added soltution to ex07

exercises/ex07/solutions/sol07.txt

+|------------------|
+| Solution of ex07 |
+|------------------|
+
+---
+7.2
+---
+
+See tsp1.mod

exercises/ex07/solutions/tsp.com

+solve;
+
+display x;

exercises/ex07/solutions/tsp.mod

+reset;
+
+set S ordered;
+param n := card {S};
+
+set SS := 1..(2^n - 2); # 1 to number of subtours
+
+set POW {k in SS} := {i in S: (k div 2^(ord(i)-1)) mod 2 = 1}; # subtours
+
+set LINKS := {i in S, j in S: ord(i) < ord(j)};
+
+param cost {LINKS} >= 0;
+
+var x {LINKS} binary;
+
+minimize tot_cost: sum {(i,j) in LINKS} cost[i,j] * x[i,j];
+
+s.t. tour: sum {(i,j) in LINKS} x[i,j] = n;
+
+s.t. subtour_elim {k in SS : 3 <= card{POW[k]} <= n-1}:
+	sum {i in POW[k], j in POW[k]: (i,j) in LINKS} x[i,j] <= card{POW[k]}-1;
+
+#data toy.dat;
+#data 10city.dat;
+#data 12city.dat;
+
+#display SS;
+#display POW;
+
+#option solver cplex;
+
+#solve;
+
+#display x;
+

exercises/ex07/solutions/tsp1.mod

+reset;
+
+set S ordered;
+param n := card {S};
+
+set LINKS := {i in S, j in S: ord(i) < ord(j)};
+
+param cost {LINKS} >= 0;
+
+var x {LINKS} binary;
+
+minimize tot_cost: sum {(i,j) in LINKS} cost[i,j] * x[i,j];
+
+s.t. tour: sum {(i,j) in LINKS} x[i,j] = n;
+
+s.t. max2 {i in S}:
+	sum {(i,j) in LINKS} x[i,j] + sum {(j,i) in LINKS} x[j,i] = 2;
+
+# subtour elimination toy.dat
+
+# subtour elimination 10city.dat
+s.t. elim0: x['a','c'] + x['a','i'] + x['b','f'] + x['b','i'] + x['c','f'] <= 4; 
+s.t. elim1: x['a','b'] + x['a','i'] + x['b','f'] + x['c','f'] + x['c','i'] <= 4; 
+
+#data toy.dat;
+data 10city.dat;
+
+option solver cplex;
+
+solve;
+
+display x;
+