We reformulate the max clique problem as a bilevel optimization problem along the lines of Motzkin-Strauss and show that producing a locally optimal solution to a BLP is a combinatorial problem over bases of the lower level. The result is analogous to Ahmadi and Zhang's for QP.

The upshot: constructing the RVF is equivalent to constructing the frontier. Exploiting this, we adapt our existing generalized cutting-plane algorithm for constructing the classical value function to the multiobjective MILP setting with an arbitrary # of objectives. Enjoy!

If you attend the session in which @schmaidt 's #ISMP talk is scheduled (WA231 — Bilevel Optimization with Discrete Decisions (I), going on now!), make sure you stick around for Federico Battista's talk about some even more recent attempts to improve performance of MibS!

A tech report discussing the source of the improvements in depth is due out anytime, so stay tuned!

Here are some URLs in case you're interested: ALPS ( BiCePS ( and BLIS (