Neural network approach for general assignment problem

Abstract

Discusses a neural network approach for the general assignment problem. This problem is the generalization of the well known assignment problem and can be formulated as a zero-one integer programming problem. The authors transform this zero-one integer programming problem into an equivalent nonlinear programming problem by replacing zero-one constraints with quadratic concave equality constraints. The authors propose two kinds of neural network structures based on a penalty function method and an augmented Lagrangian multiplier method, and compare them by theoretical analysis and numerical simulation. The authors show that the penalty function-based neural network approach is not good for the combinatorial optimization problem because it falls into the dilemma of terminating at an infeasible solution or sticking at any feasible solution, and that the augmented Lagrangian multiplier method-based neural network can alleviate this suffering in some degree.