Traffic Flow Optimisation using the D-Wave Quantum Annealer Europe... · Quantum Computing 12.04.2018 K-SI/LD | Dr. Christian Seidel 2 ... Quantum-enhanced reinforcement learning

Traffic Flow Optimisation –using the D-Wave Quantum Annealer

Qubits Europe, Munich12.04.2018 – Dr. Christian Seidel

Christian SeidelLead Quantum Computer Scientist, Volkswagen Data:Lab

Joined the Volkswagen Data:Lab at its beginning in 2014Areas of work since then:• Connected Car, Future mobility, Smart City• Internet of Things• Natural Language Processing, Semantic Analysis, • Quantum Computing

2K-SI/LD | Dr. Christian Seidel 12.04.2018

• Christian Seidel – Volkswagen Data:Lab, Munich• Florian Neukart – Volkswagen Group of America Code:Lab, San Francisco• Patrick van der Smagt – Volkswagen Data:Lab, Munich• David von Dollen – Volkswagen Group of America Code:Lab, San Francisco• Isabella Galter – Volkswagen Data:Lab, Munich• Andrea Skolik – Volkswagen Data:Lab, Munich• Michael Streif – Volkswagen Data:Lab, Munich

K-SI/LD | Dr. Christian Seidel 12.04.2018

Team

3

Quantum Computing – just a hype or a real thing?

K-SI/LD | Dr. Christian Seidel 12.04.2018 4

The Question that drove us …

Is there a real-world problemthat could be addressed with a

Quantum Computer?


Everybody knows traffic (jam) and normally nobody likes it.

12.04.2018 K-SI/LD | Dr. Christian Seidel

Image courtesy of think4photop at FreeDigitalPhotos.net

6

YES: Traffic flow optimisation

Public data set: T-Drive trajectory

https://www.microsoft.com/en-us/research/publication/t-drive-trajectory-data-sample/

Beijing• ~ 10.000 Taxis • 2.2. – 8.2.2008

data example:

12.04.2018 K-SI/LD | Dr. Christian Seidel 7

https://www.microsoft.com/en-us/research/publication/t-drive-trajectory-data-sample/

D-Wave calculation modelQuadratic Unconstraint Binary Optimisation (QUBO)


During the quantum annealing process the system evolves to the lowest energy level.

This requires your problem to be formulated as an Ising Model:

or as a QUBO:

8

Transforming the real world problem for the Quantum Computer


Example:

Simplified graph structure representing a route grid.

2 cars with 3 route options on a 2 x 2 grid.

Car Route Binary variable

Car 1 #1: s0,s3,s6,s9 Q11

Car 1 #2: s0,s3,s8,s11 Q12

Car 1 #3: s2,s7,s10,s11 Q13

Car 2 #1: s0,s3,s6,s9 Q21

Car 2 #2: s0,s3,s8,s11 Q22

Car 2 #3: s2,s7,s10,s11 Q23

9

Creating the cost function for each route segment

Street segment

Associated cost function Value

s0 (Q11 + Q12 + Q21 + Q22)2 4s3 (Q11 + Q12 + Q21 + Q22)2 4s6 (Q11 + Q21)2 1s9 (Q11 + Q21)2 1s8 (Q12 + Q22)2 1s11 (Q12 + Q22 + Q13 + Q23)2 1s2 (Q13 + Q23)2 0s7 (Q13 + Q23)2 0

s10 (Q13 + Q23)2 0


More cars on one street lead to higher costs

Example:(Q11 + Q12 + Q21 + Q22)2 + (Q11 + Q12 + Q21 + Q22)2 + (Q11 + Q21)2 + (Q11 + Q21)2

+ (Q12 + Q22)2 + (Q12 + Q22 + Q13 + Q23)2 + (Q13 + Q23)2 + (Q13 + Q23)2 + (Q13 + Q23)2 = 12

Goal: minimise the all-over-costs => distribute cars to different streets

10

Data preprocessing

• Transforming the geo-coordinats to street segments using OSMnx, a Python package for street networks

• Getting real / valid alternative routes via HERE-maps requests.https://developer.here.com


Beijing – Traffic Heatmap


Traffic in the city Detail: route to the Airport

• 418 cars• 10.000 cars

We assigned each of the 418 cars 3 possible routes to reach the airport

Size of the problem space: 3^41812

Code snippet and output


Result: un-optimised vs optimised traffic


Due to the 2,5 months project time we threated in this test all street equally. This is obviously a simplification.

Additional constraints could be:• Street capacity (highway vs alley)• Residential zone

Data set improvements:• Frequent updates to react on constantly changing traffic situations (other data set)• more cars • etc


Further Improvements

Traffic flow optimization using a quantum annealerhttps://www.frontiersin.org/articles/10.3389/fict.2017.00029/full

Quantum-enhanced reinforcement learning forfinite-episode games with discrete state spaceshttps://www.frontiersin.org/articles/10.3389/fphy.2017.00071/full

Quantum-assisted cluster analysishttps://arxiv.org/abs/1803.02886


Publications

https://www.frontiersin.org/articles/10.3389/fict.2017.00029/full

https://www.frontiersin.org/articles/10.3389/fphy.2017.00071/full

https://arxiv.org/abs/1803.02886

• Recommendation System• Use output for Clustering/Classification


Follow up projectsexample Machine Learning

• Material Simulation: talk held by Michael Streif

• Experience with using the D-Wave: talk held by Isabella Galter

University cooperation:• QASAR - Results and hands-on demonstration talk held by Sebastian Feld + Thomas Gabor

of a joint project of Volkswagen and LMU• Investigating the annealing path – talk held by Kristel Michielsen

project with the Forschungszentrum Jülich


And a lot more …

Lessons learnd

• There are sooo many projects for a Quantum Annealer out there …• The D-Wave Quantum Annealer can help solving real world problems

(Prototype was done in 2,5 months)• transforming the real world problem into a QUBO takes the most time• Problems, larger than the chip’s capacity can be solved by decomposition using a

hybrid solver (i.e. QSage, QBsolve)

Due to the chimera graph structure of the quantum chip:• The chip is not fully connected, so Qubit chains need to be created• Challenging the Precision: find the right values for chain strengths (Qubit connection)

and penalty weights

Late Easter Wish: We’d like to have a Java API for the D-WaveK-SI/LD | Dr. Christian Seidel 12.04.2018 19

Questions ?


Documents

Traffic Flow Optimisation using the D-Wave Quantum Annealer Europe... · Quantum Computing 12.04.2018 K-SI/LD | Dr. Christian Seidel 2 ... Quantum-enhanced reinforcement learning