Committing one model that was missed.

src/models/AssignmentModel.java

+package models;
+
+import ilog.concert.IloException;
+import ilog.concert.IloLinearNumExpr;
+import ilog.concert.IloNumVar;
+import ilog.cplex.IloCplex;
+import java.util.HashSet;
+import java.util.Set;
+import socialnet.Graph;
+
+/**
+ * AssignmentModel tries a formulation proposed in an answer to the OR SE post,
+ * using binary variables to assign nodes to selected nodes.
+ *
+ * @author Paul A. Rubin (rubin@msu.edu)
+ */
+public final class AssignmentModel implements AutoCloseable {
+  private static final double HALF = 0.5;  // for rounding tests
+  private final int nVertices;  // number of vertices in the graph
+
+  // CPLEX objects.
+  private final IloCplex mip;          // the MIP model
+  private final IloNumVar[] select;    // indicators for selecting vertices
+  private final IloNumVar[][] assign;  // assign[i][j] = 1 if node i is
+                                       // assigned to selected node j
+
+  /**
+   * Constructor.
+   * @param graph the graph to solve
+   * @param nSelect the number of nodes to select
+   * @param prog print progress reports every this many variables/constraints
+   * @throws IloException if the model cannot be constructed
+   */
+  public AssignmentModel(final Graph graph, final int nSelect, final int prog)
+         throws IloException {
+    System.out.println("Building the model ...");
+    nVertices = graph.getnVertices();
+    // Initialize the model.
+    mip = new IloCplex();
+    // Create the variables and simultaneously construct the objective function.
+    select = new IloNumVar[nVertices];
+    assign = new IloNumVar[nVertices][nVertices];
+    IloLinearNumExpr obj = mip.linearNumExpr();
+    long ctr = 0;
+    for (int i = 0; i < nVertices; i++) {
+      select[i] = mip.boolVar("select_" + i);
+      for (int j = 0; j < nVertices; j++) {
+        assign[j][i] = mip.boolVar("assign_" + j + "_to_" + i);
+        obj.addTerm(graph.getDistance(i, j), assign[j][i]);
+        ctr += 1;
+        if (ctr % prog == 0) {
+          System.out.println("... " + ctr + " assignment variables added");
+        }
+      }
+    }
+    // The objective is to minimize the sum of the assigned distances.
+    mip.addMinimize(obj);
+    // The number of nodes selected must match the requirement.
+    mip.addEq(mip.sum(select), nSelect, "selection_count");
+    // Every node must be assigned to exactly one selected node (possibly
+    // itself).
+    for (int i = 0; i < nVertices; i++) {
+      mip.addEq(mip.sum(assign[i]), 1.0, "assign_" + i + "_once");
+    }
+    ctr = 0;
+    // Assignments can only be made to selected nodes.
+    for (int i = 0; i < nVertices; i++) {
+      for (int j = 0; j < nVertices; j++) {
+        mip.addLe(assign[i][j], select[j], "select_" + j + "_to_assign_" + i);
+        ctr += 1;
+        if (ctr % prog == 0) {
+          System.out.println("... " + ctr + " assignment constraints added");
+        }
+      }
+    }
+  }
+
+  /**
+   * Solves the model.
+   * @param timeLimit the time limit for the solver (in seconds)
+   * @return the final solver status
+   * @throws IloException if the solution fails
+   */
+  public IloCplex.Status solve(final double timeLimit) throws IloException {
+    mip.setParam(IloCplex.DoubleParam.TimeLimit, timeLimit);
+    mip.solve();
+    return mip.getStatus();
+  }
+
+  /**
+   * Gets the final objective value.
+   * @return the objective value
+   * @throws IloException if there is no objective value
+   */
+  public double getObjValue() throws IloException {
+    return mip.getObjValue();
+  }
+
+  /**
+   * Gets the set of nodes selected by the solution.
+   * @return the set of selected nodes
+   * @throws IloException if no solution exists
+   */
+  public Set<Integer> getSolution() throws IloException {
+    HashSet<Integer> sol = new HashSet<>();
+    double[] x = mip.getValues(select);
+    for (int i = 0; i < nVertices; i++) {
+      if (x[i] > HALF) {
+        sol.add(i);
+      }
+    }
+    return sol;
+  }
+
+  /**
+   * Closes the model.
+   */
+  @Override
+  public void close() {
+    mip.close();
+  }
+}