A comparison of optimality criteria methods for stress and displacement constraints Original Research Article

Optimality criteria (OC) methods and the closely related dual method have become one of the most important class of optimization algorithms used in the practice of structural optimization. Since this class of algorithms search the optimum in the dual space of the Lagrange multipliers corresponding to the active constraints, the computational cost of the optimization is determined mostly by the number of active constraints. The efficiency of OC methods has been greatly improved recently by an OC method termed DCOC, which searches for the optimum in a usually much smaller dual subspace corresponding to only displacement multipliers. However, the relation of the DCOC with traditional OC methods is not clear, and therefore it is still difficult, even for people familiar with OC methods, to understand DCOC algorithm. This paper shows that the DCOC algorithm can be directly obtained from the traditional OC methods, which provides insights into the method. Additionally, a derivative-based version of DCOC is developed which also helps in the understanding of the method.