Publications

Journal Article

A novel approach to discrete truss design problems using mixed integer neighborhood search

authors

M. Shahabsafa, A. Mohammad–Nezhad, T. Terlaky, L. Zuluaga, S. He, J. T. Hwang, and J. R. R. A. Martins

journal

Structural and Multidisciplinary Optimization, 582411–2429, 2018

doi

10.1007/s00158-018-2099-8

PDF 
@article{Shahabsafa2018a,
  author = {Shahabsafa, Mohammad and Mohammad--Nezhad, Ali and Terlaky, Tamas and Zuluaga, Luis and He, Sicheng and Hwang, John T. and Martins, Joaquim R. R. A.},
  doi = {10.1007/s00158-018-2099-8},
  journal = {Structural and Multidisciplinary Optimization},
  month = dec,
  pages = {2411--2429},
  title = {A novel approach to discrete truss design problems using mixed integer neighborhood search},
  volume = {58},
  year = {2018}
}
Google Scholar

Discrete truss sizing problems are very challenging to solve due to their combinatorial, nonlinear, non-convex nature. Consequently, truss sizing problems become unsolvable as the size of the truss grows. To address this issue, we consider various mathematical formulations for the truss design problem with the objective of minimizing weight, while the cross-sectional areas of the bars take only discrete values. Euler buckling constraints, Hooke’s law, and bounds for stress and displacements are also considered. We propose mixed integer linear optimization (MILO) reformulations of the non-convex mixed integer models. The resulting MILO models are not solvable with existing MILO solvers as the size of the problem grows. Our novel methodology provides high-quality solutions for large-scale real truss sizing problems, as demonstrated through extensive numerical experiments.