Laboratoire d’Informatique
Fondamentale de Lille
Équipe Optimisation
Parallèle Coopérative
Modeling and solving
optimization and planification
problems in cellular networks
E-G. Talbi
OPAC – LIFL
University of Lille – CNRS – INRIA
France
www.lifl.fr/OPAC
Contracts with
France Telecom R&D and Mobinets
1
Cellular Network Planning and
Optimization

Frequency Assignment (FT R&D)

Access Network Design and
Planification (Mobinets)

Radio network design (FT R&D)

Location Area planification
(Mobinets)

Modeling (mono-objective and multiobjective mathematical programming
models)

Hybrid Metaheuristics (local search,
EAs, etc.)

Parallel Algorithms
Source : http://www.ulg.ac.be/telecom/publi/publications/mvd/Demoulin2004Principes/
2
Access Network Design




From 2G to 2.5G and 3G Networks …
Operators to be competitive and economical
(Major Cost : 1/3 of the total cost)
Transmission costs are becoming high
compared to the equipment costs
Traffic demands are increasing with the
introduction of new services
3
Access network design
to the RTCP
HLR
 Objectives : cost, availability
 Constraints : traffic, capacity, hops, …
Radio sub-network
VLR
MSC
BSC
BTS
T-Mobile & Mobinets
GSM  UMTS
4
Constraints
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Dealing with spanning trees,
Depth of the tree,
BSC / BTS / DXX degree,
BSC / BTS / DXX traffic capacity,
BTS availability,
DXX locations,
Predefined links.
5
Objectives

(1) Minimize the total cost,
min .


Li  N
cost ( Li )  Di  N cost ( Di )

(2) Maximize the overall availability
max .

Li  N
avail.( Li )

V
6
Complexity


The constrained minimum spanning
tree
 NP hard
Number of candidate topologies
V
V 1
 L   X  1
V
V
( Supposing first DXXs could only be colocated
with some BTS sites )
7
Algorithms

Greedy Heuristics : Inspired from Prim and Kruskal

Local Search

Evolutionary Algorithm

Hybrid algorithm (Genetic algorithm, Kruskal, Local
search)
8
Performance Evaluation
Instance
gsm1
gsm2
gsm3
gsm4
gsm5
Prim
116971
119724
138303
104775
124848
Average
116062
115798
138391
101950
124554
Worst
130035
126302
157024
119650
146874
Best
109803
111769
129310
97537
115507
Average
110205
113831
135341
98586
118697
Worst
112288
115525
137628
99548
121685
Best
108945
112111
131438
97515
115856
Average
108666
111803
129534
97066
116268
Worst
109430
112111
131415
97168
117868
Best
108223
111764
129310
97001
115475
Local
Search
Genetic
Algo.
Hybrid
Algo
• Both cost and robustness have been improved.
• Variance between worst and best computed topologies is low.9
Best computed maps (gsm3)
10
Location Areas Planning and
Optimisation
MSC (Mobile Switching Center)
BSC (Base Station Controller)
Cells
11
Location Areas Planning and
Optimisation
BSCs associated to MSCs
Cells associated to BSCs
Location area : To localize the user
12
Location Areas Planning and
Optimisation

1 service area =
 Associated to a MSC
 Sub-set of network cells
 Connected group

1 location area =



Inside a service zone
Sub-set of network cells
Connected group
13
Location Areas Planning and
Optimisation
When a mobile changes a
location area
Updates its position
Find a good compromise between paging and location area update
14
Some constraints

Topological Constraints :







A cell is affected to one BSC
A BSC is affected to one MSC
A cell is in a single LA
A LA is an single SA
Two areas are in two different LA
Connexity constraints
Technical Constraints (MSCs, BSCs, LAs):





Maximal traffic handled (Erlang)
Maximal number of transmitters (TRX)
Maximal number of administration canals (SDCCH)
Maximum number of tentative calls (MT-BHCA/PAG),
Maximal number of cells
15
Objectives

Minimize the location area (lup) inter-MSC
min
 f
v

w
Minimize the location area (lup) intra-MSC
min
 d
v

l
vw vw
l
vw vw
w
Minimize the traffic of signalisation (paging)


min   pv   pw 1  d vw 
vV 
wV

16
Solving strategies

Different sub-problems :





Partitioning in SA
Partitioning in LA
Assignment of BSCs to MSCs
Assignment of Cells to BSCs
Inspired from Clustering techniques



Genetic algorithms (coding, crossover, random
immigrants, …)
Local search
Hybrid algorithms (GAs, KNN)
17
Some results for hybrid approach
Evolution of the population
Mutation, Mutation PPV,
Random Immigrant
12100000
12000000
Meilleur Individu
11900000
Moyenne des
Individus
11800000
331
298
265
232
199
166
133
100
67
11700000
34

Good compromise between diversification and
intensification
Interesting results comparing to other algorithms
1

Fitness of the best Individual : 11759200
18
Radio Network Design

Radio network design : Multi-objective modelization

A Pareto evolutionary metaheuristic

Elitism, « Sharing », Hybridization.

Performance evaluation

Parallel models : cooperative, parallel evaluation, …

Results analysis

Conclusions & Perspectives
19
Radio telecommunications networks

Design challenges



Network cost : number of sites,…
Quality of service : traffic,
interferences, …
Network design


Positioning of BTS
Configuration of BTS (TRX,
antenna, …)
One site :
From 1 to 3 BTS per site
BTS : Base Transceiver Station
20
Cellular network design

Existing tools



Micro-cellular networks
 WISE of ATT


Manual or semi-automatic design
« Simplified » modelization (hexagonal cells,
…)
Thesis of P. Reininger (FT R&D)
Macro-cellular networks

MACRO
INTERIOR
European projects


STORM : mono-objective (minimization of sites,
restrictive configuration)
ARNO : non-Pareto (agregation), Genetic
algorithms, simulated annealing, tabu search, …
PUBLIC
ZONE
MIC
RO
MOBILE
RESIDENCE
21
Environment – Instance data



Discrete geographical area (grid) :
Different set of test points

Reception (RTP)

Service (STP)

Traffic (TTP)
RΤRTi / RTiP,i
SΤSTi /STiP,i
TΤTTi /TTiP,i
(Cd_ij)
(Cd_ij>Sq)
(E_i)
A set of potential sites
LLj / LjP,i
P
22
Configuration of antennas
Data
Ps
Diagram
Height
Azimuth
V Tilt
TRX
Bounds
[26, 55] dBm
3 types
[30, 50] m
[0, 359] °
[-15, 0] °
[1, 7]
Complex combinatorial
problem :
~ 600.109 solutions per
antenna
1 omni or 1-3 directive
23
Effects of configuration

Cell = covered region by a BTS
Propagation model
used : Free space
Omni-directional
60 dBm
Azimuth 50°
Directive type 1 Directive type 2
PIRE -10 dBm
Tilt -15°
24
Multi-objective model: Constraints

A set of BTS satisfying the
constraints :

Covering
STPi

is covered if
P
Cdij  S q , j
Handover (mobility)
 For each cell:

Cdij
Cdij'

HandC j  Ri : Cdij  S q and L j ' / Cdij  Cdij '  7
HandC j  
25
Multi-objective model: Objectives

Min Number of sites (cost)
min


jL
y jc j
Min Interferences
1,
yj  
0,
if L j is used
else
STi : Cdijk  Cdiu 1v 1  ...  Cdiuh vh  Cdiuh1vh1  ...  Sm
Handover sets (4 first signals)
min


iSTi
i
où i 
Max Traffic hold
max  ei x'ijk , j
iR
Interferences sets (nuisibles)
 Cd
PCd iuvI 4
Sm 
iuv
Geographical area
Used Sites
Non-used sites
Handover zone
Covered zone
1, if xijk  1 and ei  0,
 
xijk
else
0,
26
Multi-objective optimization
Dominance
y dominates z iff
i[1..n], yizi et i[1..n], yizi
Pareto Optimality
Solution
x *C is Pareto optimal iff there is no solution
xC Such that F(x) dominates F(x*)
f1
Pareto optimal solution
(efficient, non dominated)
z
y
Dominated feasible solution
f2
PO : Set of Pareto solutions
27
Multi-objective algorithms
Metaheuristic
Multiobjective
Pareto
Uni-objective
Agregation
method
 -constraint
method
Goal
programming
Populationbased
Single
solution
Genetic algorithm
Scatter search
Ant colony
Tabu-search
simulated annealing
 Exact methods: small size, bi-criteria problems
 Mono-objective methods require A-priori knowledge (weight,
constraints, goal) and modify the structure of the problem
(convexity, ...)
 Pareto approach generates a set of Pareto solutions (even
those in concave regions)
Population-based metaheuristics are suited to Pareto approach 28
Pareto Approch
Goals
Diversification : sharing,…
Convergence : ranking (order
between individuals), elitism,…
f
f
2
Feasible solutions
2
Feasible solutions
f
1
Solution found
f
Pareto front
29
1
Pareto Evolutionary Algorithm
Population
Replacement
Genetic operators
Update archive
Elitism
Evaluation
Selection « Ranking »
f
« Sharing »
2
A(1)
Ranking
NSGA
H(3)
Archive Pareto
F(2)
R3
B(1)
C(1)
Efficiency of Pareto mechanisms:
Ranking, Elitism
MO Knapsack : I. Kort (Concordia)
R1
G(2)
D(1)
R2
E(1)
f
30
1
Encoding of individuals


An individual encodes/represents a whole network
Hierarchical encoding (4 levels)
Level
Gene 1
Gene 2
1
Site 1 (0/1)
2
Omni/Dire
c
...
Site N (0/1)
An individual
Station 1/3 (0/1)
3
4
Site 2 (0/1)
Power
Azimut
Azimut
Azimuth
Diagramme
Diagramme
Diagram
Inclinaison
Inclinaison
Tilt
Puissance
Puissance
Power
Constraint : 1 to 3 directive antennas
OR 1 omnidirectional antenna
31
Crossover and Mutation operators

Geographic Crossover


Radius R around a site S
(randomly chosen)
Exchange of sites (level 1)
Site
Omni/direc
t

Station 1/3
Multi-level Mutation


Power
Diagram
Azimuth
Power
Tilt

Activation of a site
OR type and number of
antennas
OR antenna parameters
32
Sharing function
f2
Penalize the individual fitness / number of similar individuals
Niche count m( x ) 
 shdist( x, y )
f
'
( x) 
yPop.
sh
sh
f1

 1 dist x , y  
   
sh dist  x, y   

0

sh



f ( x)
m( x )
If
dist ( x, y )   sh
1
Otherwise

sh
dist
Objective space and/or Decision space (x,y) ? Objective
Combined Sharing (objective, decision) : flow-shop scheduling
(Phd. M. Basseur)
Used Metric (dist) ? : Euclidean distance
33
Adaptive niche size :
sh
M3,m1
share
n1
 AirePareto
N
M2,m3
M1,m2
f3
 sh
f2
f1
34
Constraints : Linear Penalization

Penalization / Constraint violation
Covering
Handover
Pc
1
0
0
Pho
1
0
80 100% covering

5*

Pc 


cover
100
0
2 * handover
Ph  
100
0

0
50 100% handover
4
if
4
cover >80 %
otherwise
if
handover > 50 %
otherwise
35
Cost function : Pareto Rank

Penalization of constraints (Handover and
Covering) and sharing are applied for each
objective (traffic, interferences and number of sites)
Ph(u)*Pc(u)
f (u) f(u)*
m(u)
'


Cost(Solution) = Rang_Pareto(penalized objectives)
Pareto Rank (number of dominating solutions) has
to be minimized
36
Experimental Protocol

Instance 1 : Highway
250 sites, Traffic : 3210 Erlang
Sites
36
49
70

Interf Trafic (%)
228000
72
483542
97
602930
99,75
Instance 2 : Urban zone
568 sites, Traffic : 2988 Erlang
32 sites
61 sites (cells)
(interferences)
37
Performance Evaluation
Few works in the literature realize quantitative evaluation


Exact representation of Pareto front PO [J. Teghem ’98, …]
Approximation of PO : 2 complementary measures
 Contribution, Entropy
Contribution : Compares the dominance
C: common solutions
W1: PO1 > PO2
L1: PO2 > PO1
N1 : non-dominated
PO1
PO2
C
C
C
W1  N1
2
CONT(PO1/ PO2)
C W1  N1 W2  N2
L1
W1
W2
L2
N1
N2
Ex: If PO1=PO2 Then CONT(PO1/PO2) = 0.5
If PO1>PO2 Then CONT(PO1/PO2) = 1
38
Entropy : Diversity


We define a niche for each solution of
PO*=Non-Dominated(PO1 U PO2)
E(PO1,PO2) : diversity of solutions of PO1 relatively to
niches of PO*
PO*
E(PO1,PO2) 1 ( 1 ni ln ni )
ln( ) i1 Ni PO1 PO1
PO1
PO2
Niches
39
Impact of sharing
Entropy Contribution
0.95
Sharing
Sans Sharing 0.42
Non-hold
Traffic (%)
Number of
sites
0.63
0.36
Without sharing
With sharing
Interferences
Convexity (sharing) : mean of 55%
of the front on the convex hull
40
Hybridization : Principle

Goal :

Improve the approximation found by the Genetic
Algorithm
GA
LS

Principe :


Use the GA to approximate the Pareto front (exploration
by GA).
Use a Local Search method to intensify the search.
41
Hybridization oriented by the archive
Archive
Population
Archive
GA
Local Search
Local Search
Pareto Solutions
Pareto Solutions
Archive
Archive
LS
Pareto
flow-shop scheduling and
vehicle routing (Phd M.Basseur
and N. Jozefowiez)
Restricted Neighborhood
Nb Sites Interferences
Before
After RL
Before
After RL
Before
After RL
49
49
74
65
194
191
2369352
2111651
2453859
1632346
13363674
12703674
Traffic
87,32%
88,95%
90,18%
91,30%
93,08%
93,08%
OD
SD
LD
0 45 55
0 42 52
0 66 45
0 52 36
0 166 197
0 160 188
42
Parallel Models
Goals
Improve the quality of solutions
1 - Parallel model
Migration cooperative
Speedup the search time of the algorithm
2 – Parallel model based on the parallel
asynchronous distribution of the
evaluation phase of the algorithm
3 – Parallel model based on the parallel
synchronous evaluation of a network
(partitioning of the geographical area)
43
Used Parallel Platforms



Heterogeneous Network of
Workstations : 25 Intel/Linux,
6 Sparc/solaris, 1 Mips/Irix
CLUMPS - Cluster of SMP (shared
memory): IBM SP3 (Lille) – 64
processors : 4 nodes of 16 processors
Cluster of clusters of PCs : Icluster
(Grenoble) – 216 PC : 5 clusters
44
1: Migration Cooperative Model


Parallel cooperation between GAs (large
grain parallelism)
Asynchronous migration of the Pareto
GA
archive

Number of updates of the archive
Model generalization

GA
Migration Criteria


GA
Differents parameters, operators,
algorithms, …
GA
GA
Archive
Pareto
GA
GA
45
Impact of the cooperation :
Cluster of clusters of PC
Interferences
Traffic



With migration (4 GAs, 200g)
Procs
Without migration
4
8
16
24
32
Number of sites
Efficiency
1
1.01
1.02
0.81
0.75
Migrations Cont Entr
With
0.85 0.84
Without 0.15 0.49
VRP – Vehicle Routing Problem (Phd N. Jozefowiez)
Migration improves the quality of solutions
Super-linear speedups
46
2: Distribution of solution evaluation



Parallel asynchronous evaluation (medium grain)
Complete evaluation of a network
« Steady-state » Genetic Algorithm


De-synchronization of the selection-evaluation-replacement phases
Fault-tolerant, Efficient in heterogeneous non-dedicated platforms
Selection
Asynchronous GA
candidates
for evaluation
First In First Out
Evaluator 1
Evaluator 2
Replacement
evaluated
solutions
First In First Out
...
Evaluator N
47
3: Parallel evaluation of a network


Synchronous, fine grain
parallelism
Parallel evaluation of
objectives functions and
constraints


Geographical area
Load-balancing of the partitions
Master-worker Paradigm


... Proc N
Proc
1
Proc
2
Master : partitioning and fusion
of partial results
Worker : partial evaluation
(partition)
f1 f2 f3 c1 c2 f1’ f2’ f3’ c1’ c2’
Partial evaluators
48
Speedups of models 2 and 3
Network of PCs
CLUMPS : IBM SP3
Speedup
Speedup
Number of
processors
Asynchrone evaluation: M2


Number of
processors
Partitioning model : M3
« Asynchronous evaluation » model is better in terms of
Scalability.
The different models are complementary
49
A multi-layer hierarchical
parallel/hybrid metaheuristic
Cooperative
island E.As
Distribution
of networks
Relay
hybridization
Distribution
of the
computations
Parallel evaluation
(partitioning)
Co-evolutionary
hybridization
Deployment of
incremental
Local Searches
Distribution of
the computations
50
Solving instance Arno 1.0
Platform
Cluster Grid’5000 - Lille
Wave. Prop. precalculated
Yes
Number of proc.
52 (AMD opteron 2.2 GHz)
Cumulative wall clock time
2112 h.
Wall clock time
44 h.
Parallel efficiency
0.92
Number of tasks
1038010
Number of tasks
31359
Min. cost
0.939 s.
Min. cost
0.173 s.
Max. cost
5.92 s.
Max. cost
561.303 s.
Mean cost
2.08 s.
Mean cost
173.637 s.
Cumulative time
509.5 h.
Cumulative time
1512.52 h.
Parallelization of evaluations
Parallelization of Local Searches
51
Solving instance Arno 3.0
Platform
Cluster Grid’5000 - Lille
Wave. Prop. precalculated
Yes
Number of proc.
52 (AMD opteron 2.2 GHz)
Cumulative wall clock time
1596 h.
Wall clock time
39 h.
Parallel efficiency
0.75
Number of tasks
856859
Number of tasks
56071
Min. cost
0.31 s.
Min. cost
12.5257 s.
Max. cost
11.34 s.
Max. cost
520.415 s.
Mean cost
1.14 s.
Mean cost
85.132 s.
Cumulative time
270.43 h.
Cumulative time
1325.95 h.
Parallelization of evaluations
Parallelization of Local Searches
52
Solving instance Arno 3.1
Platform
Metacomputing
Wave. Prop. precalculated
No
Parallel decomp. Model
Yes (x 2)
Number of proc.
100 (heterog. and non dedicated)
Cumulative wall clock time
30681 h.
Wall clock time
Almost 15 days
Parallel efficiency
0.98
Number of tasks
1897046
Number of tasks
15299
Min. cost
7.815 s.
Min. cost
1832.57 s.
Max. cost
247.967 s.
Max. cost
24380.7 s.
Mean cost
21.51 s.
Mean cost
4593.52 s.
Cumulative time
11340 h.
Cumulative time
19521 h.
Parallelization of evaluations
Parallelization of Local Searches
53
Some optimized networks taken from
the final archive
Arno 1.0 (highway)
Arno 3.0 (urban)
Arno 3.1 (urban)
54
Conclusions & Perspectives

ParadisEO (open source) framework (C++) for
parallel and distributed hybrid metaheuristics
(www.lifl.fr/OPAC/paradiseo).




GUIMOO (open source) software for multi-objective
performance evaluation and 2D/3D visualization of
Pareto fronts (www.lifl.fr/OPAC/guimoo)
Impact of the introduced mechanisms (sharing,
hybridization, parallelism, elitism)
A new parallel exact method (PPM) for MOPs.
Hybrid exact-metaheuristic approach for MOPs
55
Perspectives

Modelization of the problem



Extension of the model to other objectives and
constraints (homogeneity, connectivity of cells...)
Towards an interactive approach
Design and implementation on Grids (Large
network) : Project ACI GRID DOC-G (Challenges in
Combinatorial Optimisation on Grids, LIFL Lille PRISM Versailles – ID Grenoble)
56