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November
• 2014
orbit
# 23
EURO-2015 • Debat om OR artikler • Optimering af lastbildæk • Kabellayout i havvindmølleparker
leder
ORbit
medlemsblad for
Dansk Selskab
for Operationsanalyse
og
Svenska Operationsanalysföreningen
Leder
I går deltog jeg i universitetets konference på tværs af fakulteterne: BIG Data – BIG Impact. Big data er et af de Buzz words,
der for tiden giver genlyd over hele forskningsverdenen. Selv
vores eget Informs har det på agendaen. Men hvad er Big
data? Og er det en bølge vi skal med på? Som operationsanalytiker stiller jeg mig skeptisk overfor det store fokus på data,
fordi det uværdigt mindsker fokus på problemstillingerne. Vi
har en lang tradition for at koncentrere os om at løse problemer og lade data komme mere eller mindre automatisk.
Redaktion:
Ansv. Sanne Wøhlk (sw)
Tor Fog Justesen (tfj)
Tomas Gustafsson, SOAF (tg)
DORS
DTU Management, bygn. 424
Danmarkt Tekniske Universitet
DK-2800 Kgs. Lyngby
Telefon: +45 4525 3385
Fax:
+45 4588 2673
E-mail: [email protected]
Næste deadline:
1. Marts 2015
Tryk:
Print Provider Aps
Oplag: 360
ISSN 1601-8893
Forside: Colourbox
Billeder på side 4, 5, 11, 17 og 18:
Colourbox.
Gennem mit samarbejde med erhvervslivet har jeg dog erfaret, at selvom der er
rigelige mængder data tilgængeligt derude, så står brugbarheden desværre ofte
noget tilbage at ønske. Jeg oplever bl.a. mangler i data, uoverensstemmelser og
ofte så ringe datakvalitet, at der må laves et utal af antagelser. Så i min optik burde
datafokus først og fremmest handle om datakvalitet og sekundært om big.
Big data er bare en af de ting, der i øjeblikket debatteres i operationsanalysemiljøerne. En anden er den gode OR artikel. Det er et stadig større pres på akademikere for at øge forskningsoutput. I sidste ende handler det om universiteternes
økonomi. Men hvad betyder det for forskningen? I denne udgave af ORbit bringer vi
to indlæg, hvor forskere deler deres syn på den gode OR artikel.
ORbit 23 byder naturligvis også på artikler af mere traditionel karakter. Vi ser nogle
of operationsanalysens mangfoldige anvendelser i artikler om optimering af lastbildæk og af kabellayout for havvindmøller. Vi får et indblik i planerne for EURO 2015
og Trapeze Group giver os et indblik i deres arbejde.
God læselyst,
Sanne Wøhlk
Aktuelt om DORS
Medlemsskab
Kontingentsatser
Personlige medlemmer
(incl. ph.d.-studerende): 270 kr./år
Studerende: 60 kr./år
Firmamedlemmer:
3200 kr./år
Institutmedlemmer:
1800 kr./år
2
ORbit 23
Sekretariat
DORS
DTU Management
Bygning 424
Danmarks Tekniske Universitet,
2800 Kgs. Lyngby
e-mail: [email protected]
Internet: www.dorsnet.dk
indhold
Kära operationsanalysvänner
Hösten är kommen och med den börjar en aktivare period för
de flesta, även oss operationsanalytiker. Till exempel pågår ett
flertal konferenser under hösten och vintern inom operationsanalys och närliggande områden: INFORMS i San Fransisco
den 9-12 november, ICORES den 10-12 januari i Lissabon,
AAAI-15 den 25-29 januari i Austin, Texas och MathMod den
18-20 februari i Wien. Under sommaren besökte jag själv
OR2014 i Aachen med temat ”Business analytics and optimization”, vilket är passande med tanke hur mycket det pratas
om analytics och specifikt hur detta passar med operationsanalysen. För egen
del anser jag att analytics som företeelse är positiv för operationsanalysen som
område, då den senare för länge sedan har slutat vara trendig. Om du är intresserad av vad analytics är så föreslår jag att du söker på ”informs analytics”. I övrigt
önskar jag dig en härlig höst och vinter full av spännande OA-tillämpningar!
Indhold
Redaktøren har ordet
2
SOAF har ordet
3
Too much horse, too little jockey?
Subben’s checklist and the quality
of articles in OR
6
An introduction to Trapeze Group
Europe: Operational research
aspects of the people travel indu-
8
stry
Euro-2015 - i anvendelsernes
tegn
10
Optimizing truck tyres
12
Optimering af kabellayout i havvindmølleparker
Markus Bohlin,
4
16
Ordförande SOAF
Aktuellt om SOAF
Medlemsavgifter:
• Individuell medlemmar (inkl. ORbit):
160 kr
• Juniormedlem (exkl. ORbit): 80 kr
• Akademiska institutioner: 1600 kr
• Företag med 1-5 intressenter: 1600 kr
• Företag med 6-10 intressenter: 3200 kr
• Företag med fler än 10 intressenter: 4800 kr
Svenska Operationsanalysföreningen
Betala in på postgiro: 19 94 48-2
e-mail: [email protected]
Internet: www.soaf.se
ORbit 23
3
debat
By Marcel Turkensteen
Too much horse, too little jockey?
Many of the readers of this magazine
are Operations Researchers. And Operations Researchers like to have a clear
objective and minimize or maximize
something. Maybe this reflects itself in
our research. We mainly judge work by
clear objectives, such as the computation or solution quality reported. So less
computation time or less deviation from
the optimal solution (or both) equals
better. But are we going too far with
that? I think so. This issue isn’t really
new. Ackoff and his followers have pronounced the scientific discipline dead for
the same reason since the ‘80s, precisely due to its lack of consideration for
management issues.
4
ORbit 23
Before continuing, I would like to place
the warning that this article is the results
of crude generalizations based on
anecdotes, which is not the textbook
way of conducting research. It is also
based on my personal aversion against
‘horse-racing’ papers.
My motivating case is the supervision of
a student’s master thesis. He was doing
an internship at a transporter, where
demand occurs at about 40 different
locations every day. The solution for this
problem seems to be an open-and-shut
case: implement an advanced vehicle
routing problem (VRP) method and
We construct ever more advanced met- presto: you have your solution within a
hods for computational problems. Using few seconds.
ant colonies and decompositions, we
can solve large routing problems. Using The problem is that, even if the VRP
advanced analytical and stochastic itself is solved in a few seconds, the
tools, we can find cost-optimal invento- whole process takes much longer. The
ries. Why then, do practitioners fail to company doesn’t solve benchmark
use them?
instances, as we do, but real instances.
The customer data comes in manually
debat
and contains errors. It requires cleaning
up and several other operations, such
as the computation of road distances,
before it could be used. The company
should purchase software and invest
man-hours to do this. It is not clear who
should perform the computations when
the student finishes his internship: can
the planners be convinced to perform
the computations on a daily basis and
can the truck drivers be convinced to
use the schedules presented to them?
So this becomes a challenging process
that requires much more than a fast VRP
solver.
So, the student thought, maybe the literature tells me how to deal with such
implementation issues? I thought that a
journal such as Interfaces would have
ample articles on this issue. However,
when I followed the same approach
and typed ‘VRP’ in Google Scholar. This
gives me about 43900 hits; ‘Vehicle
Routing Problem’ gave me about 32700.
Now try the keywords ‘VRP “practical
implementation”’ in Google Scholar:
there are about 232 hits (some of which
refer to the ‘view reference point’). Even
then, few of those told the student how
to proceed. Does this imply that much
of the VRP literature is focusing on the online, and why don’t we focus more
wrong topic?
on how these solutions would improve
operations compared to the way things
“Hey”, will some OR scientists say, “we are currently done? Instead of showing
do solve practical problems. Your cri- that we can be better or faster for some
tique, if valid at all, does not relate to our benchmark instances, we could actually
work.” And admittedly, these scientists show that we make a difference.
are able to achieve impressive cost
savings for companies and to society. So are newly developed OR methods
However, even in this case, our focus and models getting better and more
tends to be on the ingenuity and com- advanced? Definitely. Are they pracplexity of the modeling. If you find that a tically relevant? I doubt it. Should they
simple heuristic can do the job that your be? You decide.
employer asked for, it’s simply not interesting. Bring in a few decompositions
Marcel Turkensteen works at the
and then we are in business.
Cluster for Operations Research
The pattern that I observe is that our
models and methods tend to be applicable in very specific situations, as a
consequence of their advanced nature.
They are very good, but they are not
very general. That may be the reason
that practitioners stick to simple and
seemingly outdated methods.
One obstacle may be that we often only
present our solution quality (“our firefly
colony-based method is 0.15% more
accurate than…”)? Why don’t we present solutions more often, for example
And Logistics (CORAL) at the
Faculty of Business and Social
Sciences. His research interests
include the combination of environmental impact measurement and
Operations
Research
and logistics
decision modeling
on
routing and
location.
ORbit 23
5
artikel
By Torbjörn Larsson and Michael Patriksson
Subben’s checklist
and the quality of articles in OR
This short article presents two itemed lists that
may be a helping hand during the assessment
of a scientific article in the fields of mathematical
optimization and operations research, be it your
own, a Masters’ or PhD student’s, or even a
paper that you are refereeing for a journal or a
conference. The first list (“Subben’s checklist”)
describes necessary ingredients of a complete
article, while the second list provides criteria for
assessing the quality or scientific value of an
article.
1. Subben’s checklist
One day at the Department of Mathematics, Linköping University, Linköping, Sweden, during Spring 1993, while the
second author was still affiliated with the research division in
mathematical optimization, the authors had a very interesting
conversation with our then research director, Prof. Subhash
Narula, on the principles of article writing. We specifically
discussed what – in our field of study, at least – constitutes
the necessary and sufficient core content of any complete
research article in OR. We believe that the discussion emanated from all of us recently having had the unfortunate duty to
Subhash Narula (fondly nicknamed “Subben” by the mathematical optimization team) had a very clear vision of his viewpoint on the matter, and could quite quickly establish a few
necessary “items” that must be in place in any article in our
field, in order for it to possibly be complete. The authors also
contributed, and notes were taken on the occasion. These
notes have since then been slightly updated and stored at a
place ready at hand – you never know when the list may come
in handy!
1. Relevance
motivation, need, benefit; why interesting?
2. Background
history, state of the art; framework, delimitations
3. Motivation
lack in existing knowledge or methodology
4. Remedy
proposal of actions in order to remove the lack of existing knowledge or methodology
5. Method(ology)
choice of research methodology
6. Hypothesis
description of the research question(s) considered
7. Realization
presentation of the new contributions to science
8. Analysis
validation of results, conclusions, consequences; future research opportunities
Table 1. Subben’s checklist.
6
be referees on rather poorly written papers – even incomplete
ones – and hence discussed not only the quality of papers in
general, but in particular if there were simple ways to assess
an article’s “completeness”.
ORbit 23
artikel
During the years the list and the corresponding phrases have
expanded slightly. Some 20 years after the above-mentioned
conversation the second author was enrolled in a PhD course
2. Criteria for evaluating the scientific
value of an article
on scientific methodology at Chalmers University of Technology called “Theory and Methodology of Science”, and whose Table 2 provides a (probably still incomplete) list of criteria
students (masters students as well as PhD students) typically for evaluating scientific questions, research, and results has
had research topics within finance and logistics. During a few been assembled by the authors during a period of some 10
years of enrollment in this course he gave assignments to years.
these students, in which they were supposed to read articles
in an unfamiliar territory (such as papers of the authors of
this article), to try to pinpoint whether all the items in Subben’s checklist were in fact covered. They did a very good job, As a final note, we have two suggestions to the reader:
despite the fact the most of them were not PhD students in a
quantitative field of study. In fact, the second author was sub- (a) Next time you prepare an application to a research foujected to a proposal to add to the list the now fifth item, moti- ndation, write a manuscript, or read someone else’s work as a
vated by the fact that in some fields of study represented by reviewer, examiner or supervisor, try to utilize the two lists provided in this article to assess what you are writing or reading.
the students, there were several possible “angles of attack”.
Table 1 shows the current version of “Subben’s checklist” of (b) If you have any comments on the lists, please contact the
authors, who would be very happy to receive comments.
necessary items in a complete OR paper.
Torbjörn Larsson
Michael Patriksson
Department of mathematics, Linköping University,
Linköping, Sweden, [email protected]
Department of mathematical sciences, Chalmers University of Technology, Gothenburg, Sweden, [email protected]
Relevance
Is the research question (RQ) motivated by any needs or potential benefits of results obtained?
(Relevance can be internal, for the scientific subject itself, or external, for practice.)
Generality
How comprehensive is the RQ and how universally applicable are the results?
Durability
Have the RQ and results a short or a long life? (Are they, for example, technology dependent?)
Scientific foundation
Are the RQ and research work based on a solid foundation in theory or methodology?
Scientific height
How big is the progress and the difficulty of reaching it?
Originality
Are the RQ or methodology unique, creative or innovative, or of the established kind?
News value
Is there an interest in the RQ and results (within, or outside of, the scientific world)?
Integration
How much previous knowledge is improved or summarized? Does the work connect several
scientific fields, in the paper or in possible future research?
Consequences
How big is the influence and usefulness of the work (within or outside of the scientific field)?
(Both can be about practical applicability and knowledge advancement in a field.)
Realization
Is the research methodology and approach appropriate? Have they been used correctly? Is the
work technically correct? Are any experiments (if any) possible to reproduce?
Consistency
Is the level of ambition stated in the motivation consistent with the results and conclusions?
Availability
Is the work presented such that it can be critically scrutinized? Has it been appropriately described and disseminated?
Table 2. Criteria for evaluating the scientific value of an article.
ORbit 23
7
artikel
By Tue Rauff Lind Christensen
An introduction to Trapeze Group Europe:
Operational research aspects of the
people travel industry
Trapeze Group Europe has joined DORS as an industry
member as part of a wider initiative to forge closer relations
with academia and other industry members. This paper
provides an introduction to Trapeze and some of the
operational research elements we encounter within our core
business.
Trapeze Group Europe
Trapeze Group Europe is a highly autonomous subsidiary of Trapeze Group.
Our headquarters are located in Aarhus,
Denmark and we have major branches
in numerous other countries, including
Germany, Sweden and the United Kingdom.
table (e.g. most bus and train companies), while the demand-response
business area relates to services such
as elder- and special-needs transportation, or traditional taxi services. However, the line between these two areas
is becoming increasingly obscured, with
elements such as school driving residing
in both areas depending on the local tradition, geography and business model.
Trapeze Group is a supplier of software
to the people transport industry which Our products
consists of two major areas; Demandresponse and Fixed-route. The fixed- At Trapeze we strive to offer software to
route area of the business caters to all aspects of the people transport indutransport providers that use a fixed time- stry, including planning processes, daily
management, real-time information,
Figure 2. An example of a block.
8
ORbit 23
mobile ticketing, and many other elements. Therefore our optimisation solutions cover a broad spectrum of applications and needs.
Commercial aspects of
optimisation
A major challenge in developing optimisation methods in this industry – and
one that is rarely studied in university
courses – is an algorithm’s applicability
to many clients at the same time. The
needs of clients vary greatly as they
often have different views of what is
important in a plan, or which rules apply.
Hence, what could seem like a standard
problem of creating bus driver shifts
may vary considerably, depending on:
• Regional and national labour rules
• The planner’s preferences, e.g.
number of minutes worked, number of
different kinds of shifts, total number of
shifts, etc.
• Drivers’ personal preferences
• Crew roster interaction (because an
efficient driver plan may be very hard to
place efficiently in a roster)
• Many, many other issues.
artikel
Figure 1. Two busses from the Swedish Trapeze customer Gamla Uppsala Buss AB.
Since, it is extremely time consuming
to create specific tailored algorithms
for each customer, a more effective
approach is to find a modelling and solution approach which is both flexible and
efficient. This has the advantage that the
algorithms evolve over time to accommodate new client demands. Our current algorithm for the driver shift creation
has over 50 different objectives!
such instances the dispatcher needs to Moving forward
quickly find a new solution so that the
customer on the phone can be told when Our strategy at Trapeze is to contihe or she will be collected.
nuously expand, grow, and enter new
partnerships. In the area of optimisation
Optimising Fixed-route
we are hoping this will result in:
On the fixed-route side the traditional • Domain knowledge sharing: What is
optimisation problems are more focused the relevant model for ‘the real world’
on the planning phase.
problem
This process starts with the timetable
creation, since the timetable and geography implicitly gives a lower bound
on the number of buses needed on the
road at any given time. Therefore, analysing the timetable can produce a signiOptimising Demandficant reduction in the number of buses
response
required simply by shifting the departure
Given the title, it may be expected that time of a line by only a few minutes.
no trips can be planned in advance, but
this is not always true. In fact, trips may Once the timetable is created the next
be booked some months in advance. step is to arrange these trips into an
Such a booking may be the transpor- order which forms a work schedule for a
ting of an elderly person to hospital for a bus. This is often known as blocking or
regular check-up, or transporting a pupil vehicle scheduling.
In the next two sections we will describe
in broad terms some of the most basic
problems we encounter in demandresponse and fixed-route transport.
who lives in an area with no public transportation to school. In these instances it
may be sensible to optimise such pickups and deliveries by, where possible,
putting more people in the same cab/
minibus/van.
The next phase is to create driver shifts.
It is often beneficial to consider optimising the vehicle schedules and driver
shifts simultaneously, because of the
coordination between the two.
Even the best planned solution may The final phase prior to day-to-day
change on the day of operations when operations is to create a driver roster;
people are calling in to cancel trips (e.g. another traditional optimisation problem.
due to illness), or to order new ones. In
• Data sharing: Subject to confidentiality
we can – with agreement of our client –
share their data
• Partnership for relevant funding applications (in conjunction with domain
knowledge)
Should any of this have sparked an interest we urge you to contact us.
We are happy to be a DORS member!
Tue Rauff Lind Christensen,
Consultant
& Team
Leader
PhD in
Operational
Research
ORbit 23
9
kommentar
Af David Pisinger
Euro-2015 - i anvendelsernes tegn
Næste års EURO konference afholdes
i England, nærmere bestemt i Glasgow, Skotland den 12-15 juli 2015, og
undertegnede har fornøjelsen af være
formand for programkomiteen. At have
en dansk formand for programkomiteen
til den største konference indenfor operationsanalyse er en vigtig anerkendels
af OR-miljøet i Danmark. Her skal man
tage med i betragtning at Danmark er et
af de mindre lande i EURO, og at der er
30 medlemmer af organisationen. Alligevel har Danmark haft formandsposten
3-4 gange, hvilket er væsentligt mere
end vi ellers skulle være berettiget til.
Faktisk var det tæt på at konferencen
ikke skulle holdes i England men derimod Skotland, såfremt folkeafstemningen den 18 september havde peget på
10
ORbit 23
en løsrivelse. Dette kunne have ført til
en del forviklinger, fordi Skotland ikke er
medlem af EURO, og heller ikke af EU
og Schengen. I princippet kunne man
have risikeret at have en EURO konference i et land som ikke var medlem af
EURO, hvilket sikkert havde medført en
del løftede øjnbryn. Men sådan gik det
ikke, idet 55% af befolkningen stemte
imod løsrivelsen, så værtsnationen
hedder stadig England.
England har en lang tradition for anvendelser af OR, så konferencens tema
bliver da også "OR in practice". Det
engelske OR-selskab vil udvælge en
eller flere keynote speakers som vil
præsentere spændende anvendelser
af OR. Endvidere vil der, konferencens
lokalitet taget i betragtning, naturligvis
være et bidrag om "OR i whisky produktion". Hvis muligt vil der blive arrangeret
ekskursioner til en eller flere whisky producenter. Og man skal huske at skrive
whisky" og ikke "whiskey". Jeg er flere
gange blevet irettesat af værterne hvis
jeg har brugt den forkerte stavemåde.
"Whiskey" er stavemåden i Amerika og
Irland, hvilket endelig ikke må forveksles
med en skotsk "whisky".
Ved sammensætning af programkomiteen for konferencen har jeg lagt vægt
på at få nogle yngre, lovende navne på
banen, sammen med mere erfarne folk.
På den måde får vi en vis fornyelse af
EURO konferencerne, samtidig med
at erfaringer fra tidligere konferencer
udnyttes.
Kilde:http://www.luxelistmag.com/2014/03/11/luxe-top-10-scotch-2/
kommentar
Selv om EURO konferencerne følger en bidrag indenfor anvendelser af stokafast skabelon, har vi i programkomiteen stisk programmering, optimalitets konforsøgt at skabe en række nye initiativer trol, økonomi og finans, så det bliver
således at det faglige niveau højnes. spændende at høre hans foredrag.
Først og fremmest bliver det muligt at
indsende længere abstracts end tid- De 12 keynote/tutorial foredrag vil blive
ligere. EURO har haft en tradition for holdt parallelt med de øvrige sessioner,
at et abstract højst måtte være på 600 så man kan altid gå til et keynote/tutorial
tegn fordi alle abstracts skulle printes i foredrag hvis der ikke lige er nogen af de
konferenceberetningerne. De 600 tegn andre foredrag som fænger.
levnede dog kun plads
Desværre ligger EURO
til at beskrive problemSe mere om EUROkonferencen samtidig
stillingen og derfor var
2015
på
bagsiden
med ISMP i 2015. Der
det ofte svært at vælge
af
bladet!
har været tradition for
de rigtige foredrag. Da
at EURO konferenalle abstracts nu kun
cerne lå tidligt på somfindes i elektronisk
meren,
mens
ISMP
lå sidst på sommeform er der ingen grund til at opretholde
ren.
Af
uvisse
grunde
har ISMP valgt at
pladsbegrænsningen og der bliver
ændre
denne
praksis,
uden at få koordimulighed for mere udførlige abstracts.
Dette vil forhåbentlig både højne det neret med EURO, så de to konferencer
akademiske niveau og gøre det nem- kommer til at ligge oveni hinanden.
mere at finde relevante foredrag.
EURO-2015 vil dog have et rigtig spænProgramkomiteen har også indført dende videnskabeligt program, og hvis
bedre keywords, således at man får dette ikke er nok til at tiltrække mange
nogle bedre søgefunktioner, ligesom deltagere har jeg lovet at optræde i kilt
de overordnede forskningsområder, ved åbningsceremonien. Sidstnævnte
som bruges til at inddele foredragene, må gøre udslaget for hvilken konference
er blevet opdateret. Værterne for kon- man vælger.
ferencen er ved at undersøge forskellige app's til mobiltelefoner, som skal
gøre det nemt at søge på foredrag og
finde rundt på konferencen. Endelig vil
konferencen byde på en nyskabelse i
form af debat møder. Her er tanken at
nogle markante forskere debatterer
aktuelle emner som f.eks. "hvordan kan
OR hjælpe i den tredie verden", "Is good
enough good enough?". Lidt i stil med de
to debatindlæg i dette nummer af ORbit.
Traditionen tro kommer konferencen
til at have tre plenary speakers, og 12
keynote/tutorial speakers. Et af plenary foredragene bliver holdt af Tyrell
Rockafellar, som modtog John von Neumann prisen fra Institute for Operations
Research and Management Science.
Rockafellar har leveret en række vigtige
David Pisinger
formand for programkomiteen EURO2015
http://www.euro2015.org/
David Pisinger is Professor and
Head
of
R e s e a rc h,
DTU Management
Engineering.
ORbit 23
11
artikel
By Peter Lindroth, Michael Patriksson, Zuzana Šabartová, and Ann-Brith Strömberg
Optimizing truck tyres
How to improve the realism of simulation-based
optimization through physical constraints.
The TyreOpt project
TyreOpt – Fuel consumption reduction
by tyre drag optimization is an industrial
project financed by the Swedish Energy
Agency, performed in cooperation
among Volvo Group Trucks Technology,
Chalmers University of Technology and
University of Gothenburg. Within the project we aim to find an optimal tyre configuration for each vehicle and operating
environment combination that minimizes
fuel consumption, while balancing the
other tyre-dependent features.
Simulation-based
optimization
The optimization model in TyreOpt is
simulation-based, which means that the
objective function and the constraints
can only be estimated through computationally very expensive simulations.
Optimization problems including such
simulation-based functions are often
solved by a response surface method
(Jones, 2010), in which a surrogate
model that mimics the behavior of the
simulation-based function is iteratively
shaped and optimized.
Radial basis function
interpolation
Figure 1. The main goal of the TyreOpt project is to select tyres for each vehicle configuration and operating environment specification such that its fuel consumption is minimized.
12
ORbit 23
Multivariate functions can be effectively
modeled using radial basis function
(RBF) interpolation (Wendland, 2005),
yielding good global representations of
simulation-based functions and are therefore frequently used in algorithms for
simulation-based optimization. Despite
this, the surrogate model may contain
inaccuracies and even physically absurd
values, leading to a poor correspondence
with the experts’ expectations. The latter
phenomenon occurs in our particular
tyre optimization application, whence we
have developed an algorithm framework
for obviating this problem (Šabartová et
al., 2014). The remainder of this article
explains our approach.
artikel
Algorithm 1 General response surface method
Create an initial set of sampled points and evaluate the simulation-based function on this set.
1: Construct a surrogate model using the evaluated points.
2: Select and evaluate a new sampled point using
data from the surrogate model and balancing local and global searches to further refine the surrogate model.
3: Go to step 1, unless a stopping criterion is met.
0:
Figure 2. A general response surface method iteratively constructs
the surrogate model of the simulation-based function. The resulting
surrogate model is then optimized.
Implementation of expert knowledge into
RBF interpolation
By relaxing the interpolation requirement—that the value of
the surrogate function has to meet the simulated value at each
sample point—using a least squares approach, a flexibility is
released which can be utilized to introduce expert knowledge
in terms of physical constraints; see Figure 3.
Rolling resistance
Conclusion
Simulation-based optimization models arise from many real
optimization problems. They are often solved utilizing surrogate models. We have developed a new methodology for
utilizing many kinds of expert knowledge in the construction of
a surrogate function, which is here illustrated on a simple onedimensional problem and on the function describing the RRC
of a truck tyre. The surrogate model of the rolling resistance
function is further used in the TyreOpt project to construct an
optimization model, which needs to be solved in order to find
the optimal tyres for each customer’s specifications of the
vehicle and the operating environment.
References
• D.R. Jones, “A taxonomy of global optimization methods
based on response surfaces,” Journal of Global Optimization
4, 2010, pp. 345–383.
• Z. Šabartová, P. Lindroth, A.-B. Strömberg, and M. Patriksson, “An optimization model for truck tyres' selection,” in Proceedings of the 4th International Conference on Engineering
Optimization (EngOpt 2014), Lisbon, Portugal, 8–11 September 2014.
• H. Wendland, “Scattered Data Approximation,” Cambridge
Monographs on Applied and Computational Mathematics,
Cambridge, UK, 2005.
The rolling resistance can be described as the effort required
to keep a given tyre rolling, and is characterized through the
rolling resistance coefficient (RRC), which forms the main
ingredient of the optimization model
developed to find the optimal truck tyres.
q
A computationally heavy finite element
• RBF interpolation: Sα(x) := ∑nj=1 α j φ(�x − x̄ j �)+∑k=1 αn+k pk (x),
analysis (FEA) model of a truck tyre,
where φ denotes a RBF, α j denotes the interpolation coused to determine the RRC, was replaefficients, x̄1 , . . . , x̄ n denote sample points, p k denotes
ced by a RBF interpolation of sample
certain polynomials, f denotes the real function values,
points evaluated by the FEA model.
x denotes the vector of variables.
The interpolation of the RRC contains
• Solve to find α: Aα = f, Aij := φ(�x̄i − x̄ j �)
inaccuracies and is often even physically absurd, such as providing nega• Solve to find α such that the resulting surrogate model
tive values. Therefore, we combined
obeys additional physical constraints:
the RBF interpolation with the existing
minimize �Aα − f�2 ,
expert knowledge; see Figure 4. The
α
methodology developed is illustrated
1
subject to gq (α) ≥ 0, q = 1, . . . , Q,
also in Figures 5 and 6, where we conhr (α) = 0, r = 1, . . . , R.
sider a simple one-dimensional function.
Figure 3. A mathematical representation of the methodology to combine a RBF interpolation
of sample points and the physical constraints stemming from the expert knowledge.
ORbit 23
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artikel
RRC [-]
0.006
updated model
original model
0.004
Figure 4. A cut of the original surrogate
model of the RRC illustrating that the model
does not conform to the expert knowledge.
The updated surrogate model of the RRC is
closer to the experts’ expectations.
0.002
0.000
3000
4000
5000
6000
7000
8000
9000
load [lbs]
Peter Lindroth is a PhD in mathematics working as an
optimization specialist at the Department of Chassis Strategies & Vehicle Analysis at Volvo Group Trucks Technology. His duties involve developing and applying mathematical tools for the product development of trucks.
Zuzana Šabartová is a PhD student at the Department of
Mathematical Sciences, Chalmers University of Technology and University of Gothenburg. Her research includes
the modelling and solution of optimization problems with a
focus on simulation-based optimization.
Michael Patriksson is a professor of applied mathematics
at the Department of Mathematical Sciences, Chalmers
University of Technology and University of Gothenburg.
His research focuses on theory, algorithmic development,
and applications in nonlinear, integer and combinatorial
optimization.
Ann-Brith Strömberg is an associate professor of applied
mathematics at the Department of Mathematical Sciences,
Chalmers University of Technology and University of
Gothenburg. Her research includes mathematical modelling
of industrial optimization problems as well as theoretical
and algorithmic development required for their solution.
4
4
updated model
updated model
3
3
original model
2
2
1
1
0
0
−1
0
0.5
x
1
1
Figure 5. The original interpolation contains an undesired oscillation,
which is in the updated surrogate model limited by prescribing an
additional sample point given by expert knowledge.
14
ORbit 23
−1
0
original model
0.5
x
1
Figure 6. The updated surrogate model–which utilizes the second
derivative as a smoothness measure–is smoother than the original
interpolation.
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• Industrial Optimizers AB
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Statistik, Københavns Universitet
Økonomi, SDU
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•
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Aarhus Universitet
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(DTU Management), Dan• Center for Research in the Foundamarks Tekniske Universitet
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ORbit 23
15
artikel
Af Michael Lindahl og Niels-Christian Bagger
Optimering af kabellayoutet
i havvindmølleparker
DORS prisen 2013 gik til Michael Lindahl og
Niels-Christian Bagger for deres speciale om
kabellayout ii havvindmølleparker. Redaktionen
ønsker tillykke.
Strøm fra havvindmølleparker anses for at være en vigtig
brik i at nå en mere bæredygtig energiforsyning. Mængden
af vindenergi stiger årligt med 20 %, men strømmen er i dag
stadig dyr at producere. Et mål for industrien er at reducere
omkostningerne pr. produceret kilowatttime med 50 % frem
mod 2020. En af måderne at nå det mål på er ved at bygge
endnu større havvindmølleparker hvilket også giver nogle
endnu større planlægningsproblemer.
ude i vindmølleparken ligger en substation som alle turbinerne
skal forbindes til så strømmen kan komme ind til land.
Hver turbine har præcist et udgående kabel og kan have op
til to indgående. Det vil sige at en turbine skal enten forbindes
til en anden turbine eller til substationen. Substationen kan på
samme måde højest have 12 indgående kabler.
Fordi kablerne skal pløjes ned i havbunden må kablerne ikke
I vores speciale benyttede vi operationsanalyse til at udvikle krydse hinanden da de ellers nemt ville kunne blive skadet.
et optimeringsværktøj der kunne skære op mod 11 % af udgifterne til kabelnetværket væk samt give ingeniørerne et ana- Strøm flow
lyseværktøj til at forstå konsekvensen af forskelle parametre
Hver turbine producerer en mængde strøm afhængig af hvor
langt bedre.
meget det blæser, hvilket medfører at strøm flowet skal beregProjektet blev lavet i samarbejde med DONG Energy der er nes for hvert enkelt vindscenarie. Til at beregne strøm flowet
markedslederne inden for konstruktion og drift af havvindmøl- Tabel 1. Eksempler på kabeltyper.
leparker.
Kabellayoutet
benyttes en DC-load flow model.
Et af de store planlægningsproblemer når man skal bygge en
havmøllepark er konstruktionen af kabellayoutet.
Når en turbine skal forbindes er der et valg imellem forskellige
kabeltyper. Kabler med en større diamater har en større kapaNår positionerne af vindmøllerne (turbinerne) er fastlagt skal
citet og mindre strømtab, men til gengæld er de også dyrere.
de alle sammen forbindes med kabler så strømmen kan
komme ind til land og ud til forbrugerne. Det foregår ved at der
Attributes
Cable
Figur 1. Et lille netværk med 7 turbiner og en substation.
16
ORbit 23
Resistance
[ohm/km]
I limit
[kA]
Cost
[EUR/m]
150mm2
0.15
0.45
500
240mm
2
0.10
0.55
600
500mm
2
0.05
0.75
700
artikel
Objektiv
Løsningsmetoder
Fordi kabler er en meget stor udgift ved konstruktionen af hav- Problemet blev løst ved hjælp af heltalsprogrammering. Fordi
vindmølleparken, blandt andet på grund af den store mængde strømtabet er kvadratisk afhængig af strømmen blev modelkobber, ønskes det at minimere den samlede kabelpris.
len ikke-lineær og kan også bevises til at være NP-hård. Den
samlede model kan ses i figur 2. Specialet kiggede på probleInstallationen af kablerne ind i fundamenterne er også en stor met fra to vinkler. Den ene del kiggede på generering af gyludgift og er ikke lineær da det er langt dyrere at installere to dige løsninger af høj kvalitet og den anden på nedre grænser
ekstra kabler i et fundament end et. Det ønskes derfor også at for at finde ud af hvor tæt de fundne løsninger lå på optimum.
minimere disse udgifter.
Gyldige løsninger
Til sidst ønskes det også at minimere strømtabet i netværket
da det også er tabt profit. Denne udgift udregnes udover hele På grund af den meget komplekse og store model var det ikke
parkens levetid.
muligt at finde løsninger direkte ved hjælp af en heltalsløser.
Det var derfor nødvendigt at benytte heuristiske metoder. ProAlle disse udgifter kan lægges sammen og formuleres som et blemet blev løst i to skridt. Til at finde en gyldig løsning blev
enkelt objektiv: Minimer de samlede udgifter af kabellayoutet først en simplere model uden strømtab løst for at finde en god
startløsning der minimerede kabelforbruget og installationsomkostningerne.
Bagefter blev der benyttet en mathheuristik hvor der blev
genereret en række mindre delproblemer som kunne løses
ved hjælp af en heltalsløser. For at løse problemet med det
ikke-lineære strømtab blev det lineært approksimeret.
Nedre grænser
Alene af hensyn til reduktion af omkostninger og elektriske tab
er det vigtigt at optimere kabellayoutet, men derudover har
DONG Energy ofte partnere som investerer i ejerandele af
havvindmølleparker. Der kan være forskellige meninger om,
hvad der er et godt layout, og i den sammenhæng er det vigtigt at de kan argumentere for kvaliteten af de løsninger de
leverer og nedre grænser for løsningen.
Figur 2. MINLP formuleringen af problemet.
Til at finde disse grænser benyttes en række forskellige
dekompositionsteknikker. Følgende metoder blev anvendt:
Generalized Benders’ Decomposition, Nested Benders’
Decomposition og Lagrangean Relaxation. I alle metoderne
blev der analyseret på hvordan problemets struktur kunne
udnyttes til at begrænse løsningsrummet mest muligt og
derved komme tættere på optimum.
ORbit 23
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artikel
Resultater
Hele algoritmen blev pakket ind i et add-in til Microsoft Excel
hvilket gjorde at ingeniørerne var i stand til selv at benytte
softwaret. De udviklede løsninger var i stand til at nedbringe
udgifterne til kabellayoutet op til 11.8 % i forhold til de manuelle løsninger og var i stand til at løse meget store og komplekse layouts som normalt ville tage flere uger at lave.
Samtidig viste værktøjet sig også utrolig stærkt til at analysere forskellige parametre. Det kunne f.eks. være placering
af substationen, kabeludgifter ved at tilføje ekstra turbiner og
hvordan en fordobling af spændingen i parken ville påvirke
kabellayoutet.
Projektet har derfor været utrolig vellykket og har givet DONG
Energy væsentlig ny viden omkring kabellayoutet samt et fungerende værktøj til at løse problemet.
Figur 3. Eksempel på optimeret layout.
Michael Lindahl blev kandidat fra Danmarks Tekniske
Universitet på eliteuddannelsen Industriel Matematik i
Maj 2013. Her fokuserede han på operationsanalyse
med stor interesse i at kombinere det teoretiske med det
praktiske og lavede undervejs projekter med virksomheder som DSB S-tog, Københavns Luthavne og DONG
Energy. Han har arbejdet med
mandskabsplanlægning i Københavns Lufthavn og er i februar
2014 påbegyndt en erhvervs PhD
hos MaCom A/S hvor han forsker
i optimering af skemalægning for
universiteter.
18
ORbit 23
Niels-Christian Fink Bagger blev kandidat fra Danmarks
Tekniske Universitet på eliteuddannelsen Industriel Matematik i Maj 2013. Her specialiserede han sig i operationsanalyse med stor vægt på kombinationen mellem teori
og praktisk anvendelse. Undervejs lavede han projekter
med virksomheder som MaCom A/S og DONG Energy
samt havde diverse studiejobs
som software-udvikler og hjælpelærer. Han har derefter arbejdet
med skemaplanlægningsproblemer på DTU og er netop i februar
2014 påbegyndt en erhvervs PhD
hos MaCom A/S hvor han forsker
i samme problemstilling i en mere
generel sammenhæng.
nyhed
Dansk operationsanalyseselskab
(DORS)
DORS pris 2014
DORS - Dansk Selskab for Operationsanalyse - beder hermed om indstillinger til Danmarks bedste
speciale i operationsanalyse 2014.
Invitationen er åben uden for DORS’s medlemskreds, så cirkulér gerne dette opslag.
Et speciale kan kun indstilles af vejlederen og skal overholde at:
 - Specialet er skrevet ved et dansk universitet og involverer operationsanalyse.
 - Specialet er på dansk eller engelsk.
 - Specialet er forsvaret i 2014. 
Ved uddeling af DORS-prisen lægges vægten på analyse og løsning af praktiske problemer.
Et speciale indstilles til DORS prisen ved at vejlederen senest 31. januar 2015 sender en email til [email protected]
(Tor Justesen,formand for DORS) med følgende indhold:
 - Specialet. Vedhæftes som PDF.
 - Begrundelse for, at specialet bør vinde prisen. Max. 1 side. Skrives af vejlederen. Vedhæftes som PDF.
 - Karakteren for specialet.
 - Email-adresser og telefonnumre på alle specialets forfattere og på vejlederen.
Dette sker efterfølgende:
• DORS nedsætter et udvalg på tre personer.
• Udvalget skriver inden slutningen af februar 2015 til vejledere og forfattere på de indstillede specialer med bekræftelser.
• Udvalget kårer et vinderspeciale og informerer alle deltagere inden udgangen af marts 2015.
• DORS-prisen uddeles ved generalforsamlingen for DORS til april 2015. Prisen er på 5000 kroner til deling mellem specialets forfattere. Det er en forudsætning for udbetalingen, at der laves en kort artikel til magasinet »ORbit« om specialet.
Skriv til [email protected] hvis I har spørgsmål.
ORbit 23
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