Discrete multi-load truss sizing optimization: model analysis and computational experiments

Discrete multi-load truss sizing optimization (MTSO) problems are challenging to solve due to their combinatorial, nonlinear, and non-convex nature. This study highlights two important characteristics of the feasible set of MTSO problems considered here, in which force balance equations, Hooke’s law, yield stress, bound constraints on displacements, and local bucking are taken into account. Namely, we use the linear or bilinear nature of the problem to take advantage of re-scaling properties of both the problem’s design and auxiliary variables, as well as to extend the superposition principle to the case in which nonlinear stress constraints are considered. Taking advantage of these characteristics, we extend the neighborhood search mixed-integer linear optimization (NS-MILO) method (Shahabsafa et al. in SMO 63: 21–38, 2018), which provides an effective heuristic solution approach based on exact solution methods for MILO problems. Through extensive computational experiments, we demonstrate that the extended NS-MILO method provides high-quality solutions for large-scale discrete MTSO problems in a reasonable time.