This paper presents an adaptation of an existing dynamic trajectory method for unconstrained minimization to handle constrained optimization problems. This is done by the application of a dynamic penalty parameter procedure to allow for the constraints. The method is applied to structural optimization problems that involve the determination of minimum weight structures of trusses and frames, subject to stress, displacement, and frequency constraints, under various prescribed load conditions. Because structural problems, in general, require detailed finite-element analyses to evaluate the constraint functions, the direct application of the trajectory method, requiring updated information at each step along the path, would be expensive. This problem is overcome by the successive application of the trajectory method to approximate quadratic subproblems that can be solved economically. The comprehensive new approach is called the DYNAMIC-Q method. The method is successfully applied to a number of truss and frame problems and is found to be both reliable and easy to use. © 1994.
Snyman, J. A., Stander, N., & Roux, W. J. (1994). A dynamic penalty function method for the solution of structural optimization problems. Applied Mathematical Modelling, 18(8), 453–460. https://doi.org/10.1016/0307-904X(94)90307-7