2018/03/07 by David Yang Gao, Gao, David Yang, Elaf Jaafar Ali +1
Computer Science · Engineering · Mathematics · #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Optimization and Control (math.OC) #Topology Optimization in Engineering #math.OC
paper · pdf · doi:10.48550/arxiv.1803.02615
32 pages, 11 figures, 10 tables
openalex publication_date 2018/03/07 · arxiv created 2018/06/21 · arxiv updated 2018/06/22 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
This paper demonstrates a mathematically correct and computationally powerful method for solving 3D topology optimization problems. This method is based on canonical duality theory (CDT) developed by Gao in nonconvex mechanics and global optimization. It shows that the so-called NP-hard knapsack problem in topology optimization can be solved deterministically in polynomial time via a canonical penalty-duality (CPD) method to obtain precise 0-1 global optimal solution at each volume evolution. The relation between this CPD method and Gao's pure complementary energy principle is revealed for the first time. A CPD algorithm is proposed for 3-D topology optimization of linear elastic structures. Its novelty is demonstrated by benchmark problems. Results show that without using any artificial technique, the CPD method can provide mechanically sound optimal design, also it is much more powerful than the well-known BESO and SIMP methods. Additionally, computational complexity and conceptual/mathematical mistakes in topology optimization modeling and popular methods are explicitly addressed.