Shape optimization of thin-walled steel sections using graph theory and ACO algorithm

• Applications of the graph theory to optimization of thin-walled steel sections are presented.
• Shape optimization of open sections is treated as an all-pairs shortest path problem.
• Shape optimization of closed sections is treated as a minimum mean cycle problem.
• The graph theory and the ant colony based algorithm are combined to solve the problems.
• New benchmark optimization problems for thin-walled steel sections are presented.

This paper presents an intuitive procedure for the shape and sizing optimizations of open and closed thin-walled steel sections using the graph theory. The goal is to find shapes of optimum mass and strength (bi-objectives). The shape optimization of open sections is treated as a multi-objective all-pairs shortest path problem, while that of closed sections is treated as a multi-objective minimum mean cycle problem. The sizing optimization of a predetermined shape is treated as a multi-objective single-pair shortest path problem. Multi-colony ant algorithms are formulated for solving the optimization problems. The verification and numerical examples involving the shape optimizations of open and closed thin-walled steel sections and the sizing optimization of trapezoidal roof sheeting are presented.