Optimisation for the Telecommunication Industry using Quantum Annealing

Transcription

1 Optimisation for the Telecommnication Indstry sing Qantm Annealing Catherine White, Tdor Popa BT Applied Research Plantagenet SYSTEMS

2 BT Adastral Park

3 HARD PROBLEMS IN TELECOMMUNICATIONS Resorce allocation and planning problems in telecommnications are often algorithmically hard (e.g. NP hard or #P complete) Network layot problem (Steiner Tree) Job Schedling Configration of overlapping cells (placement, power, freqency assignment) Configrations of paths and wavelengths over core networks at layer 1 (RWA problem)

4 QCAPS Project Hard Comptational Problems from Telecommnications D-Wave Approach to Optimisation (experiment) Steiner Tree Graph Coloring Using 2000Q D-Wave Processor Qantm Annealing Initial review of similar previos work by Nasa Selection of promising problems. Max-Ct Job Schedling

5 Overview of problems Infrastrctre layot Network capacity Using existing infrastrctre sch as dcts and poles, together with the possibility of creating new infrastrctre, to provide or pgrade connectivity to new premises. (Steiner spanning tree) - Simlated annealing approaches are typically sed for these problems crrently. Location of celllar network base station. Designing a network to have sfficient capacity to meet demand. Utilising an existing network to maximise capacity Network resilience Network secrity Identification of paths with disjoint nodes and edges in a graph Design of a network sch that there are mltiple paths over disjoint nodes and edges between each pair of endpoints. Optimm placement of deep packet inspection firewalls on a network Graph search problems identification of similar or of nsal clsters (identification of sspicios behavior) Content distribtion Network operation and maintenance Placement and size of content distribtion nodes Predictive downloads to content distribtion nodes Location of service hbs Location and volmes of spare network components Priority and freqency of plift (schedled, preventative maintenance) Allocation of jobs to engineers Geographic ordering of jobs (Travelling Salesman)

6 SUITABILITY FOR QUANTUM ANNEALING The problems described are discrete optimisation problems The state space is large, bt can be represented in small nmber of bits Mapping the problem to qbits is tractable and allows s to find optimm and near optimm soltions.

7 CELLULAR NETWORKS Coverage placement and power of antenna Capacity freqency assignment, interference management >These two isses may not be separable in the design problem Cell Base Station power Cell shape, distance, mltipath, obstacle shadowing, antenna characteristics SIR > threshold

8 MANET - Half dplex mesh network problem MANET Mobile Ad hoc Network. We consider a mesh network where intermediate devices relay data to provide complete commnication services between all devices on the mesh. Applications: IoT, Environmental monitoring, Disaster areas SEND STATE SEND STATE RCV STATE RCV STATE

9 MANET - Half dplex mesh network problem Half-dplex problem (mesh network of devices which can either send or receive on a single freqency) Problem of finding an optimm schedle Assme devices boot p in a sb-optimal schedle, and can commnicate their discovered neighbors to a central optimising service which will will commnicate back a schedle. Devices can synchronise clocks. SEND STATE (SCHEDULE 0) RCV STATE (SCHEDULE 1)

10 MANET - Half dplex mesh network problem Half-dplex problem maps very natrally to the D-Wave annealer Ising form. Simple 1 logical qbit per device is sfficient. SEND (SCHED 0) = -1 RECEIVE (SCHED 1) = 1 SEND STATE SEND STATE RCV STATE RCV STATE

11 MANET - Half dplex mesh network problem 2 connected node problem 3 connected node problem frstration.?

12 MANET - Half dplex mesh network problem 3 connected node problem a soltion One link is disabled (frstrated link) (There will still need to be arbitration in the protocol, e.g. handshaking becase one node commnicates with two others)

13 MANET - Half dplex mesh network problem The code is straightforward we pass the logical Ising Hamiltonian vales in a JSON string J = {(0, 1): 1, (1, 2): 1, (0, 2): 1} h = [0, 0, 0] Dwave provides a classical fnction which handles the embedding of the logical Hamiltonian onto the physical qbits. (Althogh we can optionally rn this many times, and select the best embeddings ) # Get the geometry of the hardware adj = get_hardware_adjacency(solver) # Find an embedding for the problem. emb = find_embedding(j, adj) Rn the solver. answer = solve_ising(solver, h_emb, J_emb, **dw_params) The reslts are retrned as list of measred spin vales for each qbit.

14 MANET - Half dplex mesh network problem Optimising the Half Dplex Mesh is NP Hard! 2000Q architectre is sitable for embedding and solving 100 node mesh network problems of realistic graph density.

15 MANET - Half dplex mesh network problem 300 Node Graph Optimm soltion for a 300 node graph, fond by D-Wave and verified classically.

16 Finding Exact Optimm Percentage of anneals that retrn exact optimm over a range of problem sizes between 20 and 100 logical cells.

17 Finding Near Optimm (>95% of optimm) Percentage of anneals that retrn >95% optimm over a range of problem sizes between 20 and 300 nodes.

18 Finding Near Optimm (>90% of optimm) Percentage of anneals that retrn >90% optimm over a range of problem sizes between 20 and 300 nodes.

19 Best allocation n-coloring When coloring a graph with a large nmber of colors, (freqencies) and varying demand how best to allocate channels to satisfy demand?

20 Cell Channel Allocation Problem 1. Each cell is represented by a complete graph of qbits - one qbit for each available channel. - Demand on each cell can be mapped onto the complete graph. That is, we set the copling vales sch that the minima of the isolated Hamiltonian corresponds to a channel allocation that meets bt does not exceed the ideal demand, for n channels. - To express the objective that optimm available channels to meet demand is N - Minimise ( Q. ) N 1

21 Cell Channel Allocation Problem Qbo terms, where N_i is the channel demand of cell i: Transform QUBO y 3 0,1 to Ising s 3 1,1 form: 1 - Minimise Q. N. - Transformation: y. = : ;<= 1 Sbstitte this into the QUBO - Minimise : 1 ;<= N 1. Expand, and note that for both s. = 1 and s. = 1, s 1. = 1 - Minimise.A? s. s? +. M 2N s. + const where M is nmber of colors Constant terms can be dropped Minimise G s. s?.a? + G M 2N. s.. - We can add frther details sch as penalising onsite energies corresponding to freqencies that don t perform well for that cell.

22 Cell Channel Allocation Problem 2. The constraint on neighboring cells not taking the same freqency is obtained by a 1:1 mapping between the same channels between graphs, which we cople with a strong antiferromagnetic vale (J>1).

23 Small Tests of Cell Allocation Problem: 3 cells, even distribtion Each cell: M = 3, N = 1, M 2N = 1, i, j {0,1,2} Cell interference graph terms: K^_ = 1 if cells I and J interfere I, J {Cells} G s. s? + G s. K^_ G G s^<h s _<h.a?. ^A_ hij..l Overall: Minimise G s. s?.a? + G s.. + K^_ G G s^<h s _<h ^A_ hij..l

24 Small Tests of Cell Allocation Problem: 4 cells, one with high demand M = 5, N^ij = 2, N^ {=,1,q} = 1, M 2N =,1,q = 3, M 2N j = 1 i, j {0,1,2,3,4} Cell with high demand.a? s. s? +. {=,1,q} s. Cells with normal demand.a? s. s? + 3. {=,1,q} s. Adjst the previos problem to penalise se of channels which are bad for the cell, by se of a qality factor q i. Cell with high demand.a? s. s? + q.. {=,1,q} s. Cells with normal demand.a? s. s? + q. 3. {=,1,q} s.

25 Vertex-diverse roting

26 Partially vertex disjoint paths on a core model

27 Vertex-disjoint roting: Usefl problems to solve What is the best set of partially disjoint paths between nodes s and t? What if... the probability of node compromise is different for each node? What if... we grop the nodes into shared risk grops which will all be compromised together? What if we want to load balance across all a sbset of nodes (which we define as the network edges) and we want to find an optimm set of partially diverse rotes between all pairs in this set, and we make the rle that nodes cannot be shared?...and we can look at all the same problems, bt for edge-disjointness

28 Hard problems we are trialling with DWave Half dplex mesh network Cell channel allocation Roting and Wavelength Assignment Network resilience disjoint path roting Job shop schedling Malicios traffic flow propagation and defensive strategies Plantagenet SYSTEMS

29 Conclsions D-Wave reliably generates near optimms sing a small nmber of anneal cycles. Many discrete optimisation problems from the telecommnication indstry map very well to the D-Wave If this performance can be maintained for larger processors, D-Wave will be a significant technology for this indstry. Chain-length minimisation is a big isse. Hierarchical connectivity or bespoke architectres cold be an interesting approach. Sggestion: D-Wave cold make their bilt-in fnctions very flexible, i.e. provide variations on Graph Coloring to allow n-color allocation, and to provide preference on allocated color. Plantagenet SYSTEMS

30 Thanks Thanks to domain specialists at BT Dr Keith Briggs, Dr Selina Wang, Dr Nigel Walker, Dr Tim Glover. Project leadership from Plantagenet Systems (Dr Roberto Desimone) Collaboration with or academic partners at UCL (Prof Pal Warbrton and Dr Yanlong Fang) and Bristol (Dr Ashley Montanaro and Dr Stephen Piddock). Plantagenet SYSTEMS