Logical constraints in the C++ API

Describes logical constraints in the C++ API.

In C++ applications, the class IloCplex can extract modeling objects to solve a wide variety of MIPs, as you see in Solving the model, summarized in the table in Overview. In fact, the C++ class IloCplex can extract logical constraints as well as some logical expressions. The logical constraints that IloCplex can extract are these:

  • IloAnd

  • IloOr

  • IloNot

  • IloIfThen

  • IloDiff

  • == that is, the equivalence relation

Among those extractable objects, IloAnd IloOr , IloNot , and IloDiff can also be represented in your application by means of the overloaded C++ operators:

  • || (for IloOr )

  • && (for IloAnd )

  • ! (for IloNot )

  • != that is, the exclusive-or relation (for IloDiff )

All those extractable objects accept as their arguments other linear constraints or logical constraints, so you can combine linear constraints with logical constraints in complicated expressions in your application.

For example, to express the idea that two jobs with starting times x1 and x2 and with duration d1 and d2 must not overlap, you can either use overloaded C++ operators, like this: 


model.add((x1 >= x2 + d2) || (x2 >= x1 + d1));

or you can express the same idea, like this: 


IloOr or(env)
or.add(x1 >= x2 + d2);
or.add(x2 >= x1 + d1);
model.add(or);

Since IloCplex can also extract logical constraints embedded in other logical constraints, you can also write logical constraints like this: 


IloIfThen(env, (x >= y && x >= z), IloNot(x <= 300 || y >= 700))

where x , y , and z are variables in your application.