SBB

The NEOS Server offers SBB for the solution of mixed-integer nonlinearly constrained optimization problems in GAMS format.

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

Using the NEOS Server for SBB/GAMS

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:

• It must be self contained, i.e., no $include or $batinclude statements.
• It may not execute external programs, i.e., no $call or execute statements.
• No file creation, i.e. no put files or $echo except for a file named 'results.txt'. Other files created in the GAMS model file will be deleted.

If you are unfamiliar with GAMS, the GAMS Documentation includes a GAMS Tutorial and User's Guide. 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.