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. We now summarize the methods of IloCplex which will be of use to us:

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
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    e

    of set, finds the corresponding variable
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    x_e

    and returns
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    \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

		//the degree constraints
		for(V vertex: graph.getVertices()){
			cplex.addEq(Util.integerSum(cplex, edgeVariables, 
					graph.getIncidentEdges(vertex)), 2);
		}

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
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    e

    of set, gets the corresponding variable
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    x_e

    from variables and the number
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    d_e

    from coefficients and returns an expression for
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    \sum_{e \in \text{set}} d_e x_e

    .

Solution

		//the objective
		cplex.addMinimize(Util.integerSum(
				cplex, edgeVariables, graph.getEdges(),tspInstance.getEdgeWeights()));