Currently, I am working on a problem in which I need to use MILP to model equilibrium equations in a lightweight structure. Although this is an application based question, I wondered if there is a good reference in the literature discussing the mathematical modeling of such an application based on statical concepts.

A brief discussion of structural optimization is given in chapter 15 of Linear Programming: Foundations and Extensions, by Robert J. Vanderbei.

Structural optimization is the general name that researchers use for a wide range of research topics in the literature, i.e., Shape optimization, Size optimization and also Topology optimization.

  • $\begingroup$ "use MILP to model equilibrium equations" Are those complementarity conditions? $\endgroup$ Jul 15 '19 at 17:52
  • $\begingroup$ Actually, there are two different approaches to model this kind of problems. I use the plastic form in which the forces in each joint should be in equilibrium and also the moments if the joints are welded. Those conditions are not complementarity conditions. $\endgroup$ Jul 15 '19 at 17:58
  • 1
    $\begingroup$ Given the emphasis on engineering modeling, you might have better luck at scicomp.stackexchange.com which also has a lot of optimization stuff. $\endgroup$ Jul 15 '19 at 18:00
  • $\begingroup$ @MarkL.Stone Thanks for the great suggestion, I haven’t asked my question there yet but I believe I will find good answers for my structural questions there. As you mentioned there are lots of questions covering both optimization and mechanical concepts. $\endgroup$ Jul 16 '19 at 3:57

You should have a look at the work of Mathias Stolpe. He has done a lot of modelling for structural optimization problems with integer constraints. See for example his PhD thesis. As you already written, the topic comes from a more continuous direction. See the nice book by Martin Bendsoe and Ole Sigmund for a really good overview. You can also have a look at the website of this chair.

If you provide more information on your problem I can adjust my answer to guide you to more relevant papers.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.