Q:.  + What is CBC? + 
A:.  + The COINOR Branch and Cut code + is designed to be a high quality mixed integer code provided under the terms of the + Common Public License. + CBC is written in C++, and is primarily intended to be used as a callable + library (though a rudimentary standalone executable exists). + The first documented release was .90.0 The current release is version .90.0. (JF 04/01/05) + 
Q:.  + What are some of the features of CBC? + 
A:.  + CBC allows the use of any CGL cuts and the use of heuristics and + specialized branching methods. (JF 04/01/05) + 
Q:.  + How do I obtain and install CBC? + 
A:.  + Please see the + COINOR FAQ + for details on how to + obtain + and + install + COINOR modules. (JF 04/01/05) + 
Q:.  + Is CBC reliable? + 
A:.  + CBC has been tested on many problems, + but more testing and improvement is needed before it can get to version 1.0. (JF 04/01/05) + 
Q:.  + Is there any documentation for CBC? + 
A:.  + If you can see this you have the best there is:) + Also available is a list of + CBC class descriptions generated + by Doxygen. (JF 04/01/05) + 
Q:.  + Is CBC as fast as Cplex or Xpress? + 
A:.  + No. However its design is much more flexible so advanced users + will be able to tailor CBC to their needs. (JF 04/01/05) + 
Q:.  + When will version 1.0 of CBC be available? + 
A:.  + It is expected that version 1.0 will be released in time for the 2005 + INFORMS annual meeting. (JF 04/01/05) + 
Q:.  + What can the community do to help? + 
A:.  + People from all around the world are already helping. There are + probably ten people who do not always post to the discussion mail list but are constantly + "improving" the code by demanding performance or bug fixes or enhancements. And there + are others posting questions to discussion groups. (JF 04/01/05) + + A good start is to join the coindiscuss + mailing list where CBC is discussed. Some + other possibilities include: +

+There is Doxygen content for CBC available online at + +http://www.coinor.org/Doxygen/Cbc/index.html. A local version of the +Doxygen content can be generated from the CBC distribution. To do so, in the +directory COIN/Cbc, enter make doc. +The Doxygen content will be created in the directory +COIN/Cbc/Doc/html. The same can be done for +the COIN core, from the COIN/Coin directory. +
Revision History  

Revision 0.21  May 10, 2005  RLH 
Fixed typos caught by Cole Smith, editor of the INFORMS Tutorial Book, and added place holders for needstobewritten sections, e.g., Using CGL with CBC.  
Revision 0.2  May 2, 2005  RLH 
Book chapter for CBC Tutorial at INFORMS 2005 annual meeting. Reorganized the content. Added CBC Messages. Changed the font type to distinguish functions/variables/classnames/code from text.  
Revision 0.1  April 1, 2005  JF 
First draft. The CBC documentation uses the DocBook CLP documentation created by David de la Nuez. 
Copyright Â© 2005 IBM Coportation
Table of Contents
List of Tables
List of Examples
Table of Contents
+ The COIN + ^{[1]} +Branch and Cut solver (CBC) is an opensource mixedinteger program (MIP) solver written in C++. CBC is intended to be used primarily as a callable library to create customized branchandcut solvers. A basic, standalone executable version is also available. CBC is an active opensource project led by John Forrest at www.coinor.org. +
+ The primary users of CBC are expected to be developers implementing customized branchandcut algorithms in C++ using CBC as a library. Consequently, this document assumes a working knowledge of + C++, including basic + objectoriented programming terminology, and familiarity with the fundamental concepts of + + linear programming (LP) and + + mixed integer programming (MIP). +
+ +CBC relies on other parts of the COIN repository. CBC needs a LP solver and relies on the COIN Open Solver Inteface (OSI) to communicate with the user's choice of solver. Any LP solver with an OSI interface can be used with CBC. The LP solver expected to be used most commonly is COIN's native linear program solver, CLP. For cut generators, CBC relies on the COIN Cut Generation Library (CGL). Any cut generator written to CGL standards can be used with CBC. Some of the cut generators in CGL rely on other parts of COIN, e.g., CGL's Gomory cut generator rely on the factorization functionality of CoinFactorization. This document assumes basic familiarity with OSI and CGL. +
+Technically speaking, CBC accesses the solver (and sometime the model and data it contains) through an OSISolverInterface. For the sake of simplicity, we will refer to the OsiSolverInterface as "the solver" in this document, rather than "the standard application programming interface to the solver." We hope any confusion caused by blurring this distinction will be mitigated by the shorter sentences. + +
+In summary, readers should have the following prerequisites: +
+
+
+
+ Before examining CBC in more detail, we tersely describe the basic branchandcut algorithm by way of example, (which should really be called branchandcutandbound) and show the major C++ class(es) in CBC related to each step. The major CBC classes, labeled (A) through (F), are described in TableÂ 1.1. +
+Step 1. (Bound) Given a MIP model to minimize where some variables must take on integer values (e.g., 0, 1, or 2), relax the integrality requirements (e.g., consider each "integer" variable to be continuous with a lower bound of 0.0 and an upper bound of 2.0). Solve the resulting linear model with an LP solver to obtain a lower bound on the MIP's objective function value. If the optimal LP solution has integer values for the MIP's integer variables, we are finished. Any MIPfeasible solution provides an upper bound on the objective value. The upper bound equals the lower bound; the solution is optimal. +
+Step 2. (Branch) Otherwise, there exists an "integer" variable with a nonintegral value. Choose one nonintegral variable (e.g., with value 1.3) (A)(B) and branch. Create two +^{[2]} +nodes, one with the branching variable having an upper bound of 1.0, and the other with the branching variable having a lower bound of 2.0. Add the two nodes to the search tree. +
+While (search tree is not empty) { +
+ Step 3. (Choose Node) Pick a node off the tree (C)(D) +
+ Step 4. (Reoptimize LP) Create an LP relaxation and solve. +
+ Step 5. (Bound) Interrogate the optimal LP solution, and try to prune the node by one of the following. +
+
+ Step 6. (Branch) If we were unable to prune the node, then branch. Choose one nonintegral variable to branch on (A)(B). Create two nodes and add them to the search tree. +} +
+This is the outline of a "branchandbound" algorithm. If in optimizing the linear programs, we use cuts to tighten the LP relaxations (E)(F), then we have a "branchandcut" algorithm. (Note, if cuts are only used in Step 1, the method is called a "cutandbranch" algorithm.) + +
TableÂ 1.1.Â Associated Classes
+ Note +  + Class name +  + Description + 

+ (A) +  CbcBranch...  + These classes define the nature of MIP's discontinuity. The simplest discontinuity + is a variable which must take an integral value. Other types of discontinuities + exist, e.g., lotsizing variables. + 
+ (B) +  CbcNode  + This class decides which variable/entity to branch on next. + Even advanced users will probably only interact with this class by setting + CbcModel parameters ( e.g., priorities). + 
+ (C) +  CbcTree  + All unsolved models can be thought of as being nodes on a tree where each + node (model) can branch two or more times. The interface with this class is helpful to know, but +the user can pretty safely ignore the inner workings of this class. + 
+ (D) +  CbcCompare...  + These classes are used in determine which of the unexplored nodes in the tree to consider next. These + classes are very small simple classes that can be tailored to suit the problem. + 
+ (E) +  CglCutGenerators  + Any cut generator from CGL can be used in CBC. The cut generators are passed to CBC with parameters + which modify when each generator will be tried. All cut generators should be tried to + determine which are effective. Few users will write their own cut generators. + 
+ (F) +  CbcHeuristics  + Heuristics are very important for obtaining valid solutions quickly. Some + heuristics are available, but this is an area where it is useful and interesting to + write specialized ones. + 
+ There are a number of resources available to help new CBC users get started. + This document is designed to be used in conjunction with the files in the + Samples subdirectory of the main CBC directory (COIN/Cbc/Samples). + The Samples illustrate how to use CBC and may also serve as useful starting points + for user projects. In the event that either this document or the available + Doxygen content conflicts with the observed + behavior of the source code, the comments in the header files, found in + COIN/Cbc/include, are the ultimate reference. +
^{[1] } + The complete acronym is "COINOR" which stands for the Compuational Infrastructure for Operations Research. For simplicity (and in keeping with the directory and function names) we will simply use "COIN". +
^{[2] } +The current implementation of CBC allow two branches to be created. More general number of branches could be implemented. +
Table of Contents
+ The main class in CBC is CbcModel. The CbcModel class is where most + of the parameter setting is done. The absolute minimum number of actions taken with CbcModel is two, +
+
+ The first sample program shows how to perform simple branchandbound with CBC. This program is short enough to present in full. Most of the remaining examples will take the form of small code fragments. + The complete code for all the examples in this Guide can be found in the CBC Samples directory, COIN/Cbc/Samples. + +
ExampleÂ 2.1.Â minimum.cpp
+ +// Copyright (C) 2005, International Business Machines +// Corporation and others. All Rights Reserved. + +#include "CbcModel.hpp" + +// Using CLP as the solver +#include "OsiClpSolverInterface.hpp" + +int main (int argc, const char *argv[]) +{ + OsiClpSolverInterface solver1; + + // Read in example model in MPS file format + // and assert that it is a clean model + int numMpsReadErrors = solver1.readMps("../../Mps/Sample/p0033.mps",""); + assert(numMpsReadErrors==0); + + // Pass the solver with the problem to be solved to CbcModel + CbcModel model(solver1); + + // Do complete search + model.branchAndBound(); + + /* Print the solution. CbcModel clones the solver so we + need to get current copy from the CbcModel */ + int numberColumns = model.solver()>getNumCols(); + + const double * solution = model.bestSolution(); + + for (int iColumn=0;iColumn<numberColumns;iColumn++) { + double value=solution[iColumn]; + if (fabs(value)>1.0e7&&model.solver()>isInteger(iColumn)) + printf("%d has value %g\n",iColumn,value); + } + return 0; +} + +
+ The program in ExampleÂ 2.1 creates a OsiClpSolverInterface solver interface (i.e., solver1), and reads an MPS file. If there are no errors, the program passes the problem to CbcModel which solves the problem using the branchandbound algorithm. The part of the program which solves the problem is very small (one line!) but before that one line, the LP solver (i.e., solver1) had to be created and populated with the problem. After that one line, the results were printed out. +
+The program in ExampleÂ 2.1 illustrates the dependency of CBC on + the OsiSolverInterface class. The constructor of CbcModel takes a pointer to an OsiSolverInterface (i.e., a solver). The CbcModel clones the solver, and uses its own instance of the solver. The CbcModel's solver and the original solver (e.g., solver1) are not in sync unless the user synchronizes them. The user can always access the CbcModel's solver through the model() class. To synchronize the two solvers, explicitly refreshing the original, e.g., +
+ solver1 = model.solver(); +
+CbcModel's method solver() returns a pointer to CBC's cloned solver. +
+For convenience, many of the OSI methods to access problem data have identical method names in CbcModel. (It's just more convenient to type model.getNumCols() rather than model.solver()>getNumCols()). The CbcModel refreshes its solver at certain logical points during the algorithm. At these points, the information from the CbcModel model will match the information from the model.solver(). Elsewhere, the information may vary. For instance, the method CbcModel::bestSolution() will contain the best solution so far, the OSI method getColSolution() may not. In this case, it is safer to use CbcModel::bestSolution(). +
+While all the OSI methods used in minimum.cpp have equivalent methods in CbcModel, there are some OSI methods which do not. For example, if the program produced a lot of undesired output, one might add the line +
+ model.solver()>setHintParam(OsiDoReducePrint,true,OsiHintTry); +
+ + to reduce the output. There is no setHintParam() method in CbcModel. +
+ Optimality can be checked through a call to model.isProvenOptimal(). Also + available are isProvenInfeasible(), + isSolutionLimitReached(), + isNodeLimitReached() or the feared + isAbandoned(). There is also + intÂ status() which returns 0 if finished (which includes the case when the algorithm is finished because it has been proved infeasible), 1 if stopped by user, and 2 if difficulties arose. +
+ In addition to these CbcModel methods, solution values can be accessed via OSI methods. The OSI methods pick up the current solution in the CBCModel. The current solution will match the best solution found so far if called after branchAndBound() and a solution was found. +
TableÂ 2.1.Â + Methods for Getting Solution Information from OSI +
+ Purpose +  + Name +  + Notes + 

+ Primal column solution +  const double * getColSolution()  + The OSI method will return the best solution found thus far, unless none has been found. It is safer to use CbcModel version, CbcModel::bestSolution() 
+ Dual row solution +  const double * getRowPrice()  + Identical CbcModel version available, CbcModel::getRowPrice(). + 
+ Primal row solution +  const double * getRowActivity()  + Identical CbcModel version available, CbcModel::getRowActivity(). + 
+ Dual column solution +  const double * getReducedCost()  + Identical CbcModel version available, CbcModel::gtReducedCost(). + 
+ Number of rows in model +  int getNumRows()  + Identical CbcModel version available, CbcModel::getNumRows(). Note: the number of rows can change due to cuts. + 
+ Number of columns in model +  int getNumCols()  + Identical CbcModel version available, CbcModel::getNumCols(). + 
+Most of the parameter setting in CBC is done through CbcModel methods. The most commonly used set and get methods are listed in TableÂ 2.2. +
TableÂ 2.2.Â Useful Set and Get Methods in CbcModel
+ Method(s) +  + Description + 

boolÂ setMaximumNodes(int value) intÂ getMaximumNodes() const boolÂ setMaximumSeconds(double value) doubleÂ getMaximumSeconds() boolÂ setMaximumSolutions(double value) doubleÂ getMaximumSolutions() const  + These set methods tell CBC to stop after a given number of nodes, + seconds, or solutions is reached. The get methods return the corresponding values. + 
boolÂ setIntegerTolerance(double value) const doubleÂ getIntegerTolerance() const  + An integer variable is deemed to be at an integral value if it is no further than this value (tolerance) away. + 
boolÂ setAllowableGap(double value) doubleÂ getAllowableGap() const boolÂ setAllowablePercentageGap(double value) doubleÂ getAllowablePercentageGap() const boolÂ setAllowableFractionGap(double value) doubleÂ getAllowableFractionGap() const  CbcModel returns if the gap between the best known solution and the best + possible solution is less than this value, or as a percentage, or a fraction. + 
voidÂ setNumberStrong(double value) intÂ numberStrong() +^{[a]} const  + These methods set or get the maximum number of candidates at a node to + be evaluated for strong branching. + 
voidÂ setPrintFrequency(int value) intÂ printFrequency() const  + Controls the number of nodes evaluated between status prints. + Print frequency has a very slight overhead, if value is small. + 
intÂ getNodeCount() const  + Returns number of nodes evaluated in the search. + 
intÂ numberRowsAtContinuous() const  + Returns number of rows in the problem when handed to the solver (i.e., before cuts where added). Commonly used in implementing heuristics. + 
int Â numberIntegers() const const intÂ *Â integerVariable() const  + Returns number of integer variables and an array specifying them. + 
boolÂ isBinary(int colIndex) const boolÂ isContinuous(int colIndex) const boolÂ isInteger(int colIndex) const  + Returns information on variable colIndex. OSI methods + can be used to set these attributes (before handing the model to CbcModel). + 
doubleÂ getObjValue() const  + This method returns the best objective value so far. + 
doubleÂ getCurrentObjValue() const  + This method returns the current objective value. + 
constÂ doubleÂ *Â getObjCoefficients() const  + This method return the objective coefficients. + 
constÂ doubleÂ *Â getRowLower() const constÂ doubleÂ *Â getRowUpper() const constÂ doubleÂ *Â getColLower() const constÂ doubleÂ *Â getColUpper() const  + These methods return the lower and upper bounds on row and column activities. + 
constÂ CoinPackedMatrixÂ *Â getMatrixByRow() const  + This method returns a pointer to a row copy of matrix stored as a + CoinPackedMatrix which can be further examined. + 
const CoinPackedMatrix * getMatrixByCol() const  + This method returns a pointer to a column copy of matrix stored as a + CoinPackedMatrix which can be further examined. + 
CoinBigIndexÂ getNumElements() const^{[b]}  + Returns the number of nonzero elements in the problem matrix. + 
void setObjSense(doubleÂ value) double getObjSense() const  + These methods set and get the objective sense. The parameter + value should be +1 to minimize and 1 to maximize. + 
^{[a] } +This methods (and some of the other) do not follow the "get" convention. The convention has changed over time and there are still some inconsistencies to be cleaned up. + ^{[b] } + CoinBigIndex is a typedef which in + most cases is the same as int. + 
+CbcModel is extremely flexible and customizable. The class structure of CBC is designed to make the most commonly desired customizations of branchandcut possible. These include: +
+ + +To enable this flexibility, CbcModel uses other classes in CBC (some of which are virtual and may have multiple instances). Not all classes are created equal. The two tables below list in alphabetical order the classes used by CbcModel that are of most interest and of least interest. +
TableÂ 2.3.Â Classes Used by CbcModel  Most Useful
+ Class name +  + Description +  + Notes + 

CbcCompareBase  + Controls which node on the tree is selected. +  + The default is CbcCompareDefault. Other comparison classes in CbcCompareActual.hpp include CbcCompareDepth and CbcCompareObjective. Experimenting with these classes and creating new compare classes is easy. + 
CbcCutGenerator  + A wrapper for CglCutGenerator with additional data to control when the cut generator is invoked during the tree search. +  + Other than knowing how to add a cut generator to CbcModel, there is not much the average user needs to know about this class. However, sophisticated users can implement their own cut generators. 
CbcHeuristic  + Heuristic that attempts to generate valid MIPsolutions leading to good upper bounds. +  + Specialized heuristics can dramatically improve branchandcut performance. As many different heuristics as desired can be used in CBC. Advanced users should consider implementing custom heuristics when tackling difficult problems. 
CbcObject  + Defines what it means for a variable to be satisfied. Used in branching. +  + Virtual class. CBC's concept of branching is based on the idea of an "object". An object has (i) a feasible region, (ii) can be evaluated for infeasibility, (iii) can be branched on, e.g., a method of generating a branching object, which defines an up branch and a down branch, and (iv) allows comparison of the effect of branching. Instances of objects include CbcSimpleInteger, CbcSimpleIntegerPseudoCosts, CbcClique, CbcSOS (type 1 and 2), CbcFollowOn, and CbcLotsize. + 
OsiSolverInterface  + Defines the LP solver being used and the LP model. Normally + a pointer to the desired OsiSolverInteface is passed to CbcModel before branch and cut. +  + Virtual class. The user instantiates the solver interface of their choice, e.g., + OsiClpSolverInterface. + 
+There is not much about the classes listed in TableÂ 2.4 that the average user needs to know about. +
TableÂ 2.4.Â Classes Used by CbcModel  Least Useful
+ Class name +  + Description +  + Notes + 

CbcBranchDecision  + Used in choosing which variable to branch on, however, most of + the work is done by the definitions in CbcObject. +  + Defaults to CbcBranchDefaultDecision. + 
CbcCountRowCut  + Interface to OsiRowCut. It counts the usage so cuts can gracefully vanish. +  + See OsiRowCut for more details. 
CbcNode  + Controls which variable/entity is selected to be branch on. +  + Controlled via CbcModel parameters. Information from CbcNode can be useful in creating customized node selection rules. 
CbcNodeInfo  + Contains data on bounds, basis, etc. for one node of the search tree. +  + Header is located in CbcNode.hpp. 
CbcTree  + Defines how the search tree is stored. +  + This class can be changed but it is not likely to be modified. 
CoinMessageHandler  + Deals with message handling +  + The user can inherit from CoinMessageHandler to specialize message handling. + 
CoinWarmStartBasis  + Basis representation to be used by solver + 
Table of Contents
+ The order in which the nodes of the search tree are explored can strongly influence the performance of branchandcut algorithms. CBC give users complete control over the search order, including the ability to dynamically change the node selection logic as the search progresses. The search order is controlled via the CbcCompare... class, and its method test(). Dynamic changes can be made whenever +
+CBC provides an abstract base class, CbcCompareBase, and implementations of several commonly used node selection strategies as Compare Classes, see TableÂ 3.1. +
TableÂ 3.1.Â Compare Classes Provided
+ Class name +  + Description + 

CbcCompareDepth  + This will always choose the node deepest in tree. It gives minimum + tree size but may take a long time to find the best solution. + 
CbcCompareObjective  + This will always choose the node with the best objective value. This may + give a very large tree. It is likely that the first solution found + will be the best and the search should finish soon after the first solution + is found. + 
CbcCompareDefault  + This is designed to do a mostly depthfirst search until a solution has + been found. It then use estimates that are designed to give a slightly better solution. + If a reasonable number of nodes have been explored (or a reasonable number of + solutions found), then this class will adopt a breadthfirst search (i.e., making a comparison based strictly on objective function values) unless the tree is very large, in which case it will revert to depthfirst search. A better description of CbcCompareUser is given below. + 
CbcCompareEstimate  + When pseudo costs are invoked, CBC uses the psuedo costs to guess a solution. This class uses the guessed solution. + 
+ It is relatively simple for a user to create a customized node selection by creating a new compare class instances. The code in ExampleÂ 3.1 describes how to build a new comparison class and the reasoning behind it. The complete source can be found in CbcCompareUser.hpp and CbcCompareUser.cpp, located in the CBC Samples directory. Besides the constructor, the only method the user must implement in CbcCompare is bool test(CbcNode* x, CbcNode* y)) which returns true if node y is preferred over node x. In the test() method, information from CbcNode can easily be used. TableÂ 3.2 lists some commonly used methods to access information at a node. +
TableÂ 3.2.Â Information Available from CbcNode
double objectiveValue() const  + Value of objective at the node. + 
int numberUnsatisfied() const  + Number of unsatisfied integers (assuming branching + object is an integer  otherwise it might be number of unsatisfied sets). + 
int depth() const  + Depth of the node in the search tree. + 
double guessedObjectiveValue() const  + Returns the guessed objective value, if the user was setting this (e.g., if using pseudo costs). + 
int way() const  + The way which branching would next occur from this node + (for more advanced use). + 
int variable() const  + The branching "variable" (associated with the CbcBranchingObject  for more advanced use). + 
+
+The node desired in the tree is often a function of the how the search is progressing. In the design of CBC, there is no information on the state of the tree. The CBC is designed so that the method + newSolution() is called whenever a solution is found and the method every1000Nodes() is called every 1000 nodes. When these methods are called, the user has the opportunity to modify the + behavior of test() by adjusting their common variables (e.g., weight_). Because CbcNode has a pointer to the model, the user can also influence the search through actions such as changing the maximum time CBC is allowed, once a solution has been found (e.g., CbcModel::setMaximumSeconds(double value)). In CbcCompareUser.cpp of the COIN/Cbc/Samples directory, four items of data are used. +
+
+1) The number of solutions found so far +
+2) The size of the tree (defined to be the number of active nodes) +
+3) A weight, weight_, which is initialized to 1.0 +
+4) A saved value of weight, saveWeight_ (for when weight is set back to 1.0 for special reason) +
+
+Initially, weight_ is 1.0 and the search is biased towards depth first. In +fact, test() prefers y if y has fewer unsatisfied variables. In the case of a tie, test() prefers the node with the greater depth in tree. The full code for the CbcCompareUser::test() method is given in ExampleÂ 3.1. +
ExampleÂ 3.1.Â CbcCompareUser::test()
+ +// Returns true if y better than x +bool +CbcCompareUser::test (CbcNode * x, CbcNode * y) +{ + if (weight_==1.0) { + // before solution + if (x>numberUnsatisfied() > y>numberUnsatisfied()) + return true; + else if (x>numberUnsatisfied() < y>numberUnsatisfied()) + return false; + else + return x>depth() < y>depth(); + } else { + // after solution. + // note: if weight_=0, comparison is based + // solely on objective value + double weight = CoinMax(weight_,0.0); + return x>objectiveValue()+ weight*x>numberUnsatisfied() > + y>objectiveValue() + weight*y>numberUnsatisfied(); + } +} + +
+CBC calls the method newSolution() after a new solution is found. The method newSolution() interacts with test() by means of the variable weight_. If the solution was achieved by branching, a calculation is made to determine the cost per unsatisfied integer variable to go from the continuous solution to an integer solution. The variable weight_ is then set to aim at a slightly better solution. From then on, test() returns true if it seems that y will lead to a better solution than x. This source for newSolution() in given in ExampleÂ 3.2. +
ExampleÂ 3.2.Â CbcCompareUser::newSolution()
+ +// This allows the test() method to change behavior by resetting weight_. +// It is called after each new solution is found. +void +CbcCompareUser::newSolution(CbcModel * model, + double objectiveAtContinuous, + int numberInfeasibilitiesAtContinuous) +{ + if (model>getSolutionCount()==model>getNumberHeuristicSolutions()) + return; // The number of solutions found by any means equals the + // number of solutions, so this solution was found by rounding. + // Ignore it. + + // set weight_ to get close to this solution + double costPerInteger = + (model>getObjValue()objectiveAtContinuous)/ + ((double) numberInfeasibilitiesAtContinuous); + weight_ = 0.98*costPerInteger; // this aims for a solution + // slightly better than known. + // why 0.98? why not?! Experiment yourself. + saveWeight_=weight_; // We're going to switching between depthfirst and breadthfirst + // branching strategies, depending on what we find in the tree. + // When doing depth first, we'll want to retrieve this weight. + // So, let's save it. + numberSolutions_++; + if (numberSolutions_>5) + weight_ =0.0; // comparison in test() will be + // based strictly on objective value. +} + +
+ +As the search progresses, the comparison can be modified. If many nodes (or many solutions) have been generated, then weight_ is set to 0.0 leading to a breadthfirst search. Breadthfirst search can lead to an enormous tree. If the tree size is exceeds 10000, it may be desirable to return to a search biased towards depth first. Changing the behavior in this manner is done by the method every1000Nodes shown in ExampleÂ 3.3. +
ExampleÂ 3.3.Â CbcCompareUser::every1000Nodes()
+ +// This allows the test() method to change behavior every 1000 nodes. +bool +CbcCompareUser::every1000Nodes(CbcModel * model, int numberNodes) +{ + if (numberNodes>10000) + weight_ =0.0; // compare nodes based on objective value + // get size of tree + treeSize_ = model>tree()>size(); + if (treeSize_>10000) { + // set weight to reduce size most of time + if (treeSize_>20000) + weight_=1.0; + else if ((numberNodes%4000)!=0) // Flipflop between the strategies. + // Why 4000? Why not? Experiment yourself. + weight_=1.0; + else + weight_=saveWeight_; + } + return numberNodes==11000; // resort if first time +} + +
Table of Contents
+ In practice, it is very useful to get a good solution reasonably fast. Any MIPfeasible solution produces an upper bound, and a good bound will greatly reduce the run time. Good solutions can satisfy the user + on very large problems where a complete search is impossible. Obviously, heuristics are + problem dependent, although some do have more general use. + At present there is only one heuristic in CBC itself, CbcRounding. Hopefully, the number will grow. Other heuristics are in the COIN/Cbc/Samples + directory. A heuristic tries to obtain a solution to the original + problem so it only needs to consider the original rows and does not have to use the + current bounds. CBC provides an abstract base class CbcHeuristic and a rounding heuristic in CBC. +
+ This chapter describes how to build a greedy heuristic for a set covering problem, e.g., the miplib problem fast0507. A more general (and efficient) version of the heuristic is in CbcHeuristicGreedy.hpp and CbcHeuristicGreedy.cpp located in the COIN/Cbc/Samples directory, see ChapterÂ 8, +More Samples +. +
+ The greedy heuristic will leave all variables taking value one at this node of the + tree at value one, and will initially set all other variables to value zero. + All variables are then sorted in order of their cost + divided by the number of entries in rows which are not yet covered. (We may randomize that + value a bit so that ties will be broken in different ways on different runs of the heuristic.) + The best one is choosen, and set to one. The process is repeated. Because this is + a set covering problem (i.e., all constraints are â¥), the heuristic is guaranteed to find a solution (but not necessarily an improved solution). The speed of the heuristic could be improved by just redoing those affected, but for illustrative purposes we will keep it simple. (The speed could also be improved if all elements are 1.0). +
+ The key CbcHeuristic method is intÂ solution(double & solutionValue, + doubleÂ *Â betterSolution). + The solution() method returns 0 if no solution found, and returns 1 if a solution is found, in which case it fills in the objective value and primal solution. The code in CbcHeuristicGreedy.cpp is a little more complicated than this following example. For instance, the code here assumes all variables are integer. The important bit of data is a copy of the matrix (stored by column) before any cuts have been made. The data used are bounds, objective and the matrix plus two work arrays. +
ExampleÂ 4.1.Â Data
+ + OsiSolverInterface * solver = model_>solver(); // Get solver from CbcModel + const double * columnLower = solver>getColLower(); // Column Bounds + const double * columnUpper = solver>getColUpper(); + const double * rowLower = solver>getRowLower(); // We know we only need lower bounds + const double * solution = solver>getColSolution(); + const double * objective = solver>getObjCoefficients(); // In code we also use min/max + double integerTolerance = model_>getDblParam(CbcModel::CbcIntegerTolerance); + double primalTolerance; + solver>getDblParam(OsiPrimalTolerance,primalTolerance); + int numberRows = originalNumberRows_; // This is number of rows when matrix was passed in + // Column copy of matrix (before cuts) + const double * element = matrix_.getElements(); + const int * row = matrix_.getIndices(); + const CoinBigIndex * columnStart = matrix_.getVectorStarts(); + const int * columnLength = matrix_.getVectorLengths(); + + // Get solution array for heuristic solution + int numberColumns = solver>getNumCols(); + double * newSolution = new double [numberColumns]; + // And to sum row activities + double * rowActivity = new double[numberRows]; + +
+The newSolution is then initialized to the rounded down solution. +
ExampleÂ 4.2.Â Initialize newSolution
+ + for (iColumn=0;iColumn<numberColumns;iColumn++) { + CoinBigIndex j; + double value = solution[iColumn]; + // Round down integer + if (fabs(floor(value+0.5)value)<integerTolerance) + value=floor(CoinMax(value+1.0e3,columnLower[iColumn])); + // make sure clean + value = CoinMin(value,columnUpper[iColumn]); + value = CoinMax(value,columnLower[iColumn]); + newSolution[iColumn]=value; + if (value) { + double cost = objective[iColumn]; + newSolutionValue += value*cost; + for (j=columnStart[iColumn]; + j<columnStart[iColumn]+columnLength[iColumn];j++) { + int iRow=row[j]; + rowActivity[iRow] += value*element[j]; + } + } + } + +
+ + +At this point some row activities are below their lower bound. To correct the infeasibility, the variable which is cheapest in reducing the sum of infeasibilities is found and updated, and the process repeats. This is a finite process. (The implementation could be faster, but is kept simple for illustrative purposes.) +
ExampleÂ 4.3.Â Create Feasible newSolution from Initial newSolution
+ + while (true) { + // Get column with best ratio + int bestColumn=1; + double bestRatio=COIN_DBL_MAX; + for (int iColumn=0;iColumn<numberColumns;iColumn++) { + CoinBigIndex j; + double value = newSolution[iColumn]; + double cost = direction * objective[iColumn]; + // we could use original upper rather than current + if (value+0.99<columnUpper[iColumn]) { + double sum=0.0; // Compute how much we will reduce infeasibility by + for (j=columnStart[iColumn]; + j<columnStart[iColumn]+columnLength[iColumn];j++) { + int iRow=row[j]; + double gap = rowLower[iRow]rowActivity[iRow]; + if (gap>1.0e7) { + sum += CoinMin(element[j],gap); + if (element[j]+rowActivity[iRow]<rowLower[iRow]+1.0e7) { + sum += element[j]; + } + } + if (sum>0.0) { + double ratio = (cost/sum)*(1.0+0.1*CoinDrand48()); + if (ratio<bestRatio) { + bestRatio=ratio; + bestColumn=iColumn; + } + } + } + } + if (bestColumn<0) + break; // we have finished + // Increase chosen column + newSolution[bestColumn] += 1.0; + double cost = direction * objective[bestColumn]; + newSolutionValue += cost; + for (CoinBigIndex j=columnStart[bestColumn]; + j<columnStart[bestColumn]+columnLength[bestColumn];j++) { + int iRow = row[j]; + rowActivity[iRow] += element[j]; + } + } + +
+A solution value of newSolution is compared to the best solution value. If newSolution is an improvement, its feasibility is validated. We expect newSolution to be feasible, and are trapping for unexpected numerical errors. +
ExampleÂ 4.4.Â Check Solution Quality of newSolution
+ + returnCode=0; // 0 means no good solution + if (newSolutionValue<solutionValue) { // minimization + // check feasible + memset(rowActivity,0,numberRows*sizeof(double)); + for (iColumn=0;iColumn<numberColumns;iColumn++) { + CoinBigIndex j; + double value = newSolution[iColumn]; + if (value) { + for (j=columnStart[iColumn]; + j<columnStart[iColumn]+columnLength[iColumn];j++) { + int iRow=row[j]; + rowActivity[iRow] += value*element[j]; + } + } + } + // check was approximately feasible + bool feasible=true; + for (iRow=0;iRow<numberRows;iRow++) { + if(rowActivity[iRow]<rowLower[iRow]) { + if (rowActivity[iRow]<rowLower[iRow]10.0*primalTolerance) + feasible = false; + } + } + if (feasible) { + // new solution + memcpy(betterSolution,newSolution,numberColumns*sizeof(double)); + solutionValue = newSolutionValue; + // We have good solution + returnCode=1; + } + } + +
Table of Contents
+CBC's concept of branching is based on the idea of an "object". An object has (i) a feasible region, (ii) can be evaluated for infeasibility, (iii) can be branched on, e.g., a method of generating a branching object, which defines an up branch and a down branch, and (iv) allows comparsion of the effect of branching. Instances of objects include. +
+In ChapterÂ 5, + Branching + , we give examples of how to use existing branching objects. (The next revision of this Guide should include an example of how to write your own branching object; Contributions of examples are welcome.) +
+ +If the user declares variables as integer but does no more, then CBC will treat them +as simple integer variables. In many cases the user would like to do some more fine tuning. This section shows how to create integer variables with pseudo costs. When pseudo costs are given then +it is assumed that if a variable is at 1.3 then the cost of branching that variable down will be 0.3 times the down pseudo cost and the cost of branching up would be 0.7 times the up pseudo cost. Pseudo costs can be used both for branching and for choosing a node. + The full code is in longthin.cpp located in the CBC Samples directory, see + ChapterÂ 8, +More Samples +. +
+ The idea is simple for set covering problems. + Branching up gets us much closer to an integer solution so we will encourage that direction by branch up if variable value > 0.333333. + The expected cost of going up obviously depends on the cost of the + variable. The pseudo costs are choosen to reflect that fact. + +
ExampleÂ 5.1.Â CbcSimpleIntegerPseudoCosts
+ + int iColumn; + int numberColumns = solver3>getNumCols(); + // do pseudo costs + CbcObject ** objects = new CbcObject * [numberColumns]; + // Point to objective + const double * objective = model.getObjCoefficients(); + int numberIntegers=0; + for (iColumn=0;iColumn<numberColumns;iColumn++) { + if (solver3>isInteger(iColumn)) { + double cost = objective[iColumn]; + CbcSimpleIntegerPseudoCost * newObject = + new CbcSimpleIntegerPseudoCost(&model,numberIntegers,iColumn, + 2.0*cost,cost); + newObject>setMethod(3); + objects[numberIntegers++]= newObject; + } + } + // Now add in objects (they will replace simple integers) + model.addObjects(numberIntegers,objects); + for (iColumn=0;iColumn<numberIntegers;iColumn++) + delete objects[iColumn]; + delete [] objects; + +
+The code in ExampleÂ 5.1 also tries to give more importance to variables with more +coefficients. Whether this sort of thing is worthwhile should be the subject of experimentation. + + +
+In crew scheduling, the problems are long and thin. A problem may have a few rows but many thousands of variables. Branching a variable to 1 is very powerful as it fixes many other variables to zero, but branching to zero is very weak as thousands of variables can increase from zero. In crew scheduling problems, each constraint is a flight leg, e.g., JFK airport to DFW airport. +From DFW there may be several flights the crew could take next  suppose one flight is +the 9:30 flight from DFW to LAX airport. A binary branch is that the crew arriving +at DFW either take the 9:30 flight to LAX or they don't. This "followon" branching does not +fix individual variables. Instead this branching divides all the variables with entries in the JFKDFW +constraint into two groups  those with entries in the DFWLAX constraint and those without +entries. +
+ The full sample code for followon brancing is in crew.cpp + located in the CBC Samples directory, see + ChapterÂ 8, +More Samples +). In this case, the simple integer +variables are left which may be necessary if other sorts of constraints exist. Followon branching rules are to be considered first, so the priorities are set to indicate the followon rules take precedence. Priority 1 is the highest priority. + +
ExampleÂ 5.2.Â CbcFollowOn
+ + int iColumn; + int numberColumns = solver3>getNumCols(); + /* We are going to add a single followon object but we + want to give low priority to existing integers + As the default priority is 1000 we don't actually need to give + integer priorities but it is here to show how. + */ + // Normal integer priorities + int * priority = new int [numberColumns]; + int numberIntegers=0; + for (iColumn=0;iColumn<numberColumns;iColumn++) { + if (solver3>isInteger(iColumn)) { + priority[numberIntegers++]= 100; // low priority + } + } + /* Second parameter is set to true for objects, + and false for integers. This indicates integers */ + model.passInPriorities(priority,false); + delete [] priority; + /* Add in objects before we can give them a priority. + In this case just one object +  but it shows the general method + */ + CbcObject ** objects = new CbcObject * [1]; + objects[0]=new CbcFollowOn(&model); + model.addObjects(1,objects); + delete objects[0]; + delete [] objects; + // High priority + int followPriority=1; + model.passInPriorities(&followPriority,true); + +
Table of Contents
Table of Contents
+ CBC uses a generic OsiSolverInterface and its resolve capability. + This does not give much flexibility so advanced users can inherit from their interface + of choice. This section illustrates how to implement a specialized solver for a long thin problem, e.g., fast0507 again. As with the other examples in the Guide, the sample code is not guaranteed to be the fastest way to solve the problem. The main purpose of the example is to illustrate techniques. The full source is in CbcSolver2.hpp and CbcSolver2.cpp located in the CBC Samples directory, see + ChapterÂ 8, +More Samples +. +
+The method initialSolve is called a few times in CBC, and provides a convenient starting point. The modelPtr_ derives from OsiClpSolverInterface. +
ExampleÂ 7.1.Â initialSolve()
+ + // modelPtr_ is of type ClpSimplex * + modelPtr_>setLogLevel(1); // switch on a bit of printout + modelPtr_>scaling(0); // We don't want scaling for fast0507 + setBasis(basis_,modelPtr_); // Put basis into ClpSimplex + // Do long thin by sprint + ClpSolve options; + options.setSolveType(ClpSolve::usePrimalorSprint); + options.setPresolveType(ClpSolve::presolveOff); + options.setSpecialOption(1,3,15); // Do 15 sprint iterations + modelPtr_>initialSolve(options); // solve problem + basis_ = getBasis(modelPtr_); // save basis + modelPtr_>setLogLevel(0); // switch off printout + +
+The resolve() method is more complicated than initialSolve(). The main pieces of data are a counter count_ which is incremented each solve and an integer array node_ which stores the last time +a variable was active in a solution. For the first few solves, the normal Dual Simplex is called and +node_ array is updated. +
ExampleÂ 7.2.Â First Few Solves
+ + if (count_<10) { + OsiClpSolverInterface::resolve(); // Normal resolve + if (modelPtr_>status()==0) { + count_++; // feasible  save any nonzero or basic + const double * solution = modelPtr_>primalColumnSolution(); + for (int i=0;i<numberColumns;i++) { + if (solution[i]>1.0e6modelPtr_>getStatus(i)==ClpSimplex::basic) { + node_[i]=CoinMax(count_,node_[i]); + howMany_[i]++; + } + } + } else { + printf("infeasible early on\n"); + } + } + +
+After the first few solves, only those variables which took part in a solution in the last so many +solves are used. As fast0507 is a set covering problem, any rows which are already covered can be taken out. +
ExampleÂ 7.3.Â Create Small SubProblem
+ + int * whichRow = new int[numberRows]; // Array to say which rows used + int * whichColumn = new int [numberColumns]; // Array to say which columns used + int i; + const double * lower = modelPtr_>columnLower(); + const double * upper = modelPtr_>columnUpper(); + setBasis(basis_,modelPtr_); // Set basis + int nNewCol=0; // Number of columns in small model + // Column copy of matrix + const double * element = modelPtr_>matrix()>getElements(); + const int * row = modelPtr_>matrix()>getIndices(); + const CoinBigIndex * columnStart = modelPtr_>matrix()>getVectorStarts(); + const int * columnLength = modelPtr_>matrix()>getVectorLengths(); + + int * rowActivity = new int[numberRows]; // Number of columns with entries in each row + memset(rowActivity,0,numberRows*sizeof(int)); + int * rowActivity2 = new int[numberRows]; // Lower bound on row activity for each row + memset(rowActivity2,0,numberRows*sizeof(int)); + char * mark = (char *) modelPtr_>dualColumnSolution(); // Get some space to mark columns + memset(mark,0,numberColumns); + for (i=0;i<numberColumns;i++) { + bool choose = (node_[i]>count_memory_&&node_[i]>0); // Choose if used recently + // Take if used recently or active in some sense + if ((choose&&upper[i]) + (modelPtr_>getStatus(i)!=ClpSimplex::atLowerBound&& + modelPtr_>getStatus(i)!=ClpSimplex::isFixed) + lower[i]>0.0) { + mark[i]=1; // mark as used + whichColumn[nNewCol++]=i; // add to list + CoinBigIndex j; + double value = upper[i]; + if (value) { + for (j=columnStart[i]; + j<columnStart[i]+columnLength[i];j++) { + int iRow=row[j]; + assert (element[j]==1.0); + rowActivity[iRow] ++; // This variable can cover this row + } + if (lower[i]>0.0) { + for (j=columnStart[i]; + j<columnStart[i]+columnLength[i];j++) { + int iRow=row[j]; + rowActivity2[iRow] ++; // This row redundant + } + } + } + } + } + int nOK=0; // Use to count rows which can be covered + int nNewRow=0; // Use to make list of rows needed + for (i=0;i<numberRows;i++) { + if (rowActivity[i]) + nOK++; + if (!rowActivity2[i]) + whichRow[nNewRow++]=i; // not satisfied + else + modelPtr_>setRowStatus(i,ClpSimplex::basic); // make slack basic + } + if (nOK<numberRows) { + // The variables we have do not cover rows  see if we can find any that do + for (i=0;i<numberColumns;i++) { + if (!mark[i]&&upper[i]) { + CoinBigIndex j; + int good=0; + for (j=columnStart[i]; + j<columnStart[i]+columnLength[i];j++) { + int iRow=row[j]; + if (!rowActivity[iRow]) { + rowActivity[iRow] ++; + good++; + } + } + if (good) { + nOK+=good; // This covers  put in list + whichColumn[nNewCol++]=i; + } + } + } + } + delete [] rowActivity; + delete [] rowActivity2; + if (nOK<numberRows) { + // By inspection the problem is infeasible  no need to solve + modelPtr_>setProblemStatus(1); + delete [] whichRow; + delete [] whichColumn; + printf("infeasible by inspection\n"); + return; + } + // Now make up a small model with the right rows and columns + ClpSimplex * temp = new ClpSimplex(modelPtr_,nNewRow,whichRow,nNewCol,whichColumn); + +
+If the variables cover the rows, then the problem is feasible (no cuts are being used). (If the rows +were equality constraints, then this might not be the case. More work would be needed.) After the solution to the subproblem, the reduced costs of the full problem are checked. If the reduced cost of any variable not in the subproblem is negative, the code goes back to the full problem and cleans up with Primal Simplex. +
ExampleÂ 7.4.Â Check Optimal Solution
+ + temp>setDualObjectiveLimit(1.0e50); // Switch off dual cutoff as problem is restricted + temp>dual(); // solve + double * solution = modelPtr_>primalColumnSolution(); // put back solution + const double * solution2 = temp>primalColumnSolution(); + memset(solution,0,numberColumns*sizeof(double)); + for (i=0;i<nNewCol;i++) { + int iColumn = whichColumn[i]; + solution[iColumn]=solution2[i]; + modelPtr_>setStatus(iColumn,temp>getStatus(i)); + } + double * rowSolution = modelPtr_>primalRowSolution(); + const double * rowSolution2 = temp>primalRowSolution(); + double * dual = modelPtr_>dualRowSolution(); + const double * dual2 = temp>dualRowSolution(); + memset(dual,0,numberRows*sizeof(double)); + for (i=0;i<nNewRow;i++) { + int iRow=whichRow[i]; + modelPtr_>setRowStatus(iRow,temp>getRowStatus(i)); + rowSolution[iRow]=rowSolution2[i]; + dual[iRow]=dual2[i]; + } + // See if optimal + double * dj = modelPtr_>dualColumnSolution(); + // get reduced cost for large problem + // this assumes minimization + memcpy(dj,modelPtr_>objective(),numberColumns*sizeof(double)); + modelPtr_>transposeTimes(1.0,dual,dj); + modelPtr_>setObjectiveValue(temp>objectiveValue()); + modelPtr_>setProblemStatus(0); + int nBad=0; + + for (i=0;i<numberColumns;i++) { + if (modelPtr_>getStatus(i)==ClpSimplex::atLowerBound + &&upper[i]>lower[i]&&dj[i]<1.0e5) + nBad++; + } + // If necessary clean up with primal (and save some statistics) + if (nBad) { + timesBad_++; + modelPtr_>primal(1); + iterationsBad_ += modelPtr_>numberIterations(); + } + +
+The array node_ is updated, as for the first few solves. To give some idea of the effect of this tactic, the problem fast0507 has 63,009 variables but the small problem never has more than 4,000 variables. In only about ten percent of solves was it necessary to resolve, and then the average number of iterations +on full problem was less than 20. +
+To give another example  again only for illustrative purposes  it is possible to do quadratic +MIP with CBC. In this case, we make resolve the same as +initialSolve. + The full code is in ClpQuadInterface.hpp and + ClpQuadInterface.cpp located in the CBC Samples directory, see + ChapterÂ 8, +More Samples +). +
ExampleÂ 7.5.Â Solving a Quadratic MIP
+ + // save cutoff + double cutoff = modelPtr_>dualObjectiveLimit(); + modelPtr_>setDualObjectiveLimit(1.0e50); + modelPtr_>scaling(0); + modelPtr_>setLogLevel(0); + // solve with no objective to get feasible solution + setBasis(basis_,modelPtr_); + modelPtr_>dual(); + basis_ = getBasis(modelPtr_); + modelPtr_>setDualObjectiveLimit(cutoff); + if (modelPtr_>problemStatus()) + return; // problem was infeasible + // Now pass in quadratic objective + ClpObjective * saveObjective = modelPtr_>objectiveAsObject(); + modelPtr_>setObjectivePointer(quadraticObjective_); + modelPtr_>primal(); // Th model has a quadratic objective, + // so this invokes quadratic primal. + modelPtr_>setDualObjectiveLimit(cutoff); + if (modelPtr_>objectiveValue()>cutoff) + modelPtr_>setProblemStatus(1); + modelPtr_>setObjectivePointer(saveObjective); + +
+Rather than implementing all the method from scratch, we based the quadratic solver ClpQuadInteface on the linear programming solver OsiClpSolverInterface. This is a convenient approach to take when prototyping ideas. After the merit of an idea is proven, the user can decide is a more serious implementation is warranted. +
Table of Contents
+The CBC distribution includes a number of .cpp sample files. +Users are encouraged to use them as starting points for their own CBC projects. +The files can be found in the COIN/Cbc/Samples/ directory. +For the latest information on compiling and running these samples, please see +the file COIN/Cbc/Samples/INSTALL. Most of them can be built +by
make DRIVER=name
which produces an executable testit. Below is a list of +some of the most useful sample files with a short description for each file. +
TableÂ 8.1.Â Basic Samples
+ Source fileÂ Â Â Â Â Â Â +  + Description + 

minimum.cpp  + This is a CBC "Hello, world" program. It reads a problem + in MPS file format, and solves the problem using simple branchandbound. + 
sample2.cpp  + This is designed to be a file that a user could modify to get a useful + driver program for his or her project. In particular, it demonstrates + the use of CGL's preprocess functionality. + It uses CbcBranchUser.cpp, + CbcCompareUser.cpp and + CbcHeuristicUser.cpp + with corresponding *.hpp files. + 
TableÂ 8.2.Â Advanced Samples
+ Source fileÂ Â Â Â Â Â Â +  + Description + 

crew.cpp  + This sample shows the use of advanced branching and a use of priorities. + It uses CbcCompareUser.cpp + with corresponding *.hpp files. + 
longthin.cpp  + This sample shows the advanced use of a solver. It also has coding for + a greedy heuristic. + The solver is given in CbcSolver2.hpp and + CbcSolver2.cpp. + The heuristic is given in CbcHeuristicGreedy.hpp and + CbcHeuristicGreedy.cpp. + It uses CbcBranchUser.cpp and + CbcCompareUser.cpp + with corresponding *.hpp files. + 
qmip.cpp  + This solves a quadratic MIP. It is to show advanced use of a solver. + The solver is given in ClpQuadInterface.hpp and + ClpQuadInterface.cpp. + It uses CbcBranchUser.cpp and + CbcCompareUser.cpp + with corresponding *.hpp files. + 
sos.cpp  + This artificially creates a Special Ordered Set problem. + 
lotsize.cpp  + This artificially creates a Lot Sizing problem. + 
+ Messages and codes passed by CBC are listed in the + tables below. For a complete list, see COIN/Cbc/CbcMessages.cpp. The notation used is the same as for the printf in the C programming language. +
+ +
There are several log levels. Setting the log level to be i produces the log messages for level i and all levels less than i. +
TableÂ 9.1.Â + CBC Messages Passed At Log Level 0 +
+ Code +  Â  + Text and notes +  Â 

+ 3007 +  Â  No integer variables  nothing to do  Â 
Â  + +  Â 
TableÂ 9.2.Â + CBC Messages Passed At or Above Log Level 1 +
+ Code +  Â  + Text and notes +  Â 

+ 1 +  Â  Search completed  best objective %g, took %d iterations and %d nodes +  Â 
Â  + +  Â  
+ 3 +  Â  Exiting on maximum nodes +  Â 
Â  + +  Â  
+ 4 +  Â  + Integer solution of %g found after %d iterations and %d nodes +  Â 
Â  + +  Â  
+ 5 +  Â  + Partial search  best objective %g (best possible %g), took %d iterations and %d nodes +  Â 
Â  + +  Â  
+ 6 +  Â  + The LP relaxation is infeasible or too expensive +  Â 
Â  + +  Â  
+ 9 +  Â  + Objective coefficients multiple of %g +  Â 
Â  + +  Â  
+ 10 +  Â  + After %d nodes, %d on tree, %g best solution, best possible %g +  Â 
Â  + +  Â  
+ 11 +  Â  + Exiting as integer gap of %g less than %g or %g%% +  Â 
Â  + +  Â  
+ 12 +  Â  + Integer solution of %g found by heuristic after %d iterations and %d nodes +  Â 
Â  + +  Â  
+ 13 +  Â  + At root node, %d cuts changed objective from %g to %g in %d passes +  Â 
Â  + +  Â  
+ 14 +  Â  + Cut generator %d (%s)  %d row cuts (%d active), %d column cuts %? in %g seconds  new frequency is %d +  Â 
Â  + +  Â  
+ 16 +  Â  + Integer solution of %g found by strong branching after %d iterations and %d nodes +  Â 
Â  + +  Â  
+ 17 +  Â  + %d solved, %d variables fixed, %d tightened +  Â 
Â  + +  Â  
+ 18 +  Â  + After tightenVubs, %d variables fixed, %d tightened +  Â 
Â  + +  Â  
+ 19 +  Â  + Exiting on maximum solutions +  Â 
Â  + +  Â  
+ 20 +  Â  + Exiting on maximum time +  Â 
Â  + +  Â  
+ 23 +  Â  + Cutoff set to %g  equivalent to best solution of %g +  Â 
Â  + +  Â  
+ 24 +  Â  + Integer solution of %g found by subtree after %d iterations and %d nodes +  Â 
Â  + +  Â  
+ 26 +  Â  + Setting priorities for objects %d to %d inclusive (out of %d) +  Â 
Â  + +  Â  
+ 3008 +  Â  + Strong branching is fixing too many variables, too expensively! +  Â 
Â  + +  Â 
TableÂ 9.3.Â + CBC Messages Passed At or Above Log Level 2 +
+ Code +  Â  + Text and notes +  Â 

+ 15 +  Â  + Node %d Obj %g Unsat %d depth %d +  Â 
Â  + +  Â  
+ 21 +  Â  + On closer inspection node is infeasible +  Â 
Â  + +  Â  
+ 22 +  Â  + On closer inspection objective value of %g above cutoff of %g +  Â 
Â  + +  Â  
+ 23 +  Â  + Allowing solution, even though largest row infeasibility is %g +  Â 
Â  + +  Â 
Q:.  + What is CBC? + 
A:.  + The COINOR Branch and Cut code + is designed to be a high quality mixed integer code provided under the terms of the + Common Public License. + CBC is written in C++, and is primarily intended to be used as a callable + library (though a rudimentary standalone executable exists). + The first documented release was .90.0 The current release is version .90.0. (JF 04/01/05) + 
Q:.  + What are some of the features of CBC? + 
A:.  + CBC allows the use of any CGL cuts and the use of heuristics and + specialized branching methods. (JF 04/01/05) + 
Q:.  + How do I obtain and install CBC? + 
A:.  + Please see the + COINOR FAQ + for details on how to + obtain + and + install + COINOR modules. (JF 04/01/05) + 
Q:.  + Is CBC reliable? + 
A:.  + CBC has been tested on many problems, + but more testing and improvement is needed before it can get to version 1.0. (JF 04/01/05) + 
Q:.  + Is there any documentation for CBC? + 
A:.  + If you can see this you have the best there is:) + Also available is a list of + CBC class descriptions generated + by Doxygen. (JF 04/01/05) + 
Q:.  + Is CBC as fast as Cplex or Xpress? + 
A:.  + No. However its design is much more flexible so advanced users + will be able to tailor CBC to their needs. (JF 04/01/05) + 
Q:.  + When will version 1.0 of CBC be available? + 
A:.  + It is expected that version 1.0 will be released in time for the 2005 + INFORMS annual meeting. (JF 04/01/05) + 
Q:.  + What can the community do to help? + 
A:.  + People from all around the world are already helping. There are + probably ten people who do not always post to the discussion mail list but are constantly + "improving" the code by demanding performance or bug fixes or enhancements. And there + are others posting questions to discussion groups. (JF 04/01/05) + + A good start is to join the coindiscuss + mailing list where CBC is discussed. Some + other possibilities include: +

+There is Doxygen content for CBC available online at + +http://www.coinor.org/Doxygen/Cbc/index.html. A local version of the +Doxygen content can be generated from the CBC distribution. To do so, in the +directory COIN/Cbc, enter make doc. +The Doxygen content will be created in the directory +COIN/Cbc/Doc/html. The same can be done for +the COIN core, from the COIN/Coin directory. +
Revision History  

Revision 0.21  May 10, 2005  RLH 
Fixed typos caught by Cole Smith, editor of the INFORMS Tutorial Book, and added place holders for needstobewritten sections, e.g., Using CGL with CBC.  
Revision 0.2  May 2, 2005  RLH 
Book chapter for CBC Tutorial at INFORMS 2005 annual meeting. Reorganized the content. Added CBC Messages. Changed the font type to distinguish functions/variables/classnames/code from text.  
Revision 0.1  April 1, 2005  JF 
First draft. The CBC documentation uses the DocBook CLP documentation created by David de la Nuez. 
+ The COIN + ^{[}1] +Branch and Cut solver (CBC) is an opensource mixedinteger program (MIP) solver written in C++. CBC is intended to be used primarily as a callable library to create customized branchandcut solvers. A basic, standalone executable version is also available. CBC is an active opensource project led by John Forrest at www.coinor.org. +
^{[1] } + The complete acronym is "COINOR" which stands for the Compuational Infrastructure for Operations Research. For simplicity (and in keeping with the directory and function names) we will simply use "COIN". +
+ The primary users of CBC are expected to be developers implementing customized branchandcut algorithms in C++ using CBC as a library. Consequently, this document assumes a working knowledge of + C++, including basic + objectoriented programming terminology, and familiarity with the fundamental concepts of + + linear programming (LP) and + + mixed integer programming (MIP). +
+ +CBC relies on other parts of the COIN repository. CBC needs a LP solver and relies on the COIN Open Solver Inteface (OSI) to communicate with the user's choice of solver. Any LP solver with an OSI interface can be used with CBC. The LP solver expected to be used most commonly is COIN's native linear program solver, CLP. For cut generators, CBC relies on the COIN Cut Generation Library (CGL). Any cut generator written to CGL standards can be used with CBC. Some of the cut generators in CGL rely on other parts of COIN, e.g., CGL's Gomory cut generator rely on the factorization functionality of CoinFactorization. This document assumes basic familiarity with OSI and CGL. +
+Technically speaking, CBC accesses the solver (and sometime the model and data it contains) through an OSISolverInterface. For the sake of simplicity, we will refer to the OsiSolverInterface as "the solver" in this document, rather than "the standard application programming interface to the solver." We hope any confusion caused by blurring this distinction will be mitigated by the shorter sentences. + +
+In summary, readers should have the following prerequisites: +
+
+ Before examining CBC in more detail, we tersely describe the basic branchandcut algorithm by way of example, (which should really be called branchandcutandbound) and show the major C++ class(es) in CBC related to each step. The major CBC classes, labeled (A) through (F), are described in Table 1.1. +
+Step 1. (Bound) Given a MIP model to minimize where some variables must take on integer values (e.g., 0, 1, or 2), relax the integrality requirements (e.g., consider each "integer" variable to be continuous with a lower bound of 0.0 and an upper bound of 2.0). Solve the resulting linear model with an LP solver to obtain a lower bound on the MIP's objective function value. If the optimal LP solution has integer values for the MIP's integer variables, we are finished. Any MIPfeasible solution provides an upper bound on the objective value. The upper bound equals the lower bound; the solution is optimal. +
+Step 2. (Branch) Otherwise, there exists an "integer" variable with a nonintegral value. Choose one nonintegral variable (e.g., with value 1.3) (A)(B) and branch. Create two +^{[2]} +nodes, one with the branching variable having an upper bound of 1.0, and the other with the branching variable having a lower bound of 2.0. Add the two nodes to the search tree. +
+While (search tree is not empty) { +
+ Step 3. (Choose Node) Pick a node off the tree (C)(D) +
+ Step 4. (Reoptimize LP) Create an LP relaxation and solve. +
+ Step 5. (Bound) Interrogate the optimal LP solution, and try to prune the node by one of the following. +
+
+ Step 6. (Branch) If we were unable to prune the node, then branch. Choose one nonintegral variable to branch on (A)(B). Create two nodes and add them to the search tree. +} +
+This is the outline of a "branchandbound" algorithm. If in optimizing the linear programs, we use cuts to tighten the LP relaxations (E)(F), then we have a "branchandcut" algorithm. (Note, if cuts are only used in Step 1, the method is called a "cutandbranch" algorithm.) + +
Table 1.1. Associated Classes
+ Note +  + Class name +  + Description + 

+ (A) +  CbcBranch...  + These classes define the nature of MIP's discontinuity. The simplest discontinuity + is a variable which must take an integral value. Other types of discontinuities + exist, e.g., lotsizing variables. + 
+ (B) +  CbcNode  + This class decides which variable/entity to branch on next. + Even advanced users will probably only interact with this class by setting + CbcModel parameters ( e.g., priorities). + 
+ (C) +  CbcTree  + All unsolved models can be thought of as being nodes on a tree where each + node (model) can branch two or more times. The interface with this class is helpful to know, but +the user can pretty safely ignore the inner workings of this class. + 
+ (D) +  CbcCompare...  + These classes are used in determine which of the unexplored nodes in the tree to consider next. These + classes are very small simple classes that can be tailored to suit the problem. + 
+ (E) +  CglCutGenerators  + Any cut generator from CGL can be used in CBC. The cut generators are passed to CBC with parameters + which modify when each generator will be tried. All cut generators should be tried to + determine which are effective. Few users will write their own cut generators. + 
+ (F) +  CbcHeuristics  + Heuristics are very important for obtaining valid solutions quickly. Some + heuristics are available, but this is an area where it is useful and interesting to + write specialized ones. + 
+ There are a number of resources available to help new CBC users get started. + This document is designed to be used in conjunction with the files in the + Samples subdirectory of the main CBC directory (COIN/Cbc/Samples). + The Samples illustrate how to use CBC and may also serve as useful starting points + for user projects. In the event that either this document or the available + Doxygen content conflicts with the observed + behavior of the source code, the comments in the header files, found in + COIN/Cbc/include, are the ultimate reference. +
^{[2] } +The current implementation of CBC allow two branches to be created. More general number of branches could be implemented. +
+ The program in Example 2.1 creates a OsiClpSolverInterface solver interface (i.e., solver1), and reads an MPS file. If there are no errors, the program passes the problem to CbcModel which solves the problem using the branchandbound algorithm. The part of the program which solves the problem is very small (one line!) but before that one line, the LP solver (i.e., solver1) had to be created and populated with the problem. After that one line, the results were printed out. +
+The program in Example 2.1 illustrates the dependency of CBC on + the OsiSolverInterface class. The constructor of CbcModel takes a pointer to an OsiSolverInterface (i.e., a solver). The CbcModel clones the solver, and uses its own instance of the solver. The CbcModel's solver and the original solver (e.g., solver1) are not in sync unless the user synchronizes them. The user can always access the CbcModel's solver through the model() class. To synchronize the two solvers, explicitly refreshing the original, e.g., +
+ solver1 = model.solver(); +
+CbcModel's method solver() returns a pointer to CBC's cloned solver. +
+For convenience, many of the OSI methods to access problem data have identical method names in CbcModel. (It's just more convenient to type model.getNumCols() rather than model.solver()>getNumCols()). The CbcModel refreshes its solver at certain logical points during the algorithm. At these points, the information from the CbcModel model will match the information from the model.solver(). Elsewhere, the information may vary. For instance, the method CbcModel::bestSolution() will contain the best solution so far, the OSI method getColSolution() may not. In this case, it is safer to use CbcModel::bestSolution(). +
+While all the OSI methods used in minimum.cpp have equivalent methods in CbcModel, there are some OSI methods which do not. For example, if the program produced a lot of undesired output, one might add the line +
+ model.solver()>setHintParam(OsiDoReducePrint,true,OsiHintTry); +
+ + to reduce the output. There is no setHintParam() method in CbcModel. +
Table 2.1. + Methods for Getting Solution Information from OSI +
+ Purpose +  + Name +  + Notes + 

+ Primal column solution +  const double * getColSolution()  + The OSI method will return the best solution found thus far, unless none has been found. It is safer to use CbcModel version, CbcModel::bestSolution() 
+ Dual row solution +  const double * getRowPrice()  + Identical CbcModel version available, CbcModel::getRowPrice(). + 
+ Primal row solution +  const double * getRowActivity()  + Identical CbcModel version available, CbcModel::getRowActivity(). + 
+ Dual column solution +  const double * getReducedCost()  + Identical CbcModel version available, CbcModel::gtReducedCost(). + 
+ Number of rows in model +  int getNumRows()  + Identical CbcModel version available, CbcModel::getNumRows(). Note: the number of rows can change due to cuts. + 
+ Number of columns in model +  int getNumCols()  + Identical CbcModel version available, CbcModel::getNumCols(). + 
+Most of the parameter setting in CBC is done through CbcModel methods. The most commonly used set and get methods are listed in Table 2.2. +
Table 2.2. Useful Set and Get Methods in CbcModel
+ Method(s) +  + Description + 

bool setMaximumNodes(int value) int getMaximumNodes() const bool setMaximumSeconds(double value) double getMaximumSeconds() bool setMaximumSolutions(double value) double getMaximumSolutions() const  + These set methods tell CBC to stop after a given number of nodes, + seconds, or solutions is reached. The get methods return the corresponding values. + 
bool setIntegerTolerance(double value) const double getIntegerTolerance() const  + An integer variable is deemed to be at an integral value if it is no further than this value (tolerance) away. + 
bool setAllowableGap(double value) double getAllowableGap() const bool setAllowablePercentageGap(double value) double getAllowablePercentageGap() const bool setAllowableFractionGap(double value) double getAllowableFractionGap() const  CbcModel returns if the gap between the best known solution and the best + possible solution is less than this value, or as a percentage, or a fraction. + 
void setNumberStrong(double value) int numberStrong() +^{[a]} const  + These methods set or get the maximum number of candidates at a node to + be evaluated for strong branching. + 
void setPrintFrequency(int value) int printFrequency() const  + Controls the number of nodes evaluated between status prints. + Print frequency has a very slight overhead, if value is small. + 
int getNodeCount() const  + Returns number of nodes evaluated in the search. + 
int numberRowsAtContinuous() const  + Returns number of rows in the problem when handed to the solver (i.e., before cuts where added). Commonly used in implementing heuristics. + 
int numberIntegers() const const int * integerVariable() const  + Returns number of integer variables and an array specifying them. + 
bool isBinary(int colIndex) const bool isContinuous(int colIndex) const bool isInteger(int colIndex) const  + Returns information on variable colIndex. OSI methods + can be used to set these attributes (before handing the model to CbcModel). + 
double getObjValue() const  + This method returns the best objective value so far. + 
double getCurrentObjValue() const  + This method returns the current objective value. + 
const double * getObjCoefficients() const  + This method return the objective coefficients. + 
const double * getRowLower() const const double * getRowUpper() const const double * getColLower() const const double * getColUpper() const  + These methods return the lower and upper bounds on row and column activities. + 
const CoinPackedMatrix * getMatrixByRow() const  + This method returns a pointer to a row copy of matrix stored as a + CoinPackedMatrix which can be further examined. + 
const CoinPackedMatrix * getMatrixByCol() const  + This method returns a pointer to a column copy of matrix stored as a + CoinPackedMatrix which can be further examined. + 
CoinBigIndex getNumElements() const^{[b]}  + Returns the number of nonzero elements in the problem matrix. + 
void setObjSense(double value) double getObjSense() const  + These methods set and get the objective sense. The parameter + value should be +1 to minimize and 1 to maximize. + 
^{[a] } +This methods (and some of the other) do not follow the "get" convention. The convention has changed over time and there are still some inconsistencies to be cleaned up. + ^{[b] } + CoinBigIndex is a typedef which in + most cases is the same as int. + 
Table 2.3. Classes Used by CbcModel  Most Useful
+ Class name +  + Description +  + Notes + 

CbcCompareBase  + Controls which node on the tree is selected. +  + The default is CbcCompareDefault. Other comparison classes in CbcCompareActual.hpp include CbcCompareDepth and CbcCompareObjective. Experimenting with these classes and creating new compare classes is easy. + 
CbcCutGenerator  + A wrapper for CglCutGenerator with additional data to control when the cut generator is invoked during the tree search. +  + Other than knowing how to add a cut generator to CbcModel, there is not much the average user needs to know about this class. However, sophisticated users can implement their own cut generators. 
CbcHeuristic  + Heuristic that attempts to generate valid MIPsolutions leading to good upper bounds. +  + Specialized heuristics can dramatically improve branchandcut performance. As many different heuristics as desired can be used in CBC. Advanced users should consider implementing custom heuristics when tackling difficult problems. 
CbcObject  + Defines what it means for a variable to be satisfied. Used in branching. +  + Virtual class. CBC's concept of branching is based on the idea of an "object". An object has (i) a feasible region, (ii) can be evaluated for infeasibility, (iii) can be branched on, e.g., a method of generating a branching object, which defines an up branch and a down branch, and (iv) allows comparison of the effect of branching. Instances of objects include CbcSimpleInteger, CbcSimpleIntegerPseudoCosts, CbcClique, CbcSOS (type 1 and 2), CbcFollowOn, and CbcLotsize. + 
OsiSolverInterface  + Defines the LP solver being used and the LP model. Normally + a pointer to the desired OsiSolverInteface is passed to CbcModel before branch and cut. +  + Virtual class. The user instantiates the solver interface of their choice, e.g., + OsiClpSolverInterface. + 
+There is not much about the classes listed in Table 2.4 that the average user needs to know about. +
Table 2.4. Classes Used by CbcModel  Least Useful
+ Class name +  + Description +  + Notes + 

CbcBranchDecision  + Used in choosing which variable to branch on, however, most of + the work is done by the definitions in CbcObject. +  + Defaults to CbcBranchDefaultDecision. + 
CbcCountRowCut  + Interface to OsiRowCut. It counts the usage so cuts can gracefully vanish. +  + See OsiRowCut for more details. 
CbcNode  + Controls which variable/entity is selected to be branch on. +  + Controlled via CbcModel parameters. Information from CbcNode can be useful in creating customized node selection rules. 
CbcNodeInfo  + Contains data on bounds, basis, etc. for one node of the search tree. +  + Header is located in CbcNode.hpp. 
CbcTree  + Defines how the search tree is stored. +  + This class can be changed but it is not likely to be modified. 
CoinMessageHandler  + Deals with message handling +  + The user can inherit from CoinMessageHandler to specialize message handling. + 
CoinWarmStartBasis  + Basis representation to be used by solver + 
Table 2.4. Classes Used by CbcModel  Most Useful
+ Class name +  + Description +  + Notes + 

CbcCompareBase  + Controls which node on tree is selected +  + The default is CbcCompareDefault. Other comparison classes in CbcCompareActual.hpp include + CbcCompareDepth and CbcCompareObjective. It is very easy for user to + experiment with different comparisons. + 
CbcCutGenerator  + A wrapper for CglCutGenerator with additional data to control when the cut generator is used. +  + Other than knowing how to add a cut generator to CbcModel, there is not much the average user needs to know about this class. 
CbcHeuristic  + Heuristic that attempts to generate valid solutions +  + Users can get a lot of value out of coding specialized heuristics. There can be + as many different heuristics as you like. 
CbcObject  + Defines what it means for a variable to be satisfied. +  + Virtual class. The branching model used in CBC is based on the idea of an "object". An object has (i) feasible region, (ii) can be evaluated for infeaibility, (iii) can be branched on, e.g., a method of generating a branching object, which defines an up branch and a down branch and (iv) allows comparsion of the effect of branching. Instances include simple integer, simple integer with pseudocosts, SOS (type 1 and 2), and lotsizing (see CbcBranch....hpp). + 
OsiSolverInterface  + Defines the LP solver being used and the LP model. Normally + a pointer to the desired OsiSolverInteface is passed to CbcModel before branch and cut. +  + Virtual class. The user instantiates the solver interface of their choice, e.g., + OsiClpSolverInterface. + 
Table 2.5. Classes Used by CbcModel  Least Useful
+ Class name +  + Description +  + Notes + 

CbcBranchDecision  + Used in choosing which variable to branch on, however, most of + the work is done by the definitions in CbcObject. +  + Defaults to CbcBranchDefaultDecision. + 
CbcCountRowCut  + Interface to OsiRowCut. It counts the usage so cuts can gracefully vanish. +  + See OsiRowCut for more details. 
CbcNode  + Controls which variable/entity is selected to be branch on. +  + Controlled via CbcModel parameters. 
CbcNodeInfo  + Contains data on bounds, basis, etc. for one node of the search tree. +  + Header is located in CbcNode.hpp. 
CbcTree  + Defines how the search tree is stored. +  + This class can be changed but it is not likely to be modified. 
CoinMessageHandler  + Deals with message handling +  + The user can inherit from CoinMessageHandler to specialize message handling. + 
CoinWarmStartBasis  + Basis representation to be used by solver + 
+CBC provides an abstract base class, CbcCompareBase, and implementations of several commonly used node selection strategies as Compare Classes, see Table 3.1. +
Table 3.1. Compare Classes Provided
+ Class name +  + Description + 

CbcCompareDepth  + This will always choose the node deepest in tree. It gives minimum + tree size but may take a long time to find the best solution. + 
CbcCompareObjective  + This will always choose the node with the best objective value. This may + give a very large tree. It is likely that the first solution found + will be the best and the search should finish soon after the first solution + is found. + 
CbcCompareDefault  + This is designed to do a mostly depthfirst search until a solution has + been found. It then use estimates that are designed to give a slightly better solution. + If a reasonable number of nodes have been explored (or a reasonable number of + solutions found), then this class will adopt a breadthfirst search (i.e., making a comparison based strictly on objective function values) unless the tree is very large, in which case it will revert to depthfirst search. A better description of CbcCompareUser is given below. + 
CbcCompareEstimate  + When pseudo costs are invoked, CBC uses the psuedo costs to guess a solution. This class uses the guessed solution. + 
+ It is relatively simple for a user to create a customized node selection by creating a new compare class instances. The code in Example 3.1 describes how to build a new comparison class and the reasoning behind it. The complete source can be found in CbcCompareUser.hpp and CbcCompareUser.cpp, located in the CBC Samples directory. Besides the constructor, the only method the user must implement in CbcCompare is bool test(CbcNode* x, CbcNode* y)) which returns true if node y is preferred over node x. In the test() method, information from CbcNode can easily be used. Table 3.2 lists some commonly used methods to access information at a node. +
Table 3.2. Information Available from CbcNode
double objectiveValue() const  + Value of objective at the node. + 
int numberUnsatisfied() const  + Number of unsatisfied integers (assuming branching + object is an integer  otherwise it might be number of unsatisfied sets). + 
int depth() const  + Depth of the node in the search tree. + 
double guessedObjectiveValue() const  + Returns the guessed objective value, if the user was setting this (e.g., if using pseudo costs). + 
int way() const  + The way which branching would next occur from this node + (for more advanced use). + 
int variable() const  + The branching "variable" (associated with the CbcBranchingObject  for more advanced use). + 
+Initially, weight_ is 1.0 and the search is biased towards depth first. In +fact, test() prefers y if y has fewer unsatisfied variables. In the case of a tie, test() prefers the node with the greater depth in tree. The full code for the CbcCompareUser::test() method is given in Example 3.1. +
+CBC calls the method newSolution() after a new solution is found. The method newSolution() interacts with test() by means of the variable weight_. If the solution was achieved by branching, a calculation is made to determine the cost per unsatisfied integer variable to go from the continuous solution to an integer solution. The variable weight_ is then set to aim at a slightly better solution. From then on, test() returns true if it seems that y will lead to a better solution than x. This source for newSolution() in given in Example 3.2. +
+ +As the search progresses, the comparison can be modified. If many nodes (or many solutions) have been generated, then weight_ is set to 0.0 leading to a breadthfirst search. Breadthfirst search can lead to an enormous tree. If the tree size is exceeds 10000, it may be desirable to return to a search biased towards depth first. Changing the behavior in this manner is done by the method every1000Nodes shown in Example 3.3. +
+ This describes how to build a greedy heuristic for a set covering problem. + A more general version is in CbcHeuristicGreedy.hpp and + CbcHeuristicGreedy.cpp which can be found in the COIN/Cbc/Samples directory, see Chapter 6, +More Samples +. + + The heuristic we will code will leave all variables which are at one at this node of the + tree to that value and will + initially set all others to zero. We then sort all variables in order of their cost + divided by the number of entries in rows which are not yet covered. We may randomize that + value a bit so that ties will be broken in different ways on different runs of the heuristic. + We then choose the best one and set it to one and repeat the exercise. Because this is + a set covering problem ≥ we are guaranteed to find a solution (not necessarily a + better one though). We could + improve the speed by just redoing those affected but in this text we will keep it simple. + Also if all elements are 1.0 then we could do faster. + The key CbcHeuristic method is int solution(double & solutionValue, + double * betterSolution) + which returns 0 if no solution found and 1 if found when it fills in the objective value + and primal solution. The actual code in CbcHeuristicGreedy.cpp is + a little more complicated but this will work and gives the basic idea. For instance + the code here assumes all variables are integer. + The important bit of data is a copy of the matrix (stored by column) + before any cuts have been made. The data used are bounds, objective and the matrix + plus two work arrays. +
+Then we initialize newSolution as rounded down solution. +
+We have finished so now we need to see if solution is better and doublecheck +we are feasible. +
+If the user declares variables as integer but does no more, then Cbc will treat them +as simple integer variables. In many cases the user would like to do some more fine tuning. This shows how to create integer variables with pseudo costs. When pseudo costs are given then +it is assumed that if a variable is at 1.3 then the cost of branching that variable down will be 0.3 times the down pseudo cost and the cost of branching up would be 0.7 times the up pseudo cost. This can be used both for branching and for choosing a node. + The full code is in longthin.cpp + (this code can be found in the CBC Samples directory, see + Chapter 5, +More Samples +). + The idea is simple for set covering problems. + Branching up gets us much closer to an integer solution so we want + to encourage up  so we will branch up if variable value > 0.333333. + The expected cost of going up obviously depends on the cost of the + variable so we just choose pseudo costs to reflect that. +
+The actual coding in the example also tries to give more importance to variables with more +coefficients. Whether this sort of thing is worthwhile should be the subject of experimentation. +Here is another example which is for crew scheduling problems. In this case the problem has +few rows but many thousands of variables. Branching a variable to 1 is very powerful as it +fixes many other variables to zero, but branching to zero is very weak as thousands of variables +can increase from zero. But in crew scheduling each constraint is a flight leg e.g. JFK to DFW. +From DFW (Dallas) there may be several flights the crew could take next  suppose one flight is +the 9:30 flight from DFW to LAX (Los Angeles). Then a binary branch is that the crew arriving +at DFW either take the 9:30 flight to LAX or they don't. This followon branching does not +fix individual variables but instead divides all the variables with entries in the JFKDFW +constraint into two groups  those with entries in the DFWLAX constraint and those without +entries. + The full code is in crew.cpp + (this code can be found in the CBC Samples directory, see + Chapter 5, +More Samples +). In this case we may as well leave the simple integer +variables and we may have to if there are other sorts of constraints. But we want to +branch on the followon rules first so we use priorities to say that those are the +important ones. +
+ Coin Branch and Cut uses a generic OsiSolverInterface and its resolve capability. + This does not give much flexibility so advanced users can inherit from the interface + of choice. This describes such a solver for a long thin problem e.g. fast0507 again. + As with all these examples it is not guaranteed that this is the fastest way to solve + any of these problems  they are to illustrate techniques. + The full code is in CbcSolver2.hpp and + CbcSolver2.cpp + (this code can be found in the CBC Samples directory, see + Chapter 5, +More Samples +). + initialSolve is called a few times so although we will not gain much + this is a simpler place to start. The example derives from OsiClpSolverInterface and the code + is: +
+We then update node_ array as for the first few solves. To give some idea of the effect of this +tactic fast0507 has 63,009 variables and the small problem never has more than 4,000 variables. +In just over ten percent of solves did we have to resolve and then the average number of iterations +on full problem was less than 20. +To give another example  again only for illustrative purposes it is possible to do quadratic +mip. In this case we make resolve the same as +initialSolve. + The full code is in ClpQuadInterface.hpp and + ClpQuadInterface.cpp + (this code can be found in the CBC Samples directory, see + Chapter 5, +More Samples +). +
+ This chapter describes how to build a greedy heuristic for a set covering problem, e.g., the miplib problem fast0507. A more general (and efficient) version of the heuristic is in CbcHeuristicGreedy.hpp and CbcHeuristicGreedy.cpp located in the COIN/Cbc/Samples directory, see Chapter 8, +More Samples +. +
+ The greedy heuristic will leave all variables taking value one at this node of the + tree at value one, and will initially set all other variables to value zero. + All variables are then sorted in order of their cost + divided by the number of entries in rows which are not yet covered. (We may randomize that + value a bit so that ties will be broken in different ways on different runs of the heuristic.) + The best one is choosen, and set to one. The process is repeated. Because this is + a set covering problem (i.e., all constraints are ≥), the heuristic is guaranteed to find a solution (but not necessarily an improved solution). The speed of the heuristic could be improved by just redoing those affected, but for illustrative purposes we will keep it simple. (The speed could also be improved if all elements are 1.0). +
+ The key CbcHeuristic method is int solution(double & solutionValue, + double * betterSolution). + The solution() method returns 0 if no solution found, and returns 1 if a solution is found, in which case it fills in the objective value and primal solution. The code in CbcHeuristicGreedy.cpp is a little more complicated than this following example. For instance, the code here assumes all variables are integer. The important bit of data is a copy of the matrix (stored by column) before any cuts have been made. The data used are bounds, objective and the matrix plus two work arrays. +
+The newSolution is then initialized to the rounded down solution. +
+ Coin Branch and Cut uses a generic OsiSolverInterface and its resolve capability. + This does not give much flexibility so advanced users can inherit from the interface + of choice. This describes such a solver for a long thin problem e.g. fast0507 again. + As with all these examples it is not guaranteed that this is the fastest way to solve + any of these problems  they are to illustrate techniques. + The full code is in CbcSolver2.hpp and + CbcSolver2.cpp + (this code can be found in the CBC Samples directory, see + Chapter 6, +More Samples +). + initialSolve is called a few times so although we will not gain much + this is a simpler place to start. The example derives from OsiClpSolverInterface and the code + is: +
+We then update node_ array as for the first few solves. To give some idea of the effect of this +tactic fast0507 has 63,009 variables and the small problem never has more than 4,000 variables. +In just over ten percent of solves did we have to resolve and then the average number of iterations +on full problem was less than 20. +To give another example  again only for illustrative purposes it is possible to do quadratic +mip. In this case we make resolve the same as +initialSolve. + The full code is in ClpQuadInterface.hpp and + ClpQuadInterface.cpp + (this code can be found in the CBC Samples directory, see + Chapter 6, +More Samples +). +
+In Chapter 5, + Branching + , we give examples of how to use existing branching objects. (The next revision of this Guide should include an example of how to write your own branching object; Contributions of examples are welcome.) +
+ +If the user declares variables as integer but does no more, then CBC will treat them +as simple integer variables. In many cases the user would like to do some more fine tuning. This section shows how to create integer variables with pseudo costs. When pseudo costs are given then +it is assumed that if a variable is at 1.3 then the cost of branching that variable down will be 0.3 times the down pseudo cost and the cost of branching up would be 0.7 times the up pseudo cost. Pseudo costs can be used both for branching and for choosing a node. + The full code is in longthin.cpp located in the CBC Samples directory, see + Chapter 8, +More Samples +. +
+ The idea is simple for set covering problems. + Branching up gets us much closer to an integer solution so we will encourage that direction by branch up if variable value > 0.333333. + The expected cost of going up obviously depends on the cost of the + variable. The pseudo costs are choosen to reflect that fact. + +
+The code in Example 5.1 also tries to give more importance to variables with more +coefficients. Whether this sort of thing is worthwhile should be the subject of experimentation. + + +
+ The full sample code for followon brancing is in crew.cpp + located in the CBC Samples directory, see + Chapter 8, +More Samples +). In this case, the simple integer +variables are left which may be necessary if other sorts of constraints exist. Followon branching rules are to be considered first, so the priorities are set to indicate the followon rules take precedence. Priority 1 is the highest priority. + +
+To give another example  again only for illustrative purposes  it is possible to do quadratic +MIP with CBC. In this case, we make resolve the same as +initialSolve. + The full code is in ClpQuadInterface.hpp and + ClpQuadInterface.cpp located in the CBC Samples directory, see + Chapter 7, +More Samples +). +
+ CBC uses a generic OsiSolverInterface and its resolve capability. + This does not give much flexibility so advanced users can inherit from their interface + of choice. This section illustrates how to implement a specialized solver for a long thin problem, e.g., fast0507 again. As with the other examples in the Guide, the sample code is not guaranteed to be the fastest way to solve the problem. The main purpose of the example is to illustrate techniques. The full source is in CbcSolver2.hpp and CbcSolver2.cpp located in the CBC Samples directory, see + Chapter 8, +More Samples +. +
+The method initialSolve is called a few times in CBC, and provides a convenient starting point. The modelPtr_ derives from OsiClpSolverInterface. +
+To give another example  again only for illustrative purposes  it is possible to do quadratic +MIP with CBC. In this case, we make resolve the same as +initialSolve. + The full code is in ClpQuadInterface.hpp and + ClpQuadInterface.cpp located in the CBC Samples directory, see + Chapter 8, +More Samples +). +
make DRIVER=name
Table 8.1. Basic Samples
+ Source file +  + Description + 

minimum.cpp  + This is a CBC "Hello, world" program. It reads a problem + in MPS file format, and solves the problem using simple branchandbound. + 
sample2.cpp  + This is designed to be a file that a user could modify to get a useful + driver program for his or her project. In particular, it demonstrates + the use of CGL's preprocess functionality. + It uses CbcBranchUser.cpp, + CbcCompareUser.cpp and + CbcHeuristicUser.cpp + with corresponding *.hpp files. + 
Table 8.2. Advanced Samples
+ Source file +  + Description + 

crew.cpp  + This sample shows the use of advanced branching and a use of priorities. + It uses CbcCompareUser.cpp + with corresponding *.hpp files. + 
longthin.cpp  + This sample shows the advanced use of a solver. It also has coding for + a greedy heuristic. + The solver is given in CbcSolver2.hpp and + CbcSolver2.cpp. + The heuristic is given in CbcHeuristicGreedy.hpp and + CbcHeuristicGreedy.cpp. + It uses CbcBranchUser.cpp and + CbcCompareUser.cpp + with corresponding *.hpp files. + 
qmip.cpp  + This solves a quadratic MIP. It is to show advanced use of a solver. + The solver is given in ClpQuadInterface.hpp and + ClpQuadInterface.cpp. + It uses CbcBranchUser.cpp and + CbcCompareUser.cpp + with corresponding *.hpp files. + 
sos.cpp  + This artificially creates a Special Ordered Set problem. + 
lotsize.cpp  + This artificially creates a Lot Sizing problem. + 
Table 9.1. + CBC Messages Passed At Log Level 0 +
+ Code +  + Text and notes +  

+ 3007 +  No integer variables  nothing to do  
+ + 
Table 9.2. + CBC Messages Passed At or Above Log Level 1 +
+ Code +  + Text and notes +  

+ 1 +  Search completed  best objective %g, took %d iterations and %d nodes +  
+ +  
+ 3 +  Exiting on maximum nodes +  
+ +  
+ 4 +  + Integer solution of %g found after %d iterations and %d nodes +  
+ +  
+ 5 +  + Partial search  best objective %g (best possible %g), took %d iterations and %d nodes +  
+ +  
+ 6 +  + The LP relaxation is infeasible or too expensive +  
+ +  
+ 9 +  + Objective coefficients multiple of %g +  
+ +  
+ 10 +  + After %d nodes, %d on tree, %g best solution, best possible %g +  
+ +  
+ 11 +  + Exiting as integer gap of %g less than %g or %g%% +  
+ +  
+ 12 +  + Integer solution of %g found by heuristic after %d iterations and %d nodes +  
+ +  
+ 13 +  + At root node, %d cuts changed objective from %g to %g in %d passes +  
+ +  
+ 14 +  + Cut generator %d (%s)  %d row cuts (%d active), %d column cuts %? in %g seconds  new frequency is %d +  
+ +  
+ 16 +  + Integer solution of %g found by strong branching after %d iterations and %d nodes +  
+ +  
+ 17 +  + %d solved, %d variables fixed, %d tightened +  
+ +  
+ 18 +  + After tightenVubs, %d variables fixed, %d tightened +  
+ +  
+ 19 +  + Exiting on maximum solutions +  
+ +  
+ 20 +  + Exiting on maximum time +  
+ +  
+ 23 +  + Cutoff set to %g  equivalent to best solution of %g +  
+ +  
+ 24 +  + Integer solution of %g found by subtree after %d iterations and %d nodes +  
+ +  
+ 26 +  + Setting priorities for objects %d to %d inclusive (out of %d) +  
+ +  
+ 3008 +  + Strong branching is fixing too many variables, too expensively! +  
+ + 
Table 9.3. + CBC Messages Passed At or Above Log Level 2 +
+ Code +  + Text and notes +  

+ 15 +  + Node %d Obj %g Unsat %d depth %d +  
+ +  
+ 21 +  + On closer inspection node is infeasible +  
+ +  
+ 22 +  + On closer inspection objective value of %g above cutoff of %g +  
+ +  
+ 23 +  + Allowing solution, even though largest row infeasibility is %g +  
+ + 
Table 9.4. + CBC Messages Passed At or Above Log Level 3 +
+ Code +  + Text and notes +  

+ 7 +  + Strong branching on %d (%d), down %g (%d) up %g (%d) value %g +  
+ +  
+ 25 +  + %d cleanup iterations before strong branching +  
+ + 
Table of Contents
List of Tables
List of Examples