaled currents. PSPICE simulation results are presented for a chosen optimization problem and are found to agree with the algebraic solution.