[Couenne] Cut generation options for mixed integer bilinear & quadratic

[Pietro Belotti]

Akshay,

there are quite a few options that are usually turned off, some of
them because they might be quite computationally expensive and some
because they are not always useful in the general case.

First, you may activate MILP cuts from Cbc/Cgl. The following options
add cuts based on the MILP relaxation of the MINLP. The absolute value
gives every how many nodes separation is called, and they're all
negative to mean "if this separator doesn't do anything at the root
node, stop calling it":

Gomory_cuts    -2
probing_cuts   -2
cover_cuts     -5
mir_cuts       -10
2mir_cuts      -6
clique_cuts    -10
flow_covers_cuts       -10
reduce_split_cuts      -10

You may also consider a set of MINLP-specific procedures: first, a
quite expensive bound reduction procedure based on pairs of linear
inequalities (I'm specifying typical values for these options).

two_implied_bt -1
two_implied_max_trials 2
twoimpl_depth_level 3
twoimpl_depth_stop 9

If you are solving a nonconvex MIQCQP, try the following to obtain a
convex quadratic relaxation (akin to what is done in LaGO and in the
alpha-convexification procedure) to which Outer Approximation is
applied (among other advantages, it reduces the number of auxiliary
variables):

use_quadratic yes

Also, you can try SDP cuts (mutually exclusive with use_quadratic) for
generating linear cuts that approximate the SDP relaxation of a QCQP:

sdp_cuts                    -10
sdp_cuts_num_ev        2
sdp_cuts_neg_ev          yes
sdp_cuts_sparsify         no
sdp_cuts_fillmissing      yes

Finally, the following two options specify how many round of
linearization cuts are performed per node and, for convex univariate
functions, how many Outer Approximation cuts are added at the
beginning, respectively. For good lower bounds at the root you may
want to increase these values.

num_cut_passes 3
convexification_points 4

Hope this helps.

Regards,
Pietro


On Fri, Jun 6, 2014 at 5:18 PM, Akshay Gupte <agupte at clemson.edu> wrote:
> Hello all,
>
> I am solving mixed integer bilinear and nonconvex quadratic problems using
> Couenne (integers are bounded but not necessarily {0,1}). Are there specific
> cut generation options I should tune in order to improve the lower bound at
> the root node?
>
> Best,
> Akshay
>
>
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