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-% -------------------------------------------------------------------------
-% Copyright (c) 2018 AT&T Intellectual Property
-%
-% Licensed under the Apache License, Version 2.0 (the "License");
-% you may not use this file except in compliance with the License.
-% You may obtain a copy of the License at
-%
-% http://www.apache.org/licenses/LICENSE-2.0
-%
-% Unless required by applicable law or agreed to in writing, software
-% distributed under the License is distributed on an "AS IS" BASIS,
-% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-% See the License for the specific language governing permissions and
-% limitations under the License.
-%
-% -------------------------------------------------------------------------
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Parameters and its assertions
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% Number of cells/radios.
-int: NUM_NODES;
-
-% Maximum number of Physical Cell Identifiers to be assigned to the nodes.
-int: NUM_PCIS;
-
-% Number of edges between neighbor nodes. There is a edge (i,j) if and only
-% if nodes i and j are neighbors, i.e., an user equipment (UE) can make
-% handoff between i and j. Such edges are used to avoid **COLLISION**, i.e.,
-% to guarantee that nodes i and j have different PCIs.
-int: NUM_NEIGHBORS;
-
-% Each line represents an edge between direct neighbors as defined before.
-array[1..NUM_NEIGHBORS, 1..2] of int: NEIGHBORS;
-
-% Number of undirect neighbor pairs (j, k) such that both j and k are direct
-% neighbors of node i, i.e., (j, k) exits if and only if exists (i, j) and
-% (i, k). Nodes (i, k) can generate "confunsions" in the network if they have
-% the same PCI. Such edges are used to avoid/minimize **CONFUSIONS**.
-int: NUM_SECOND_LEVEL_NEIGHBORS;
-
-% Each line represents an edge between undirect neighbors as defined before.
-array[1..NUM_SECOND_LEVEL_NEIGHBORS, 1..2] of int: SECOND_LEVEL_NEIGHBORS;
-
-% Number of ignorable neighbor links. Such links can be ignored during
-% optimization if needed.
-int: NUM_IGNORABLE_NEIGHBOR_LINKS;
-
-% The links that can be ignored if needed. Each line represents the two ends
-% of the links, like the previous structures.
-array[1..NUM_IGNORABLE_NEIGHBOR_LINKS, 1..2] of int: IGNORABLE_NEIGHBOR_LINKS;
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Decision variables
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% Defines the PCI for each node.
-array[0..NUM_NODES-1] of var 0..NUM_PCIS-1: pci;
-
-array[1..NUM_IGNORABLE_NEIGHBOR_LINKS] of var 0..1: used_ignorables;
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Constraints
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% Direct neighbors must have different PCIs for avoid **COLLISION**.
-% Forced links.
-constraint
-forall(i in 1..NUM_NEIGHBORS, j in 1..NUM_IGNORABLE_NEIGHBOR_LINKS
- where
- NEIGHBORS[i, 1] != IGNORABLE_NEIGHBOR_LINKS[j, 1] \/
- NEIGHBORS[i, 2] != IGNORABLE_NEIGHBOR_LINKS[j, 2]
-)(
- pci[NEIGHBORS[i, 1]] != pci[NEIGHBORS[i, 2]]
-);
-
-
-% Ignorable links.
-constraint
-forall(i in 1..NUM_NEIGHBORS, j in 1..NUM_IGNORABLE_NEIGHBOR_LINKS
- where
- NEIGHBORS[i, 1] == IGNORABLE_NEIGHBOR_LINKS[j, 1] /\
- NEIGHBORS[i, 2] == IGNORABLE_NEIGHBOR_LINKS[j, 2]
-)(
- used_ignorables[j] >= bool2int(pci[NEIGHBORS[i, 1]] == pci[NEIGHBORS[i, 2]])
-);
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Objective function
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% Total number of confusions.
-var int: total_confusions =
- sum([bool2int(pci[SECOND_LEVEL_NEIGHBORS[i, 1]] ==
- pci[SECOND_LEVEL_NEIGHBORS[i, 2]])
- | i in 1..NUM_SECOND_LEVEL_NEIGHBORS]);
-
-% Total number of used ignorables links.
-var int: total_used_ignorables = sum(used_ignorables);
-
-solve :: int_search(pci, smallest, indomain_min, complete)
-
-% Minimize the total number of confusions.
-%minimize total_confusions;
-
-% Minimize the total number of confusions first,
-% then the number of used ignorables links.
-minimize (2 * NUM_IGNORABLE_NEIGHBOR_LINKS * total_confusions) +
- total_used_ignorables;
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Output
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-output
-["PCI assigment"] ++
-["\nnode,pci"] ++
-[
- "\n" ++ show(node) ++ "," ++ show(pci[node])
-| node in 0..NUM_NODES-1
-] ++
-["\n\nTotal used ignorables links: " ++ show(total_used_ignorables)] ++
-["\nUsed ignorables links: "] ++
-[
- "\n" ++ show(IGNORABLE_NEIGHBOR_LINKS[i, 1]) ++
- "," ++ show(IGNORABLE_NEIGHBOR_LINKS[i, 2])
- | i in 1..NUM_IGNORABLE_NEIGHBOR_LINKS where fix(used_ignorables[i] > 0)
-] ++
-["\n\nConfusions"] ++
-["\nTotal confusions: " ++ show(total_confusions)] ++
-["\nConfusion pairs"] ++
-[
- "\n" ++ show(SECOND_LEVEL_NEIGHBORS[i, 1]) ++ "," ++
- show(SECOND_LEVEL_NEIGHBORS[i, 2])
- | i in 1..NUM_SECOND_LEVEL_NEIGHBORS where
- fix(pci[SECOND_LEVEL_NEIGHBORS[i, 1]] == pci[SECOND_LEVEL_NEIGHBORS[i, 2]])
-]
-