A dynamic adaptive particle swarm optimization and genetic algorithm is presented to solve constrained engineering optimization problems. A dynamic adaptive inertia factor is introduced in the basic particle swarm optimization algorithm to balance the convergence rate and global optima search ability by adaptively adjusting searching velocity during search process. Genetic algorithm–related operators including a selection operator with time-varying selection probability, crossover operator, and n-point random mutation operator are incorporated in the particle swarm optimization algorithm to further exploit optimal solutions generated by the particle swarm optimization algorithm. These operators are used to diversify the swarm and prevent premature convergence. Tests on nine constrained mechanical engineering design optimization problems with different kinds of objective functions, constraints, and design variables in nature demonstrate the superiority of the dynamic adaptive particle swarm optimization and genetic algorithm against several other meta-heuristic algorithms in terms of solution quality, robustness, and convergence rate in most cases.

The rolled aluminum alloy sheets usually have anisotropic properties that affect its ductile fracture behavior. In order to study the plastic anisotropy and ductile fracture behavior of aluminum alloy 6016 sheet, the Hill48 anisotropic yield criterion is introduced into the Gurson–Tvergaard–Needleman (GTN) model forming an anisotropic GTN model. In this model, two groups of Hill48 anisotropic yield constants, which are respectively calculated by Lankford's coefficient $R$ in different directions and the combination of the Lankford's coefficient $R$ and yield stress ${\sigma }_y$in different directions, are separately used to describe anisotropic mechanical behaviors. The failure void volume fraction $f_F$ is identified through microstructure analysis and the other damage parameters are calibrated through a finite element (FE) inverse calibration method. The abilities of these two groups of Hill48 anisotropic yield constants in predicting anisotropic mechanical behaviors of aluminum alloy 6016 sheet are examined by performing FE simulations of 0°, 45°, and 90° plate tensile tests, deep-drawing tests and Erichsen cupping tests. Results show that the Hill48 anisotropic yield constants calculated by the Lankford's coefficient $R$in different directions have a better ability to predict local anisotropic plastic deformation especially the earing effect in the deep-drawing test, but the Hill48 anisotropic yield constants calculated by the combination of the Lankford's coefficient $R$ and yield stress ${\sigma }_y$ in different directions have a better prediction ability in predicting global anisotropic mechanical behaviors of the aluminum alloy 6016 sheet.