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Unformatted text preview: ll be given for a method that
involves an enumeration over all possible paths (in the objective or constraints). Hint. For
each node i, let Pi denote the maximum of k∈P pk over all paths P from the source node 1
to node i (so P max = Pn ).
(b) Carry out your method on the problem instance given in interdict_alloc_data.m. The data
ﬁle contains the data a, xmax , B , and the graph incidence matrix A ∈ Rn×m , where −1 if edge j leaves node i
+1 if edge j enters node i
Aij = 0
130 Give P max⋆ , the optimal value of P max , and compare it to the value of P max obtained with
uniform allocation of resources, i.e., with x = (B/m)1.
Hint. Given a vector z ∈ Rn , AT z is the vector of edge diﬀerences: (AT z )j = zk − zl if edge j
goes from node l to node k . 131 The following ﬁgure shows the topology of the graph in question. (The data ﬁle contains A;
this ﬁgure, which is not needed to solve the problem, is shown here so you can visualize the
Node 1 Node 2 Node 4 Node 3 Node 6 Node 5 Node 7 Node 8 Node 9 Node 10 15.5 Network sizing. We c...
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- Fall '13
- The Aeneid