Discrete topology and sizing optimization of frame structures with compliance constraints: A semidefinite programming-based approach

Abstract

The discrete topology and sizing optimization of frame structures with compliance constraints is studied using a novel approach, which is capable of finding the theoretical lower bounds and high-quality discrete solutions in an efficient manner. The proposed approach works by reformulating the discrete problem as a relaxed semidefinite programming (SDP) problem. This reformulation is made possible by a linear relaxation of the original discrete space and the elimination of the nonconvex equilibrium equation using a semidefinite constraint. A continuous global optimum is first derived using existing solvers and then the discrete solution is discovered by the neighborhood search. Numerical examples are presented, including the sizing optimization of 2-Bay 6-Story frame and 3-Bay 10-Story frame, the topology and sizing optimization of 2-Bay 6-Story braced frame. A topology and sizing example with multiple load cases is also provided. The proposed approach and three other metaheuristic algorithms are used to solve these examples. Theoretical lower bounds for these examples can be efficiently discovered by the proposed approach. For the sizing problems, the discrete solutions by the proposed approach are all better than the other algorithms. For the topology and sizing problems, the proposed approach achieves discrete solutions better than genetic algorithm, but worse than the other metaheuristics. The computational superiority of the proposed approach is validated in all the examples.

Iterative design of satellite structures and topology optimisation methods

“…Several alternative concepts seeking to employ meta-heuristic methodologies in TO have been proposed but have not undergone further development. For instance, there are strategies such as multiobjective TO grounded in bacterial chemotaxis [150], a ground structure approach utilising curved elements [151], a binary bat algorithm [152], a hybrid firefly and particle swarm optimisation (PSO) algorithm [153], and a semi-definite programming-based approach coupled with a GA [154].…”

On Topology Optimisation Methods and Additive Manufacture for Satellite Structures: A Review

“…There exist a plethora of other proposals aiming to apply metaheuristic approaches with TO, but they have not experienced further development. We observed a multi-objective TO based on bacterial chemotaxis [211], a joint firefly and particle swarm optimisation (PSO) algorithm [212], a symbiotic organisms search algorithm [213], an improved electrosearch algorithm [214], a plasma generation optimisation [215], a binary bat algorithm [216], an enhanced binary GA along with morphological reconstruction [217], a semi-definite programming-based approach combined with a GA [218], as well as a ground structure approach based on curved elements [219]. A constant in metaheuristic methods is the large quantity of iterations needed to converge which makes them difficult to extend to 3D design spaces where the computational burden increases considerably.…”