Novel multi-objective topology optimization method for stiffness and stress of continuum structures

In this paper, a topology optimization method combining Bi-directional Evolutionary Structural Optimization (BESO) and Fast Non-dominated Sorting Genetic Algorithm II (NSGA-II) is proposed, which is called BESO-NSGA-II. To effectively fuse the two algorithms, a semi-random double-penalized crossover and mutation operator is developed. The proposed algorithm extends the traditional single-objective optimization to a double objective optimization problem, and investigates the influence of the stress norm parameters on the optimization results. To verify the effectiveness of the new method, several examples of 2D structural stiffness and stress optimization are given. At the same time, the optimization design of each model was repeated six times to demonstrate the ability of the new method to converge to a solution. Compared with BESO, BESO-NSGA-II can effectively realize the double objective optimization of stiffness and stress, and eliminate the stress concentration phenomenon on the premise of ensuring that the structure has greater stiffness.