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The Java Interface to CPLEX

The use of CPLEX in Java is based around the class IloCplex (documented here). The basic idea is that you create an IloCplex object for your optimization problem, then add variables, the objective, and constraints using methods in the class IloCplex. The IloCplex object can produce IloNumVar objects and their subclass IloIntVar objects, when are then used as arguments to further methods from IloCplex to make the objective and constraints. The IloCplex interface is somewhat confusing. It is very large, has lots of redundant methods, and lots of methods that appear to be the same but produce very different results. We now summarize the methods of IloCplex which will be of use to us:

Name

Return Type

Arguments

Description

boolVar

IloIntVar

 

Creates and returns a new Boolean variable (domain 0,1).

boolVarArray

IloIntVar[]

int n

Creates and returns an array of n new Boolean variables (domain 0,1)

linearIntExpr

IloLinearIntExpr

 

Creates and returns an integer linear expression initialized as 0 (zero).

addGe

IloRange

IloNumExpr e, double v

Creates and returns a range representing the constraint

Unknown macro: {mathinline}

e \geq v

addEq

IloRange

IloNumExpr e, double v

Creates and returns a range representing the constraint

Unknown macro: {mathinline}

e = v

addMinimize

IloObjective

IloNumExpr e

Creates and returns an objective to minimize the expression and adds it to the invoking model.

For a IloNumExpr e and a double v, calling cplex.addGe(e,v) and cplex.addGe(v,e) are both allowed but do not produce the same result! The first gives the constraint

Unknown macro: {mathinline}

e \geq v

while the second gives the constraint

Unknown macro: {mathinline}

v \geq e

.

For a IloNumExpr e and a double v, calling cplex.ge(e,v) and cplex.addGe(e,v) are both allowed but do not produce the same result! While both return an object for the constraint

Unknown macro: {mathinline}

e \geq v

, only the latter adds the constraint to the model! We will actually have use cplex.ge(e,v) later when we add constraints through callbacks instead of adding them directly to the model.

Using CPLEX in TspIpSolver

First, we need to set up the objective and the degree constraints. First, add the following fields to the class

private IloCplex cplex;
private TspInstance<V,E> tspInstance;
private final ImmutableBiMap<E,IloIntVar> edgeVariables;

and initialize them, as below.

	public TspIpSolver(TspInstance<V,E> tspInstance, EnumSet<Option> options) throws IloException{
		this.options = options;
		this.tspInstance = tspInstance;
		this.cplex = new IloCplex();
		UndirectedGraph<V,E> graph = tspInstance.getGraph(); //for convenience, we will be using this a lot
		this.edgeVariables = Util.makeBinaryVariables(cplex, graph.getEdges());
		//the degree constraints
		//the objective		
	}

The constraints and objective still need to be added to the cplex object. Try adding them yourself! The following methods should be useful for making the constraints:

  • From Util, public static <T> IloLinearIntExpr integerSum(IloCplex cplex, BiMap<T,IloIntVar> variables, Iterable<T> set)
    • For each element
      Unknown macro: {mathinline}

      e

      of set, finds the corresponding variable
      Unknown macro: {mathinline}

      x_e

      and returns
      Unknown macro: {mathinline}

      \sum_{e \in \text{set}} x_e

  • From IloCplex, public IloRange addEq(IloNumExpr e, double v)
    • Adds the equality constraint e = v
  • From UndirectedGraph<V,E>, public Collection<E> getIncidentEdges(V vertex)
    • returns the edges of the graph that are incident to vertex

If you are unfamiliar with Java, consider viewing the solution for the constraint, then trying the objective yourself.
Solution

For the objective, we need the functions:

  • From Util, public static <T> IloLinearNumExpr sum(IloCplex cplex, BiMap<T,IloIntVar> variables, Iterable<T> set, Function<? super T,? extends Number> coefficients)
    • For every element
      Unknown macro: {mathinline}

      e

      of set, gets the corresponding variable
      Unknown macro: {mathinline}

      x_e

      from variables and the number
      Unknown macro: {mathinline}

      d_e

      from coefficients and returns an expression for
      Unknown macro: {mathinline}

      \sum_{e \in \text{set}} d_e x_e

      .

Solution

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