SCIP at Work
Examples and Case Studies
Ambros M. Gleixner
Zuse Institute Berlin·MATHEON·Berlin Mathematical School
5th Porto Meeting on Mathematics for Industry, April 1011, 2014, Porto
Outline
SCIP at Work
Industry Projects
Application-driven Research Cycle
Hands on: cutting circles from area-minimizing rectangles
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Outline
SCIP at Work
Industry Projects
Application-driven Research Cycle
Hands on: cutting circles from area-minimizing rectangles
Chip Design Verication
Goal: (computer-)proof, that a design is free of errors Method: property checking using CIPs
Result:
5 10 15 20 25 30 35 40
12 h 1 h 32 h 2 h
register width
time
Boolean satisability
Constraint Integer Programming
constraints 422 152026
variables 3714 50756 Duration: 2003-2008
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Siemens Cooperation
Longstanding cooperation with Department Modeling, Simulation, Optimization . rst licensee (1996) of SoPlex
. steady use of SCIP/SoPlex in various optimization modules
placement robots in circuit board production
optimal operation of water networks
Supply Chain Management
Huge, numerically challenging problems
-50 0 50 100
SNP Opt. 7.0
SCIP
VersionSCIP 1.2 2.0.1 2.0.1
tuned 2.1.0 2.1.1 3.0.0
∅Score
Topics:
I LP solver
I presolving
I numerical stability
I multi-level objective Industry partner:
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Optimization of Gas Transport
Stochastic Mixed-IntegerNonlinearConstraint Program
Gasflow on Entry vs. Temperature
-5 0 5 10 15 20 25
over alarge network.
Goal:
. develop algorithms to solve such problems to global optimality!
. rather: attempt to integrate as many aspects as possible
Industry partner:
Optimization of Gas Transport
Stochastic Mixed-IntegerNonlinearConstraint Program
Gasflow on Entry vs. Temperature
-5 0 5 10 15 20 25
over alarge network.
Goal:
. develop algorithms to solve such problems to global optimality!
. rather: attempt to integrate as many aspects as possible
Industry partner:
7
Outline
SCIP at Work
Industry Projects
Application-driven Research Cycle
Hands on: cutting circles from area-minimizing rectangles
Application-driven Research at ZIB
Problem specific approaches
Telecom Traffic
Gas • separa.on
• column genera.on
• nonlineari.es
• …
General purpose solver SCIP Op.miza.on Suite (SCIP, SoPlex, ZIMPL, GCG, UG)
Generaliza5on
Our Group
• mul. commodity flow network cuts
• quadra.c constraints
• abs-‐power
• …
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Outline
SCIP at Work
Industry Projects
Application-driven Research Cycle
Hands on: cutting circles from area-minimizing rectangles
Cutting circles from area-minimizing rectangles
TaskGiven n circles of radii r1, . . . ,rn>0, nd a rectangle of width w and height h such that all circles t into the rectangle without overlap and the area hw is minimized.
area = 12.66
Download
. http://www.zib.de/gleixner/download/exercise-circlecut.pdf . SCIP binary from http://scip.zib.de
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An NLP Model
min h·w
s.t. q
(xi−xj)2+ (yi−yj)2 ≥ ri+rj for all i,j:i<j ri ≤ xi ≤ w−ri for all i
ri ≤ yi ≤ h−ri for all i x,y ∈Rn≥0
h,w ∈R≥0
An NLP Model
min h·w
s.t. q
(xi−xj)2+ (yi−yj)2 ≥ ri+rj for all i,j:i<j
ri ≤ xi ≤ w−ri for all i ri ≤ yi ≤ h−ri for all i
x,y ∈Rn≥0
h,w ∈R≥0
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An NLP Model
min h·w s.t.
q
(xi−xj)2+ (yi−yj)2 ≥ ri+rj for all i,j:i<j ri ≤ xi ≤ w−ri for all i
ri ≤ yi ≤ h−ri for all i x,y ∈Rn≥0
h,w ∈R≥0
An NLP Model
min h·w
s.t. q
(xi−xj)2+ (yi−yj)2 ≥ ri+rj for all i,j:i<j ri ≤ xi ≤ w−ri for all i
ri ≤ yi ≤ h−ri for all i h≤w
x,y ∈Rn≥0
h,w ∈R≥0
12
An NLP Model
min h·w
s.t. q
(xi−xj)2+ (yi−yj)2 ≥ ri+rj for all i,j:i<j ri ≤ xi ≤ w−ri for all i
ri ≤ yi ≤ h−ri for all i h≤w
x1≤w/2 x,y ∈Rn≥0
h,w ∈R≥0
An NLP Model
min h·w
s.t. q
(xi−xj)2+ (yi−yj)2 ≥ ri+rj for all i,j:i<j ri ≤ xi ≤ w−ri for all i
ri ≤ yi ≤ h−ri for all i h≤w
x1≤w/2 y1≤h/2 x,y ∈Rn≥0
h,w ∈R≥0
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To be continued?
Thank you very much for your attention!
Muito obrigado!
More slides and exercisesat http://scip.zib.de/ and http://co-at-work.zib.de/.
SCIP at Work
Examples and Case Studies
Ambros M. Gleixner
Zuse Institute Berlin·MATHEON·Berlin Mathematical School
5th Porto Meeting on Mathematics for Industry, April 1011, 2014, Porto
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