bmibnb duality gap

[Karsten Molka]

Hi Johan,

is there any way of returning the duality gap that is shown in the progress log during the optimisation with bmibnb? I would like to automate some experiments run with the global solver and record the gap that was reached after a set timeout.

Many thanks,

Karsten

[Johan Löfberg]

Turn on the option savesolveroutput and it will be in the output from solvesdp

[Karsten Molka]

Thanks a lot!

[Johan Löfberg]

Btw, I hope you know there are much better alternatives to bmibnb in yalmip now, for some problem classes (SCIP, BARON)

[Karsten Molka]

Yes, I am actually experimenting with all of these solvers in combination with the OptiToolbox. My optimisation problem is a non-convex load balancing problem that uses non-linear constraints to integrate an analytic approximation for a closed queueing network model. 

The issue is, that I have no access to the full BARON license.

So far, I noticed that the combination of bmibnb with ipopt and glpk works out best for my test problem with 4 servers and 22 query classes, which YALMIP transforms into a model with the following constraints:

|   #1|   Numeric value|                 Element-wise inequality 8x1|

|   #2|   Numeric value|      Element-wise inequality (bilinear) 8x1|

|   #3|   Numeric value|               Element-wise inequality 176x1|

|   #4|   Numeric value|                Element-wise inequality 88x1|

|   #5|   Numeric value|   Element-wise inequality (polynomial) 88x1|

* Branch-variables : 352

bmibnb reaches a relative gap of 5% after approx. 10 hours, whereas SCIP converges really slowly and generally starts with a very low bound. However, I didn't get to use any specific SCIP options yet, such as the bound tightening used by bmibnb by default.

[Johan Löfberg]

Wow, i would never expect bmibnb to beat scip would you mind sharing the model (feel free to send it by mail privately). Would like to understand why it performs so well compared to scip (and use as benchmark to improve code)