Modified Ant Colony Optimization for Topology Optimization of Geometrically Nonlinear Structures

Abstract

Standard Ant Colony Optimization (ACO) algorithm cannot provide an optimal topology for geometrically nonlinear structural problems. The reason is that the tangential stiffness matrix of low-density elements may become zero or negative, which leads to serious numerical instability problems, or the standard ACO algorithm cannot search the really efficient elements because of improper element search method. A modified ant colony optimization (MACO) algorithm is suggested to improve computational efficiency and suitability of standard ACO algorithm in topology optimization for these problems. A continuous variable, called the "Element Contribution Significance (ECS)," is introduced, which serves to replace the positions of ants in the standard ACO algorithm, and assess the importance of each element in the optimization process. The optimized topologies based on MACO algorithm are compared to those of the other topology methods. From the comparison, it is verified that MACO algorithm can successfully be applied to topology optimization for geometrically nonlinear structures, as well as provide stable and robust topologies.