COIN-OR Stefan Vigerske, Humboldt University Berlin, Germany Contents 1 Introduction .......................................... 1 2 CoinBonmin .......................................... 2 2.1 Model requirements ...................................... 3 2.2 Usage of CoinBonmin ..................................... 3 2.3 Specification of CoinBonmin Options ............................. 3 2.4 Description of CoinBonmin Options ............................. 3 3 CoinCbc ............................................. 14 3.1 Model requirements ...................................... 14 3.2 Usage of CoinCbc ....................................... 14 3.3 Summary of CoinCBC Options ................................ 15 3.4 Detailed Descriptions of CoinCBC Options ......................... 16 4 CoinGlpk ............................................ 25 4.1 Model requirements ...................................... 25 4.2 Usage of CoinGlpk ....................................... 25 4.3 Summary of CoinGlpk Options ................................ 26 4.4 Detailed Descriptions of CoinGlpk Options ......................... 26 5 CoinIpopt ............................................ 28 5.1 Model requirements ...................................... 28 5.2 Usage of CoinIpopt ....................................... 28 5.3 Output ............................................. 29 5.4 Specification of CoinIpopt Options .............................. 30 5.5 Detailed Description of CoinIpopt Options ......................... 31 1 Introduction COIN-OR (COmputational INfrastructure for Operations Research, http://www.coin-or.org) is an initiative to spur the development of open-source software for the operations research community. One of the projects hosted at COIN-OR is the GAMSlinks project (https://projects.coin-or.org/GAMSlinks). It is dedicated to the development of interfaces between GAMS and open source solvers. Some of these links and solvers have also found their way into the regular GAMS distribution. They are currently available for Linux (32 and 64 bit), Windows (32 bit), Sun Solaris (Intel 64 bit), and Darwin (Intel 32 bit) systems. As of GAMS Distribution 22.6, available solvers include: • CoinBonmin 0.9: Basic Open-source Nonlinear Mixed Integer programming (model types: LP, RMIP, MIP, DNLP, NLP, RMINLP, MINLP, QCP, RMIQCP, MIQCP) COIN-OR 2 • CoinCbc 2.0: COIN-OR Branch and Cut (model types: LP, MIP, RMIP) • CoinGlpk 4.22: Gnu Linear Programming Kit (model types: LP, MIP, RMIP) • CoinIpopt 3.3: Interior Point Optimizer (model types: LP, RMIP, DNLP, NLP, RMINLP, QCP, RMIQCP) With the availability of source code for the GAMS/COIN-OR links the user is not limited to the out of the box GAMS/COIN-OR solvers that come with a regular GAMS distribution. For more information see the COIN-OR/GAMSlinks web site at https://projects.coin-or.org/GAMSlinks. 2 CoinBonmin GAMS/CoinBonmin brings the open source MINLP solver Bonmin from the COIN-OR foundation to the broad audience of GAMS users. Bonmin (Basic Open-source Nonlinear Mixed Integer programming) 0.9 is an open-source solver for mixed- integer nonlinear programming (MINLPs), whereof some parts are still experimental. The code is developed in a joined project of IBM and the Carnegie Mellon University. The COIN-OR project leader for Bonmin is Pierre Bonami. Bonmin implements five different algorithms: • B-BB: a simple branch-and-bound algorithm based on solving a continuous nonlinear program at each node of the search tree and branching on variables • B-OA: an outer-approximation based decomposition algorithm • B-QG: an outer-approximation based branch-and-cut algorithm (by Queseda and Grossmann) • B-Hyb: a hybrid outer-approximation/nonlinear programming based branch-and-cut algorithm (default) • B-Ecp: an ECP cuts based branch-and-cut algorithm a la FilMINT The algorithms are exact when the problem is convex, otherwise they are heuristics. For convex MINLPs, experiments on a reasonably large test set of problems have shown that B-Hyp is the algorithm of choice (it solved most of the problems in 3 hours of computing time). Therefore, it is the default algorithm in Bonmin. Nevertheless, there are cases where B-OA is much faster than B-Hyb and others where B-BB is interesting. B-QG corresponds mainly to a specific parameter setting of B-Hyb where some features are disabled. B-Ecp has just been added to Bonmin and is still experimental. For nonconvex MINLPs, it is strongly recommend to use B-BB, even though it is only a heuristic for such problems too. For more information we refer to • the Bonmin web site https://projects.coin-or.org/Bonmin and • the paper P. Bonami, L.T. Biegler, A.R. Conn, G. Cornuejols, I.E. Grossmann, C.D. Laird, J. Lee, A. Lodi, F. Margot, N.Sawaya and A. W¨achter, An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs, IBM Research Report RC23771, Oct. 2005. Most of the Bonmin documentation in the section was copied from the Bonmin manual available on the Bonmin web site. COIN-OR 3 2.1 Model requirements Bonmin can handle mixed-integer nonlinear programming models which functions can be nonconvex, but should be twice continuously differentiable. The Bonmin link in GAMS supports continuous, binary, and integer variables, special ordered sets, branching priorities, but no semi-continuous or semi-integer variables (see chapter 17.1 of the GAMS User’s Guide). If GAMS/CoinBonmin is called for a model with only continuous variables, the interface directly calls Ipopt. 2.2 Usage of CoinBonmin The following statement can be used inside your GAMS program to specify using CoinBonmin Option MINLP = CoinBonmin; { or LP, RMIP, MIP, DNLP, NLP, RMINLP, QCP, RMIQCP, MIQCP } The above statement should appear before the Solve statement. If CoinBonmin was specified as the default solver during GAMS installation, the above statement is not necessary. 2.3 Specification of CoinBonmin Options A Bonmin option file contains both Ipopt and Bonmin options, for clarity all Bonmin options should be preceded with the prefix “bonmin.”. The scheme to name option files is the same as for all other GAMS solvers. Specifying optfile=1 let Gams/CoinBonmin read coinbonmin.opt, optfile=2 corresponds to coinbonmin.op2, and so on. The format of the option file is the same as for Ipopt (see Section 5.4). The most important option in Bonmin is the choice of the solution algorithm. This can be set by using the option named bonmin.algorithm which can be set to B-BB, B-OA, B-QG, B-Hyb, or B-Ecp (its default value is B-Hyb). Depending on the value of this option, certain other options may be available or not. In the context of outer approximation decomposition, several options are available for configuring the MIP sub- solver CBC. By setting the option bonmin.milp subsolver to Cbc Par, a version of CBC is chosen that can be parameterized by the user. The options that can be set are the node-selection strategy, the number of strong- branching candidates, the number of branches before pseudo costs are to be trusted, and the frequency of some cut generators. Their name coincide with Bonmins options, except that the “bonmin.” prefix is replaced with “milp sub.”. An example of a bonmin.opt file is the following: bonmin.algorithm B-Hyb bonmin.oa_log_level 4 bonmin.milp_subsolver Cbc_Par milp_sub.cover_cuts 0 print_level 6 This sets the algorithm to be used to the hybrid algorithm, the level of outer approximation related output to 4, the print level for Ipopt to 6, the MIP subsolver for outer approximation to a parameterized version of CBC, and switches off cover cutting planes for the MIP subsolver. GAMS/CoinBonmin understands currently the following GAMS parameters: reslim (time limit), iterlim (iteration limit), nodlim (node limit), cutoff, optca (absolute gap tolerance), and optcr (relative gap tolerance). You can set them either on the command line, e.g. nodlim=1000, or inside your GAMS program, e.g. Option nodlim=1000;. 2.4 Description of CoinBonmin Options The following tables gives the list of options together with their types, default values and availability in each of the four main algorithms. The column labeled ‘type’ indicates the type of the parameter (‘F’ stands for float, ‘I’ for integer, and ‘S’ for string). The column labeled ‘default’ indicates the global default value. Then for each COIN-OR 4 of the four algorithm B-BB, B-OA, B-QG, and B-Hyb, ‘+’ indicates that the option is available for that particular algorithm while ‘−’ indicates that it is not. Options that are marked with ∗ are those that can be used to configure the MIP subsolver. Option type default B-BB B-OA B-QG B-Hyb Algorithm choice algorithm S BHyb + + + + Branch-and-bound allowable fraction gap F optrc (0.1) + + + + allowable gap F optca (0) + + + + cutoff F cutoff or 10100 + + + + cutoff decr F 10−5 + + + + integer tolerance F 10−6 + + + + iteration limit I ∞ + + + + nlp failure behavior S stop + + + + node comparison∗ S dynamic + + + + node limit I nodlim or iterlim (10000) + + + + num cut passes I 1 – + + + num cut passes at root I 20 – + + + number before trust∗ I 8 + + + + number strong branch∗ I 20 + + + + solution limit I ∞ + + + + time limit F reslim (1000) + + + + tree search strategy S topnode + + + + varselect stra S strongbranching + + + + Outer Approximation decomposition milp subsolver S Cbc D – + – + oa dec time limit F 30 + + + + Outer Approximation cuts add only violated oa S no – + + + cut strengthening type S none – + + + disjunctive cut type S none – + + + oa cuts scope S global – + + + tiny element F 10−8 – + + + very tiny element F 10−7