Multi-constraint and multi-objective optimization of free-form reticulated shells using improved optimization algorithm

• A novel hybrid multi-objective optimization algorithm is proposed. • The computational efficiency of the optimization algorithm is improved. • A novel multi-constraint optimization method of the free-form grid structures is proposed. • An integrated multi-attribute decision-making method was used in the multi-objective optimization. • The mechanical, economic, and geometric property of the structure are improved. This paper proposes a novel multi-constraint and multi-objective optimization method to improve the integrated performance of a free-form surface reticulated shell. A geometric model was established using a non-uniform rational basis spline (NURBS) technology and bidirectional parameter line bisecting method. The height of the control points and section size of the rods were taken as optimization variables. The strain energy, economic index, and geometric integrated index were taken as optimization objectives. The sensitivity-NSGA-III hybrid multi-objective optimization algorithm (SH-NSGA-III) is developed. The SH-NSGA-III algorithm has significantly better efficiency than the NSGA-III, MOEA/D, and SPEA2 algorithms. The concept of constrained non-dominant sorting was introduced into the hybrid algorithm to process the constraints in a multi-constraint and multi-objective optimization problem. Meanwhile, an integrated multi-attribute decision-making method was used to select the optimal solution based on the Pareto optimal solution set. The multi-constraint and multi-objective optimization of a free-form surface reticulated shell was performed using the proposed method. The results demonstrated that the Pareto optimal solution set could effectively satisfy the constraints. The strain energy, economic index, and geometric integrated index were reduced by 61.4%, 36.8%, and 19.5%, respectively, and the geometric indexes were reduced by 22%, 11.5%, 20.8%, and 18.4%.