added solition to ex08

exercises/ex08/solutions/qap.mod

+reset;
+
+param n;
+
+var x{i in 1..n, j in 1..n} binary := 0;
+
+param a{1..n,1..n};
+param b{1..n,1..n};
+
+minimize obj:
+	sum{i in 1..n, k in 1..n, l in 1..n, m in 1..n} a[i,k]*x[k,l]*b[l,m]*x[i,m];
+
+s.t. c0{i in 1..n}: sum{j in 1..n} x[i,j] = 1;
+s.t. c1{i in 1..n}: sum{j in 1..n} x[j,i] = 1;
+
+data qap10.dat;
+
+option solver cplex;
+option cplex_options "mipdisplay=2";
+
+#option solver gurobi;
+#option gurobi_options "outlev=1";
+
+#option solver mosek;
+#option gurobi_options "outlev=2";
+
+#option solver scip;
+
+#option solver xpress;
+#option xpress_options "outlev=0";
+
+#option solver bonmin;
+
+#option solver couenne;
+
+solve;
+
+display x;
+
+var y{i in 1..n, j in 1..n} = sum{k in 1..n, l in 1..n} x[i,k]*b[k,l]*x[j,l];
+
+display y;

exercises/ex08/solutions/qap1.mod

+reset;
+
+param n;
+
+set I := 1..n;
+
+var x{I,I} binary;
+var y{I,I,I,I} binary;
+
+param a{I,I};
+param b{I,I};
+
+minimize obj:
+	sum{i in I, k in I, l in I, m in I} a[i,k]*b[l,m]*y[k,l,i,m];
+
+s.t. c0{i in I}: sum{j in I} x[i,j] = 1;
+s.t. c1{i in I}: sum{j in I} x[j,i] = 1;
+s.t. c2{k in I, l in I, i in I, m in I}: y[k,l,i,m] = x[k,l]*x[i,m];

exercises/ex08/solutions/qap2.mod

+reset;
+
+param n;
+
+set I = 1..n;
+
+var t;
+var x{i in I, j in I} binary := 0;
+
+param a{I,I};
+param b{I,I};
+
+minimize obj: t;
+
+s.t. cobj: sum{i in I, k in I, l in I, m in I} a[i,k]*x[k,l]*b[l,m]*x[i,m] <= t;
+
+s.t. c0{i in 1..n}: sum{j in 1..n} x[i,j] = 1;
+s.t. c1{i in 1..n}: sum{j in 1..n} x[j,i] = 1;
+
+#data qap10.dat;
+data nug10.dat;
+
+#option solver cplex;
+#option cplex_options "mipdisplay=2";
+
+#option solver gurobi;
+#option gurobi_options "outlev=1";
+
+#option solver scip;
+
+option solver xpress;
+option xpress_options "outlev=0";
+
+solve;
+
+display x;
+
+#var y{i in 1..n, j in 1..n} = sum{k in 1..n, l in 1..n} x[i,k]*b[k,l]*x[j,l];
+
+#display y;

exercises/ex08/solutions/sol08.txt

+|------------------|
+| Solution of ex08 |
+|------------------|
+
+
+---
+8.1
+---
+
+See qap10.dat
+The idea is that it respresent a possible tour through the locations 1-2-...-10.
+Then, at the solution the permuation matrix X will find the optimal tour.
+
+
+---
+8.2
+---
+
+See qap.mod
+
+
+
+---
+8.3
+---
+
+See qap1.mod
+
+
+
+---
+8.4
+---
+
+See qap2.mod
+
+
+
+---
+8.5
+---
+
+Use the data in nug10.dat (and if you dare, nug12.dat ;-) )
+
+