The NEOS Server offers SBB for the solution of mixed-integer nonlinearly
constrained optimization problems in GAMS
SBB is based on a combination of the standard branch-and-bound method known
from mixed-integer linear programming and nonlinear programming solvers
supported by GAMS.
Initially, the Relaxed Mixed Integer Nonlinear Programming (RMINLP) model is
solved using the initial values provided by the modeler. SBB will stop
immediately if the RMINLP model is unbounded or infeasible or fails. If all
discrete variables in the RMINLP model are integer, SBB will return this
solution as the optimal integer solution. Otherwise, the current solution
is stored and the Branch and Bound procedure will start.
During the Branch and Bound process the feasible region for the discrete
variables is subdivided and bounds on discrete variables are tightened to
new integer values to cut the current non-integer solutions off. Each time a
bound is tightened, a new tighter NLP submodel is solved starting from the
optimal solution to the previous looser submodel. The objective function
values from each of these NLP submodel are assumed to be lower bounds on the
objective in the restricted feasible space (assuming minimization) even
though the local optimum found by the NLP solver may not be a global
optimum. If the NLP solver returns a Locally Infeasible status for a
submodel, it is usually assumed that there is indeed no feasible solution to
the submodel, even though the infeasibility only has been determined locally
(see option infeasseq below for an exception). If the model is convex then
these assumptions will be satisfied and SBB will provide correct bounds. If
the model is not convex, the objective bounds may not be correct and there
may exist better solutions in other unexplored parts of the search space.
SBB was developed by
ARKI Consulting and Development
Bagsvaerdvej 246 A
DK-2880 Bagsvaerd, Denmark
The user must submit a model in GAMS
format to solve an optimization problem. For security purposes, the model
submitted must adhere to the following conventions:
If you are unfamiliar with GAMS, the
GAMS Documentation includes a
GAMS Tutorial and
Examples of models in GAMS format can be found in the
GAMS model library.
By default, the NEOS Server limits the amount of output generated in the listing
file by turning off the symbol and unique element list, symbol cross references,
and restricting the rows and columns listed to zero. This behavior can be changed
by specifying the appropriate options in the model file. See the
documentation on GAMS output
for further information.
You may optionally submit an options file if you wish to override the default parameter settings for the solver.
Currently, the NEOS Server can only use optfile=1 with GAMS input. Therefore, any model that specifies a different options file will not work as intended.
<modelname>.optfile = 1 ;
optfile = 1