Problem Formulation

First, we will add the following fields to the class so we can easily reference our problem data from any method. Add

private EnumSet<Option> options;
private IloCplex cplex;
private TspInstance<V,E> tspInstance;
private 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		
	}

Next, we need to add the objective and the degree constraints to the IloCplex instance. Try adding them yourself! The following methods (as defined in Solver Specification and Java Style for CPLEX) should be useful for making the degree constraints:

• From Util, the static method integerSum(IloCplex cplex, BiMap<T,IloIntVar> variables, Iterable<T> set)
• From IloCplex, the method addEq(IloNumExpr e, double v)
• From UndirectedGraph<V,E>, the method getIncidentEdges(V vertex)

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, the static method sum(IloCplex cplex, BiMap<T,IloIntVar> variables, Iterable<T> set, Function<? super T,? extends Number> coefficients)
• From UndirectedGraph<V,E>, the method getEdges()
• From TspInstance, the method getEdgeWeights

Solution

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

Solving and Extracting the Solution