optimization of gas transport - zib · project b20 optimization of gas transport martin grötschel...
TRANSCRIPT
DFG Research CenterMATHEON
mathematics forkey technologieswww.matheon.de
Project B20
Optimization of gas transport
Martin Grötschel René Henrion Thorsten Koch Werner RömischTimo Berthold Stefan Heinz Stefan Vigerske
W e ie rstra ß -In stitu t fü r A n g e w a n d te A n a ly s is u n d S to ch a stik
Domain of Expertise: Energy and utilities
Background
⊲ political regulations (e.g., Gasnetzzugangs-verordnung) led to a strict separation of gastrading and gas transport in Germany
⊲ these newly imposed political requirements in-fluence the technical processes of gas transport
⊲ as a result, the already complex task of plan-ning and operating gas networks becomes evenmore challenging
⊲ however, suitable algorithms or software arecurrently not available to solve today’s gastransport optimization problems
Project Goal
Integration of Aspects from Mixed IntegerProgramming, Nonlinear Programming,Constraint Programming, and StochasticProgramming into a general purpose solver.
SCIPHeuristic
actcons
divingcoef
diving
cross
over
dins
feaspump
fixand
infer
fracdiving
guided
diving
intdiving
int
shifting
linesearch
diving
local
branching
mutation
objpscost
diving
octane oneopt
pscost
diving
rens
rins
rootsol
diving
rounding
shifting simple
rounding
veclen
diving
Variable
· · ·
Branch
allfull
strong
full
strong
in
ference
leastinf
mostinf
pscostrandom
relps
cost
Conflict
Constraint
Handler
and
bound
disjunc.
count
sols
indi
cator
integral
knap
sack
linear logicor
or
setppc
sos1
sos2
var
bound
xor
Cutpool
LP
clp
cpx msk
none
qso
spx
xprs
Dialog
default
Display
default
Node
selector
bfs
dfs
estimate
hybrid
estim
restart
dfs
Event
default
Presolver
bound
shift
dualfix
implics
intto
binaryprobing
trivial
Impli
cations
Tree
Reader
ccg
cip
cnf
fix
lp
mpsopb
ppm
rlp
sol
sos
zpl
Pricer
Separator
clique
cmir
flow
cover
gomoryimplied
bounds
intobj
mcf
redcost
strong
cg
zero
half
Relaxer
Propa
gator
pseudo
obj
root
redcost
Mathematical Aspects of Gas Transport
Mixed Integer Programming
Network Configuration and Design
qu,v = 0 ∨qmin
u,v≤ qu,v ≤ qmax
u,v
pu = pv
⇒ Combinatorial decisions
Nonlinear Programming
Fuel Consumption of a Compressor
c ·
(
(
pv
pu
)
κ−1
κ
− 1
)
|qu,v| ≤ fmax
u,v
⇒ Nonlinear nonconvex constraints
Constraint Programming
Complicated legal concepts thatare difficult to model algebraically,e.g., pipelines shared betweencompanies⇒ Global constraints
Stochastic Programming
Demand of gas underliesuncertainties, e.g., weather⇒ Chance constraints
Gasflow on Exitvs. Date
June February July
Currently implemented
⊲ support for quadratic constraints (released with SCIP 1.2)⊲ support for second-order cone constraints⊲ support for nonlinear pressure loss constraints f |f | = c(p − q)
⊲ Nonlinear Relaxation-Enforced Neighbourhood Search heuristic⊲ interfaces to GAMS and ZIMPL
Performance on 80 MIQQP benchmark instances
instances taken fromMINLPLib and testsets ofJ.N. Hooker, H. Mittelmann,J.P. Vielma, and an IBM/CMUproject⋆LP solver: CPLEX 11.2,
NLP solver: IPOPT 3.8
Future plans
Further transfer of MIP/CP technology to MINLP:
⊲ primal heuristics⊲ branching rules⊲ domain store relaxation and disconnected domains⊲ conflict analysis⊲ lift and project for MIQQPs
Detecting and exploiting problem structure:
⊲ preprocessing by symbolic algebra using REDUCE⊲ upgrading of constraints⊲ detection of convexity and symmetry
Evaluation, derivation, relaxation of chance constraints