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Modeling and solving optimization and planification problems in cellular networks

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

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Modeling and solving optimization and planification problems in cellular networks

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  1. Laboratoire d’InformatiqueFondamentale de Lille Équipe OptimisationParallèle 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

  2. 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 multi-objective mathematical programming models) • Hybrid Metaheuristics (local search, EAs, etc.) • Parallel Algorithms Source : http://www.ulg.ac.be/telecom/publi/publications/mvd/Demoulin2004Principes/

  3. 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

  4. Access network design to the RTCP HLR VLR MSC • Objectives : cost, availability • Constraints : traffic, capacity, hops, … BSC Radio sub-network BTS T-Mobile & Mobinets GSM  UMTS

  5. Constraints (1) Dealing with spanning trees, (2) Depth of the tree, (3) BSC / BTS / DXX degree, (4) BSC / BTS / DXX traffic capacity, (5) BTS availability, (6) DXX locations, (7) Predefined links.

  6. Objectives • (1) Minimize the total cost, • (2)Maximize the overall availability

  7. Complexity • The constrained minimum spanning tree NP hard • Number of candidate topologies ( Supposing first DXXs could only be colocated with some BTS sites )

  8. Algorithms • Greedy Heuristics : Inspired from Prim and Kruskal • Local Search • Evolutionary Algorithm • Hybrid algorithm (Genetic algorithm, Kruskal, Local search)

  9. Performance Evaluation • Both cost and robustness have been improved. • Variance between worst and best computed topologies is low.

  10. Best computed maps (gsm3)

  11. Location Areas Planning and Optimisation MSC (Mobile Switching Center) BSC (Base Station Controller) Cells

  12. Location Areas Planning and Optimisation BSCs associated to MSCs Cells associated to BSCs Location area : To localize the user

  13. 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

  14. 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

  15. 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

  16. Objectives • Minimize the location area (lup) inter-MSC • Minimize the location area (lup) intra-MSC • Minimize the traffic of signalisation (paging)

  17. 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)

  18. Some results for hybrid approach • Good compromise between diversification and intensification • Interesting results comparing to other algorithms Fitness of the best Individual : 11759200

  19. 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

  20. Radio telecommunications networks One site : From 1 to 3 BTS per site • Design challenges • Network cost : number of sites,… • Quality of service : traffic, interferences, … • Network design • Positioning of BTS • Configuration of BTS (TRX, antenna, …) BTS : Base Transceiver Station

  21. MACRO INTERIOR PUBLIC ZONE MICRO MOBILE RESIDENCE Cellular network design • Existing tools • Manual or semi-automatic design • « Simplified » modelization (hexagonal cells, …) • Micro-cellular networks • WISE of ATT • Thesis of P. Reininger (FT R&D) • Macro-cellular networks • European projects • STORM : mono-objective (minimization of sites, restrictive configuration) • ARNO : non-Pareto (agregation), Genetic algorithms, simulated annealing, tabu search, …

  22. Environment – Instance data • Discrete geographical area (grid) : • Different set of test points • Reception (RTP) (Cd_ij) • Service (STP) (Cd_ij>Sq) • Traffic (TTP) (E_i) • A set of potential sites

  23. Configuration of antennas Complex combinatorial problem : ~ 600.109 solutions per antenna 1 omni or 1-3 directive

  24. Effects of configuration • Cell = covered region by a BTS Propagation model used : Free space Omni-directional 60 dBm Directive type 1 Directive type 2 Azimuth 50° PIRE -10 dBm Tilt -15°

  25. is covered if Multi-objective model: Constraints • A set of BTS satisfying the constraints : • Covering • Handover (mobility) P • For each cell:

  26. Multi-objective model: Objectives • Min Number of sites (cost) • Min Interferences • Max Traffic hold STi : Handover sets (4 first signals) Interferences sets (nuisibles) Geographical area Used Sites Non-used sites Handover zone Covered zone

  27. Multi-objective optimization Dominance y dominates z iff Pareto Optimality Solution is Pareto optimal iff there is no solution 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

  28. Multi-objective algorithms  • 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

  29. Pareto Approch Goals Convergence : ranking(order between individuals), elitism,… Diversification : sharing,… Feasible solutions Feasible solutions Solution found Pareto front

  30. Ranking NSGA Elitism Update archive A(1) R3 H(3) Archive Pareto F(2) B(1) C(1) G(2) R2 R1 D(1) E(1) Pareto Evolutionary Algorithm Population Evaluation Replacement « Ranking» « Sharing » Selection Genetic operators Efficiency of Pareto mechanisms: Ranking, Elitism MO Knapsack : I. Kort (Concordia)

  31. Encoding of individuals • An individual encodes/represents a whole network • Hierarchical encoding (4 levels) Level Gene 1 Gene 2 ... An individual Site 1 (0/1) Site 2 (0/1) Site N (0/1) 1 Omni/Direc 2 Station 1/3 (0/1) 3 Azimut Diagramme Inclinaison Puissance Azimut Diagramme Inclinaison Puissance Azimuth Diagram Tilt Power Power 4 Constraint : 1 to 3 directive antennas OR 1 omnidirectional antenna

  32. Crossover and Mutation operators • Geographic Crossover • Radius R around a site S (randomly chosen) • Exchange of sites (level 1) Site • Multi-level Mutation • Activation of a site • OR type and number of antennas • OR antenna parameters Omni/direct Station 1/3 Diagram Azimuth Power Tilt Power

  33. sh 1 sh dist Sharing function Penalize the individual fitness / number of similar individuals f2 Niche count f1 If Otherwise • Objective space and/or Decision space (x,y) ? Objective • Combined Sharing (objective, decision) :flow-shop scheduling (Phd. M. Basseur) • Used Metric (dist) ? : Euclidean distance

  34. f3 f2 f1 Adaptive niche size : sh M3,m1 M2,m3 M1,m2

  35. ( ) ì cover - > 5 * 4 if cover 80 % = P í 100 c 0 otherwise î ( ) ì handover - > 2 * 4 if handover 50 % = P í 100 h 0 otherwise î Constraints : Linear Penalization • Penalization / Constraint violation Covering Handover Pc Pho 1 1 0 0 0 0 100%covering 50 80 100% handover

  36. Cost function : Pareto Rank • Penalization of constraints(Handover and Covering) and sharing are applied for each objective (traffic, interferences and number of sites) • Cost(Solution) = Rang_Pareto(penalized objectives) • Pareto Rank (number of dominating solutions) has to be minimized

  37. Experimental Protocol • Instance 1 : Highway250 sites, Traffic : 3210 Erlang • Instance 2 : Urban zone 568 sites, Traffic : 2988 Erlang 32 sites (interferences) 61 sites (cells)

  38. 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 L1 N1 W1 C L2 W2 N2 PO2 C Ex: If PO1=PO2 Then CONT(PO1/PO2) = 0.5 If PO1>PO2 Then CONT(PO1/PO2) = 1

  39. 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* PO1 PO2 Niches

  40. Impact of sharing Entropy Contribution 0.63 0.36 0.95 0.42 Without sharing Sharing Sans Sharing Non-hold Traffic (%) With sharing Number of sites Interferences Convexity (sharing) : mean of 55% of the front on the convex hull

  41. GA LS Hybridization : Principle • Goal : • Improve the approximation found by the Genetic Algorithm • Principe : • Use the GA to approximate the Pareto front (exploration by GA). • Use a Local Search method to intensify the search.

  42. Archive Archive Population Archive GA Archive LS Before 49 2369352 87,32% 0 45 55 Pareto After RL 49 2111651 88,95% 0 42 52 Before 74 2453859 90,18% 0 66 45 After RL 65 1632346 91,30% 0 52 36 Before 194 13363674 93,08% 0 166 197 After RL 191 12703674 93,08% 0 160 188 Hybridization oriented by the archive flow-shop scheduling and vehicle routing (Phd M.Basseur and N. Jozefowiez) Local Search Local Search Pareto Solutions Pareto Solutions Restricted Neighborhood Nb Sites Traffic Interferences OD SD LD

  43. Parallel Models Goals • 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) • Improve the quality of solutions • 1 - Parallel modelMigration cooperative

  44. 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

  45. 1: Migration Cooperative Model • Parallel cooperation between GAs (large grain parallelism) • Asynchronous migration of the Pareto archive • Migration Criteria • Number of updates of the archive • Model generalization • Differents parameters, operators, algorithms, … GA GA GA GA GA Archive Pareto GA GA

  46. Impact of the cooperation : Cluster of clusters of PC With migration (4 GAs, 200g) Procs Efficiency 4 1 8 1.01 16 1.02 24 0.81 32 0.75 • VRP – Vehicle Routing Problem (Phd N. Jozefowiez) • Migration improves the quality of solutions • Super-linear speedups Interferences Without migration Migrations Cont Entr With 0.85 0.84 Without 0.15 0.49 Number of sites Traffic

  47. 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 Replacement Asynchronous GA candidatesfor evaluation evaluatedsolutions First In First Out First In First Out ... Evaluator 1 Evaluator 2 Evaluator N

  48. f1 f2 f3 c1 c2 f1’ f2’ f3’ c1’ c2’ 3: Parallel evaluation of a network Geographical area • Synchronous, fine grain parallelism • Parallel evaluation of objectives functions and constraints • Load-balancing of the partitions • Master-worker Paradigm • Master : partitioning and fusionof partial results • Worker : partial evaluation (partition) ... Proc 1 Proc 2 Proc N Partial evaluators

  49. Speedups of models 2 and 3 Network of PCs CLUMPS : IBMSP3 Speedup Speedup • « Asynchronous evaluation » model is better in terms of Scalability. • The different models are complementary Number of processors Number of processors Asynchrone evaluation: M2 Partitioning model : M3

  50. A multi-layer hierarchical parallel/hybrid metaheuristic Cooperativeisland E.As Distributionof networks Relayhybridization Distributionof thecomputations Deployment ofincrementalLocal Searches Co-evolutionaryhybridization Parallel evaluation(partitioning) Distribution ofthe computations

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