(!*******************************************************
Mosel Example Problems
======================
file vpn_design.mos
```````````````````
Robust network optimization
(c) 2014 Fair Isaac Corporation
author: P. Belotti, Apr. 2014, rev. Jun. 2015
*******************************************************!)
model "Robust Network"
uses "mmrobust", "mmxprs"
parameters
vpn_data="vpn_data.dat"
end-parameters
declarations
NODES: range ! Set of nodes
ARCCOST: dynamic array(NODES, NODES) of real ! Per-unit cost of arc (i,j)
DEM_IN: array(NODES) of real ! Total INCOMING demand at each node
DEM_OUT: array(NODES) of real ! Total OUTGOING demand at each node
UNITCAP: integer ! Per-unit capacity (independent of arc)
NETCOST: linctr ! Objective function
! Decision variables
flow: dynamic array(NODES, NODES, NODES, NODES) of mpvar
! flow(i,j,h,k) is 1 iff demand h->k uses arc (i,j)
capacity: dynamic array(NODES, NODES) of mpvar ! Capacity to install on arc (i,j)
! Uncertain parameters
demand: array(NODES, NODES) of uncertain ! Uncertain traffic demand
RobustCap: array(NODES, NODES) of robustctr ! Uncertain traffic demand, formulated at each arc
end-declarations
! The following option is necessary to allow uncertain demands to be
! used across multiple capacity constraints
setparam("robust_uncertain_overlap", true)
! Set verbosity level
setparam("xprs_verbose", true)
!**** Data input ****
initializations from vpn_data
NODES ARCCOST
DEM_IN DEM_OUT
UNITCAP
end-initializations
!**** Model formulation ****
forall(i in NODES, j in NODES, h in NODES, k in NODES |
exists(ARCCOST(i,j)) and ARCCOST(i,j) > 0 and h <> k) do
create(flow(i,j,h,k))
flow(i,j,h,k) is_binary
end-do
forall(i in NODES, j in NODES | exists(ARCCOST(i,j)) and ARCCOST(i,j) > 0) do
create(capacity(i,j))
capacity(i,j) is_integer
end-do
! Flow balance at intermediate nodes for each demand(h,k)
forall(i in NODES, h in NODES, k in NODES | i <> h and i <> k and k <> h)
sum(j in NODES | exists(flow(i,j,h,k))) flow(i,j,h,k) -
sum(j in NODES | exists(flow(j,i,h,k))) flow(j,i,h,k) = 0
! Flow balance at source nodes (unnecessary for sink nodes)
forall(i in NODES, h=i, k in NODES | k <> h)
sum(j in NODES | exists(flow(i,j,h,k)) ) flow(i,j,h,k) -
sum(j in NODES | exists(flow(j,i,h,k)) ) flow(j,i,h,k) = 1
! Capacity (robust) constraint
forall(i in NODES, j in NODES | exists(ARCCOST(i,j)) and ARCCOST(i,j) > 0)
RobustCap(i,j) :=
sum(h in NODES, k in NODES | h <> k) demand(h,k) * flow(i,j,h,k) <=
UNITCAP * capacity(i,j)
! Uncertainty set: all demands are nonnegative and constrained by
! total outgoing and incoming demand
forall(h in NODES, k in NODES | h <> k) demand(h,k) >= 0
forall(h in NODES) sum(k in NODES | h <> k) demand(h,k) <= DEM_OUT(h)
forall(h in NODES) sum(k in NODES | h <> k) demand(k,h) <= DEM_IN(h)
! Shortest path length
NetCost := sum(i in NODES, j in NODES | exists(ARCCOST(i,j)) and ARCCOST(i,j) > 0)
ARCCOST(i,j) * capacity(i,j)
!**** Solving ****
minimize(NetCost)
declarations
curNode: integer ! Local variable used in following the path of each demand
end-declarations
! Printing capacities
writeln("Robust solution has total cost ", getobjval)
forall(i in NODES, j in NODES | exists(capacity(i,j)) and capacity(i,j).sol > 0)
writeln("arc ", i, " -- ", j, ": ", capacity(i,j).sol, " units")
writeln("Paths:")
forall(h in NODES, k in NODES | h <> k) do
write("Demand ", h, " --> ", k, ": ")
curNode := h
write(h)
while(curNode <> k) do
forall(j in NODES | flow(curNode, j, h, k).sol > 0.5) do
write(" -- ", j)
curNode := j
end-do
end-do
writeln
end-do
writeln("Active demands at each arc:")
forall(i in NODES, j in NODES | exists(ARCCOST(i,j)) and ARCCOST(i,j) > 0 and
sum(h in NODES, k in NODES) getsol(demand(h,k), RobustCap(i,j)) > 0) do
write("Arc (", i, ",", j, "): ")
forall(h in NODES, k in NODES | getsol(demand(h,k), RobustCap(i,j)) > 0)
write(h, "-->", k, " (", getsol(demand(h,k), RobustCap(i,j)), "); ")
writeln
end-do
end-model
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