Parametric optimization of bar structures with discrete and continuous design variables using improved gradient projection method

Abstract

The paper considers a parametric optimization problem for the bar structures formulated as nonlinear programming task, where the purpose function and non-linear constraints of the mathematical model are continuously differentiable functions of the design variables. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimization problem. A discretization technique for the design variables that should vary discretely has been proposed. The discretization of the optimal design solution obtained in the continuous space of the design variables is performed by the purposefully selecting discrete points around the point of the continuous optimum. The comparison of the optimization results presented by the paper demonstrates that improved gradient method together with proposed discretization technique for the discrete design variables converges to better solutions of the problem comparing to the meta-heuristic algorithms.