抄録
In design problems of actual engineering systems, many design variables take discrete and not continuous values on account of the inherent characteristics. Hence, the optimization of the design is considered as a combinatorial optimization problem. Branch-and-Bound method has been the traditional technique to solve such problems. Recently, Hopfield, J.J. showed that some combinatorial optimization problems can be solved on an artificial neural network system.
In this paper, an algorithmic procedure with neural networks for solving combinatorial optimization problems is proposed which attains very good (not necessarily best) solutions by systematically changing the Lagrange multipliers vector for the constraint equations in the problem. The proposed method can be applied to both linear and quadratic programming problems with discrete control variables. Numerical examples for optimum design problems of frame structures are provided to illustrate the basic properties and applicability of the proposed method.
The neural network system that can solve combinatorial optimization problems performing parallel computation is extremely attractive as a future CAD system.
