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Build a model

Examples:bilinear, diet, facility, gc_pwl, gc_pwl_func, genconstr, matrix1, mip1, multiobj, multiscenario, piecewise, poolsearch, qcp, qp, sensitivity, sos, sudoku, workforce1, workforce_batchmode, workforce2, workforce3, workforce4, workforce5

Several of the Gurobi examples build models from scratch. We start by focusing on two:mip1andsos. Both build very simple models to illustrate the basic process.

Typically, the first step in building a model is to create an empty model. This is done using theGRBnewmodelfunction in C:

/* Create an empty model */ error = GRBnewmodel(env, &model, "mip1", 0, NULL, NULL, NULL, NULL, NULL); if (error) goto QUIT;

You can optionally create a set of variables when you create the model, as well as specifying bounds, objective coefficients, and names for these variables. These examples add new variables separately.

In C++, C#, and Java, you create a new model using theGRBModelconstructor. In Java, this looks like:

// Create empty model GRBModel model = new GRBModel(env);

In Python, the class is calledModel, and its constructor is similar to theGRBModelconstructor for C++ and Java:

# Create a new model m = gp.Model("mip1")

Once the model has been created, the typical next step is to add variables. In C, you use theGRBaddvarsfunction to add one or more variables:

error = GRBaddvars(model, 3, 0, NULL, NULL, NULL, obj, NULL, NULL, vtype, NULL); if (error) goto QUIT;

In C++, Java, and Python, you use theaddVarmethod on theModelobject (AddVarin C#). In Java, this looks like:

GRBVar x = model.addVar(0.0, 1.0, 0.0, GRB.BINARY, "x");

The new variable's lower bound, upper bound, objective coefficient, type, and name are specified as arguments. In C++ and Python, you can omit these arguments and use default values; see theGurobi Reference Manualfor details.

The next step is to add constraints to the model. Linear constraints are added through theGRBaddconstrfunction in C:

error = GRBaddconstr(model, 3, ind, val, GRB_LESS_EQUAL, 4.0, "c0");

To add a linear constraint in C, you must specify a list of variable indices and coefficients for the left-hand side, a sense for the constraint (e.g.,GRB_LESS_EQUAL), and a right-hand side constant. You can also give the constraint a name; if you omit the name, Gurobi will assign a default name for the constraint.

In C++, C#, Java, and Python, you build a linear constraint by first building linear expressions for the left- and right-hand sides. In Java, which doesn't support operator overloading, you build an expression as follows:

// Set objective: maximize x + y + 2 z GRBLinExpr expr = new GRBLinExpr(); expr.addTerm(1.0, x); expr.addTerm(1.0, y); expr.addTerm(2.0, z);

You then use theaddConstrmethod on theGRBModelobject to add a constraint using these linear expressions for the left- and right-hand sides:

model.addConstr(expr, GRB.LESS_EQUAL, 4.0, "c0");

For C++, C#, and Python, the standard mathematical operators such as +, *, <= have been overloaded so that the linear expression resembles a traditional mathematical expression. In C++:

model.AddConstr(x + 2 * y + 3 * z <= 4.0, "c0");

Once the model has been built, the typical next step is to optimize it (usingGRBoptimizein C,model.optimizein C++, Java, and Python, ormodel.Optimizein C#). You can then query theXattribute on the variables to retrieve the solution (and theVarName属性retrieve the variable name for each variable). In C, theXattribute is retrieved as follows:

error = GRBgetdblattrarray(model, GRB_DBL_ATTR_X, 0, 3, sol);

In C++:

cout << x.get(GRB_StringAttr_VarName) << " " << x.get(GRB_DoubleAttr_X) << endl; cout << y.get(GRB_StringAttr_VarName) << " " << y.get(GRB_DoubleAttr_X) << endl; cout << z.get(GRB_StringAttr_VarName) << " " << z.get(GRB_DoubleAttr_X) << endl;

In Java:

System.out.println(x.get(GRB.StringAttr.VarName) + " " +x.get(GRB.DoubleAttr.X)); System.out.println(y.get(GRB.StringAttr.VarName) + " " +y.get(GRB.DoubleAttr.X)); System.out.println(z.get(GRB.StringAttr.VarName) + " " +z.get(GRB.DoubleAttr.X));

In C#:

Console.WriteLine (x。VarName + " " + x.X);控制台。WriteLine(y.VarName + " " + y.X); Console.WriteLine(z.VarName + " " + z.X);

In Python:

for v in m.getVars(): print('%s %g' % (v.VarName, v.X))

When querying or modifying attribute values for an array of constraints or variables, it is generally more efficient to perform the action on the whole array at once. This is quite natural in the C interface, where most of the attribute routines take array arguments. In the C++, C#, Java, and Python interfaces, you can use thegetandsetmethods on theGRBModelobject to work directly with arrays of attribute values (getAttr/setAttrin Python). In thesudokuJava example, this is done as follows:

double[][][] x = model.get(GRB.DoubleAttr.X, vars);

We should point out one important subtlety in our interface. We use alazy updateapproach to building and modifying a model. When you make changes, they are added to a queue. The queue is only flushed when you optimize the model (or write it to a file). In the uncommon situation where you want to query information about your model before optimizing it, you should call theupdatemethod before making your query.