This study aims at utilizing the dynamic behavior of artificial neural networks (ANNs) to solve multiobjective programming (MOP) and multilevel programming (MLP) problems. The traditional and non-traditional approaches to the MLP are first classified into five categories. Then, based on the approach proposed by Hopfield and Tank , the optimization problem is converted into a system of nonlinear differential equations through the use of an energy function and Lagrange multipliers. Finally, the procedure is extended to MOP and MLP problems. To solve the resulting differential equations, a steepest descent search technique is used. This proposed nontraditional algorithm is efficient for solving complex problems, and is especially useful for implementation on a large-scale VLSI, in which the MOP and MLP problems can be solved on a real time basis. To illustrate the approach, several numerical examples are solved and compared.
Computers & Mathematics with Applications 48(1–2), pp.95–108