CONSTRAINED CONJUGATE DIRECTIONS METHODS FOR DESIGN OPTIMIZATION OF LARGE SYSTEMS

The concept of conjugate directions for unconstrained optimization is extended to solve general dense constrained minimization problems that have no special structure to exploit sparse matrix techniques. The constrained steepest descent (CSD) directions obtained as the solution of a quadratic programming (QP) subproblem are used to generate the constrained conjugate directions (CCD). The resulting algorithm is quite simple, and its finite convergence and other properties have been proved for convex quadratic programming problems. For general problems, restart procedures, step size determination, and potential constraint strategy are discussed. A set of 41 structural design test problems having 2-489 design variables and 7-1051 constraints, excluding the simple bounds, is used to evaluate the method and its variations. The new method performs much better than the CSD method; however, its performance is not as good as the sequential quadratic programming (SQP) method for moderate size problems. This result is expected and is quite similar to the one for the unconstrained counterpart of the method. For a large-scale problem, the new method performs better than both the CSD and the SQP methods. It is concluded that the basic concept of constrained conjugate directions is a viable approach for large-scale optimization problems. It needs to be fully developed and evaluated for such problems.