Mathematical Optimization at Siemens

Corporate Technology

Mathematical Optimization at Siemens

Michael Hofmeister

Outline

ƒ

Siemens Company – a short introduction

ƒ

Mathematics at Siemens Corporate Technology

ƒ

Assembly of printed circuit boards

ƒ

Water supply network planning

ƒ

The internet of things

Siemens Company

Siemens' innovations have changed the world

From the first electronic controls –

to fully automated factories

From the invention of the dynamo –

to the world's most efficient gas

turbines

From the first interior view of the body –

to full-body 3D scans

Healthcare

Healthcare

Industry

Industry

Energy

Energy

Siemens Company

Milestones for Three Centuries

1881: Electrical streetcar 1993: Electron Microscope 1924: Traffic light 1881: Telephone switchboard 1879: Electrical railway 1866: Dynamo 1847: Telegraph 1905: Tantalum lamp 1905: First R&D laboratory 1962: Thyristor for energy 1965: Integrated circuits 1935: Coax cable 1974: Computer tomography scanner 1980: EWSD (digital switching technology 1988: Megabit chip 1958: Heart pacemaker

1931: „Hot air shower“

(hair-dryer)

1906: Vacuum cleaner 1953: Very clean silicon

1985: High speed train ICE (300 km/h) 1959: Transistor based universal computer 1984: Hicom telephone switchboard 2003: Maglev in Shanghai 2004: Bio-lab on

chip 2005: Electronic wedge brake

2000: Piezo Injection

for diesel engines

2000: syngo GUI 2004: Full length

MR tomography 2005: Home entertainment 2004: 64 lines computer tomography scanner 1994: High temperature fuel cell

1998: Terabit switch 1998: Most efficient

Power plant Sales in 2005: 75,445 Billion Euro Employees in 2005: 461,000

Information and Communication Energy Industry Automation Mobility Healthcare Lighting Technology Household Appliance Innovation for: Loga rith m ic sc ale 1847: Werner von Siemens founded the company

Bracknell Lissabon Zaragoza Toulouse Eynsham Brüssel Mailand Roke Manor Paris Zürich Porto Tel Aviv Burlington Auburn Hills Mülheim Salzburg Graz Karlsruhe Regensburg Erlangen-Nürnberg Berlin Dresden Istanbul Helsinki Arlington Orlando Buenos Aires Curitiba Penang Taipei Seoul Shanghai Bombay Issaquah Bangalore Peking _Tokio Lake Mary Austin Newport News

PrincetonPiscataway Norcross Melbourne Sydney Linz Changchun Xi‘an Chengdu Nanjing Tianjin _Ichon Tilbury Peterboroug h Drummondville Chatham Knoxville

Johnson City Madrid

Sophia Antipolis Netanya Neu-Delhi Kakegaw_a Kawasaki Yokohama Hong Kong Goa Berkeley Concord Santa Clara San Diego Mountain View Sacramento San José Athen St. Petersburg Treviso Oslo Moskau Pretoria Göteborg Pandrup München Wien Danvers Budapest Bratislava Pittsburgh Hoffman n Estates London Sao Paulo Zagreb Bogota Breda Hengelo Amsterdam Timisoara Prag Guadalajara Singapur

Siemens Company

Corporate Technology

Innovation Network of the Integrated Company

Chief Technology Officer (CTO) ƒEvaluation of innovation strategy ƒTechnology based support of synergies ƒassurance of innovative power ƒEvaluation of technologies ƒGuidance

Customers

Corporate Intellectual Property and Functions (CT I)

ƒ Intellectual Property Services & Strategy ƒ Standardization, Environmental Affairs ƒ Global Information Research

Corporate Research and Technologies (CT T)

ƒ Global Technology Fields with multiple impact ƒ Pictures of the Future

ƒ Accelerators for new business opportunities

Corporate Technology (CT)

Re

gions

Sectors / Divisions

Industry

Energy

Healthcare

Chief Technology Office (CT O)

ƒ Direct support of CTO

Siemens IT Solutions and Services (SIS)

Siemens Financial Services (SFS)

Corporate Technology

Modeling, Simulation, Optimization

Control Systems

Localization Technologies Digital Product

Mathematical Engineering Smart Decision Support

Autonomous Learning, Prognosis and Diagnosis

Discrete Optimization Lear ning Syst ems Vir_tua l D es ign

Research and Innovation

The Mindset

Mathematics evolves its impact

most effectively if it appears as

a PARTNER together with other

Giants …

• GUI

… and Dragons

• Commissioning • Data base • Software Engineering • Incorrect inputs • Bug Fixing • Interfaces • 100k LOC • Operating system • Middleware • External systems

Research and Innovation

The Mindset

Dwarfs and elves

• Modeling

• Theorems and proofs • Algorithms

Research and Innovation

From Modeling to Application

Modeling

Realization

Distribute components to all

stations in order to achieve a

well-balanced line

Assembly of Printed Circuit Boards

Optimizing the automaton

Construct short paths on

the board for each head

for fast placement

Arrange component

feeders for fast picking

sequences

Select and configure

nozzles for each head

such that the number

of placement cycles

is minimized

Assembly of Printed Circuit Boards

Coherence in Systems Hierarchy

Factory

ƒ

Layout

ƒ

Dispatching and scheduling

ƒ

Staff assignment

ƒ

Material supply

ƒ

Maintenance planning

Production Lines

ƒ

Matched line configuration of machines

ƒ

Optimum component feed along the line

ƒ

Trade-off between set-up times and processing

times

Machine Level

ƒ

Timing and spatial constraints of single

machines

ƒ

Necessary resources behavior

ƒ

Availability

Coherence

o

f Models

ÍÎ

Semantic

Cou

p

lin

g

Assembly of Printed Circuit Boards

Nozzle Selection

Given:

ƒ

Bipartite Graph such that

Component type u may be

placed through nozzle type v

ƒ

For every node u

∈ U a component

number

ƒ

For every edge ( u,v )

∈ E an integer

variable

ƒ

For every node v

∈ V an integer

variable

ƒ k = Number of nozzle positions at the

placement head

ƒ

Variable z = Number of placement cycles

)

,

(

U

V

E

G

=

∪

⇔

∈

)

,

(

u

v

E

u

b

uv

y

v

x

Nonlinear model:

integers

nonegative

variables

All

:

:

such that

min

) , ( : ) , ( :

k

x

zx

y

V

v

b

y

U

u

z

V v v v E v u u uv u E v u v uv

≤

≤

∈

∀

=

∈

∀

∑

∑

∑

∈ ∈ ∈ Minimize no. of placement cycles All components have to be placed Set up a sufficient number of nozzles at placement head

Upper limit for nozzle segments

Water Supply Network Planning

Required: Schedule of pump

switches for the planning horizon (24h) Required: Schedule for valves

Objectives:

1. Safe operation

2. Full supply of consumers

Required: Fill levels for the reservoirs

Input: Contract with other water suppliers

Water Supply Network Planning

Inputs and Goals

Required: Schedule of pump

switches for the planning horizon (24h) Required: Schedule for valves

Objectives:

1. Safe operation

2. Full supply of consumers

3. Minimal costs for water and energy 4. As few as possible pump switches

Required: Fill levels for the reservoirs

Input: Contract with other water suppliers

Water Supply Network Planning

Inputs and Goals

Input: Demand forecast for consumers (districts)

Water Supply Network Planning

General Setting for Optimization

• Demand forecast on a hourly basis;

Planning period: 24 h

Water Supply Network Planning

Subnets

Subnet 1

Subnet 2

Water Supply Network Planning

Graph Model

Subnet 1

Subnet 2

Subnet 3

Feeder 1

Supplier

Consumer 1

Consumer 2

Spring

Well

Min cost flow solutions

v

_B

f

_P

t

t

Schedules / fill levels

v

_B

f

_P

t

t

Water Supply Network Planning

Creating pump switches

Solutions of the model have to be

transformed into switching points of

time for the pumps and fill level curves

for the reservoirs

Water Supply Network Planning

The Real Planning Cycle

Compute schedule:

Pump switches, fill level curves

Evaluate schedule:

Pressure progression

Modify specifications

Activate schedule

Initialize planning:

Set current constraints

Optimization

Water Supply Network Planning

The Toolset

ƒ

Siwa-Plan is a toolset for the

management of water supply

networks, including planning and

control functions.

ƒ

Using Siwa-Plan, the first step is the

engineering of the water net under

consideration.

ƒ

In addition to the implementation of

optimization and simulation routines,

the challenge is to generate an

appropriate optimizer and simulator.

OPTIM Schedule Administration, Prognosis SEWER Sewer Control LEAK Leak Monito-ring SIM TRAIN Simulation BEP Pump Optimization VIM Engineering Tools

Water Supply Network Planning

Integration Into Control Equipment

Bürowelt / Office

@aGlance / OPC-Server Internet/Intranet

O&M

Terminal Bus Ethernet

OS Clients / Multi-Clients

OS-Server Service

Engineering Station ES

Industrial Ethernet / System Bus

OS OP ET 200M PROFIBUS-DP PROFIBUS-PA PROFIBUS-DP ET PROFIBUS-PA ET 200M Ex-I/O

The Internet of Things

Routing Goods Like Data

Baggage handling at

Beijing airport

Mail distribution centers

The Internet of Things –

A public funded project *)

*) German Federal Ministry of Education and Research

The Internet of Things

Hierarchical Structure of Commissioning Systems

Hardware

The Internet of Things

Basic Concepts

New controls architectures

ƒ

Migration of “Intelligence" to field level (e.g.,

"intelligent drives")

ƒ

Distributed controlling functions

ƒ

Vernetzung of devices at field level ("industrial

ethernet")

ƒ

Web based services for the level of controls

("one homepage for every motor")

New systems architectures

ƒ

Distributed software systems

ƒ

Decentralized controls (e.g., agent technology)

ƒ

"Aware objects" (RFID, RF-based systems)

ƒ

Pervasive computing

New material flow strategies

ƒ

"Routing goods like data" (e.g., like e-mail)

ƒ

Methods of network management (e.g., IP

The Internet of Things

Negotiations of Local Agents

…

OK, I have to be

X-rayed next …

Ouuh, I am skeptic.

I have to work off the

main baggage stream

for Flight No. XYZ.

I decline.

Well, I can do the job.

I expect you in five

minutes.

The Internet of Things

Localization of Agents

Where to localize the agents?

ƒ

At the field modules

¾

Module agents have to manage their own

workload in order to avoid congestion

ƒ

At the material to be conveyed

¾

Baggage agents are responsible for their route

through the net

The Internet of Things

State Space of Agent Systems

ƒ

Available information

ƒ

Much: global,

up-to-date

ƒ

Little: local,

out-of-date

ƒ

Algorithmic complexity

ƒ

High: Complex

computations

ƒ

Low:

Simple conditional rules

ƒ

Scenarios

ƒ

Topology, dispatching, error

handling, etc.

Algorithmic

complexity

Available

information

Scenarios

Much

Little

High

Low

Own space

→ difficult to formalize

E.g., density of topology network

?

The Internet of Things

A Simple Scenario

Sorter

Sorter

Transfer

Check in

The Internet of Things

Three Scenarios

B: What is your length? C: x meters

B: What is your expected workload at time t₁? C: y parcels

B: Expect me at time t₂! C: Well, I will update my Knowledge about itself:

ƒ Length

ƒ Expected work load

progression Algorithm: Dijkstra

Required edge information:

ƒ Lengths of edges

ƒ Expected workload at time t

(-> Dynamic penality cost) Anticipatory

B: What is your length? C: x meters

B: What is your current workload?

C: y parcels Knowledge about itself:

ƒ Length

ƒ Current workload

Algorithm: Dijkstra

Required edge information:

ƒ Length of edges

ƒ Current workload

(-> Penality cost) Up-to-date

B: What is your length? C: x meters

Knowledge about itself:

ƒ Length

Algorithm: Dijkstra

Required edge information:

ƒ Lengths of edges Stupid Communication Conveyor agent Baggage agent Scenario name

For all scenarios:

Baggage agents plan their route exactly once, at Check In.

Congested edges will be ignored.

The Internet of Things

Stupid Routing – Situation Short After Dispatching

check in

transfer

_sorter

The Internet of Things

Anticipatory Routing – Situation Short After Dispatching

check in

transfer

_sorter

Conclusion

ƒ

The rapid increasing complexity of industrial challenges

requires usage of mathematical methods of modeling,

simulation and optimization to a great extend.

ƒ

Mathematicians and computer scientists are invited,

¾

To improve available tools and methods continuously, and

¾

To assist usage of such methods within projects along the

complete life cycle of products, plants and systems.

ƒ

The tight, project related collaboration with engineers and users

is essential for the successful application of such methods.

Thank you for your

attention!

Contact:

Michael Hofmeister

Siemens AG, CT PP 7

Otto-Hahn-Ring 6

D-81730 Munich

[email protected]