CPLEX sets variable with zero objective coefficient to positive value

Question

I need to stop CPLEX from doing that and do not know how.

• I have a min problem and it is a MIP.
• There is a variable x with coefficient zero in the objective.
• All constraints are "less than or equal to"-constraints.
• x appears only with non-negative coefficients in the constraint matrix.
• CPLEX returns a solution where x is set to a positive value, which is strange because it does not improve the objective function value, and in the constraint matrix, x only "takes away capacity".

The model is solved multiple times in an iterative procedure. In each iteration the objective changes. Hence, I checked the model and solution of the previous iteration and found that x had a negative coefficient then and was set to positive value. I conclude that this behavior must be related to some warm start of CPLEX.

How can that be prevented?

I rather not add the variables with positive coefficients to the objective because there are many.

Here is an example in Java:

    IloCplex cplex = new IloCplex();

    /* Variables */
    IloNumVar x = cplex.intVar(0, Integer.MAX_VALUE, "x");

    /* Objectiv */
    IloLinearNumExpr objExpr = cplex.linearNumExpr();
    objExpr.addTerm(1.0, x);
    IloObjective objective = cplex.addMaximize();
    objective.setExpr(objExpr);

    /* Constraints */
    IloLinearNumExpr expr = cplex.linearNumExpr();
    expr.addTerm(1.0, x);
    cplex.addLe(expr, 2.5);

    System.out.println(cplex.getModel().toString());
    cplex.solve();
    System.out.println("x = " + cplex.getValue(x) + "\n"); // x = 2.0

    objective.clearExpr();
    IloLinearNumExpr newObjexpr = cplex.linearNumExpr();
    objective.setExpr(newObjexpr);

    System.out.println(cplex.getModel().toString());
    cplex.solve();
    System.out.println("x = " + cplex.getValue(x) + "\n"); // x = 2.0

Answer 1

Try

cplex.setParam(IloCplex.Param.Advance, 0);