Case Study 3: Applications of Computational Optimization under Uncertainty in Decision Support (Computational Optimization)
Submitting InstitutionImperial College London
Unit of AssessmentComputer Science and Informatics
Summary Impact TypeTechnological
Research Subject Area(s)
Mathematical Sciences: Applied Mathematics, Numerical and Computational Mathematics, Statistics
Summary of the impact
The Computational Optimization Group (COG) in the Department of Computing
produced new models, algorithms, and approximations for supporting
confident decision-making under uncertainty — when computational
alternatives are scarce or unavailable. The impact of this research is
exemplified by the following:
Axioma (a firm that provides factor-based risk models and
portfolio construction tools for equity investors) now offers insurance
to equity portfolios with efficient calculation of coherent risk
measures — allowing diverse assets in portfolios.
Commerzbank now has improved risk management for proprietary
indices used in funds and options, increasing their revenue of
- The consultancy Decision Tree uses scenario tree based
valuation of swing options to create better decision-support software,
which attracted new clients in the energy sector.
- The utility provider Trianel now saves over two million Euros
annually by adopting tools that rely on our new optimization techniques.
- The energy trading company e&t bought software based on
our research that optimizes coal procurement contracts for a 750MW
coal-fired power plant.
Decision support under uncertainty is usually based on deterministic
computational models. In many important applications, these models are now
becoming so complex that their solution can only be achieved with vast
computing resources and speed-up techniques such as parallelization. This
has led to more abstract models. The problem becomes worse since solutions
based on deterministic models are not reliable predictions of the
future and having such reliability is the essence of trustworthy
decision-support systems. Therefore, these models need to be revised and
resolved frequently, making the overall approach significantly less
accurate and feasible. An alternative that we adopt is to devise methods
that optimize against an entire set of uncertain values in order to
accommodate even worst-case scenarios. The latter is especially relevant
in view of recent worst-case realizations of uncertainties in finance and
The Computational Optimization Group (COG) at Imperial College London has
carried out the underpinning research described in this case study. The
group has been founded by Professor Berc Rustem in 1995 and was
strengthened by the arrivals of Dr Daniel Kuhn in 2006 and Dr Panos Parpas
in 2011. The underpinning research strategically addresses the problems of
deterministic models by
- using non-deterministic models to gain reliability of
predictions under uncertainty,
- using approximating models to get better scalability of model
- using theoretical results to get confidence measures into the quality
of used approximations in relation to the concrete application that they
The research breakthroughs achieved are in the areas of robust
optimization, stochastic programming, and decision rules. Details of the
research are described below.
Risk Management & Optimization in Finance [i, ii, iii]: COG
pioneered the development of discrete minimax techniques for rival market
forecasts in  to inject robustness into portfolio optimization. This
includes novel robust portfolios for the cases when the uncertainty set is
defined over a continuous domain [1-2]. COG have created efficient
approaches for portfolios that are robust to uncertainties in asset
returns with performance guarantees, and where the portfolio may contain
European-style options. This was achieved with the use of second order
cone programming and duality . The approximations developed in 
enabled the efficient solutions of models and provide efficient and robust
decision support with confidence. This research does not only enable the
modelling uncertainty of physical events, it also enables the modelling of
uncertainty in the underlying probability distributions. This research
therefore also renders models for distributionally robust decisions .
Risk Management & Optimization in the Energy Sector [iv, v]:
COG's energy research has focused on the development of computationally
tractable models for multi-stage problems. This has been done through the
development of time aggregation methods for continuous time problems in
multi-stage stochastic programming [4, 5], and through the use of decision
rules and duality theory to validate approximated models and their
applicability for swing options in energy trading and
production/procurement planning . In order to use multi-stage
stochastic programming in applications, it is necessary to discretize
continuous stochastic programs so that they become more scalable. Although
such approximations may improve performance, they do not give estimates of
their quality. COG's research in  developed an approach in which an
original multi-stage stochastic programming problem was abstracted into
two discrete, state-aggregated stochastic programs that provide,
respectively, a lower and an upper bound on the optimal value of the
original problem. Here, scenario-free stochastic programming uses decision
rules in order to characterize the optimal decision. Then duality theory
is used to measure the "duality gap" that results from the use of
approximations. That measure is an accepted indication of the quality of
the approximation. These research outcomes therefore enable trading off
the precision of the abstractions with the precision of the computed
approximations of optimal values. This also facilitates the assessment of
the quality of these approximations in relation to the precise model. The
approximations developed in  can be computed numerically, since they
contain only finitely many constraints and finitely many decisions.
The underpinning research above is grouped into two parts, reflecting
impact in two different sectors. However, the underlying techniques are
not limited to applicability in those sectors. The grant [vi] below, for
example, had led to impact in the Defence sector and enabled some of the
underpinning research that is now having impact in software in the defence
sector. The nature of that software prevents us from documenting this
References to the research
Publications that directly describe the underpinning research
* References that best indicate quality of underpinning research.
 *D. Kuhn. An Information-Based Approximation Scheme for Stochastic
Optimization Problems in Continuous Time. Math. of Operations Research
34(2): 428-444, 2009.
 *B. Rustem and M. Howe. Algorithms for Worst-case Design and
Applications to Risk Management, Princeton University Press, Princeton NJ
(2002). ISBN: 9780691091549
Grants that directly funded the underpinning research
[i] Uncertainty and Risk Optimisation Algorithms for Food Processing.
EPSRC EP/C513584/1, B. Rustem (PI), £239,507, March 2005 — Feb 2008.
[ii] Systems Engineering — Worse-case Analysis and Parametric/Stochastic
Programming. EPSRC GR/T02560/01, B. Rustem (PI), £418,439, October 2004 — April 2008.
[iii] Risk Management of Queuing Systems. B. Rustem (CI), EPSRC
GR/S27849/01, £237,227 Sept 2003 — January 2007.
[iv] Robust Optimization of Nonlinear Processes under Uncertainty. EPSRC
EP/I014640/1, B. Rustem (CI), D. Kuhn (CI), £767,492, April 2011 — March
[v] Scenario-Free Stochastic Programming. EPSRC EP/H020454/1, D. Kuhn
(PI), £99,963, June 2010 — May 2011.
[vi] Software Programming for Decision Making Under Uncertainty. DTC BAE
Systems (Operations) Ltd, B. Rustem (PI), £1,207,150, August 2005 — August
Details of the impact
The research outcomes of our underpinning research give those who need
decision support under uncertainty a new tool-box with enhanced
capabilities of solving more complex problems and of judging reliably
whether these solutions are trustworthy. The transfer of this knowledge
and technology is recent and on-going, but it has already had some
measurable impact, which is detailed below for each of the five
1. Axioma: Robust decision models require the
specification of the set in which the realized value of uncertainty is
expected to reside. Our research in [1, 2] now gives similar robustness
guarantees when the uncertainty is realized outside of that
specified uncertainty set. Since these outcomes were put into the public
domain for free usage, Axioma was able to immediately implement
and market software based on the model developed in . Axioma "creates
flexible tools to help portfolio managers quickly and accurately
implement their strategies"[A] Its flagship product is the Axioma
Portfolio Optimizer TM. According to the June 2011 Axioma Advisor,
[B], the extension of a risk measure to portfolios containing options
produced in  is now implemented and used on that flagship product.
Axioma is a software company whose clients are financial institutions that
manage trillions of dollars using these tools.
2. Commerzbank: COG's research results on minimax
and optimization  are currently used in financial products by research
collaborators from Commerzbank's Indices & Strategies team.
The mission of that team is to design proprietary indices for products
such as funds and options. These are large institutional funds whose
clients are professional investors such as pension funds, hedge funds, and
very wealthy individuals. COG's research has had direct impact on the
management of these funds, as evidenced in [C, D] where the Managing
Director, Commerzbank states "The robust optimization concepts
described in your papers ... have been carefully studied and some of
them are incorporated within several proprietary indices and tool".
He goes on to say that "Investors regard these risk management tools
as an absolute prerequisite". The latter suggests indirect impact of
COG's research outcomes as they provide better assurance of risk
modelling. Although Commerzbank cannot reveal even the order of
magnitude of the value of these managed funds the Managing Director has
stated that "The actual value of the funds being managed by these
tools ... is respectable."
3. Decision Trees offers commercial software and
consultancy to those who produce or trade in energy. They achieve this by
transferring scientific research into usable methods in the energy sector.
One of the recent challenges in this sector is the high degree of
uncertainty in pricing and reserves of energy, caused by the increased use
of renewable but less predictable energy. They therefore recognize the
value of stochastic optimization for dealing with such uncertainty in the
creation of client plans that can increase profits whilst minimizing risk
under such uncertainty. A Manager of Decision Trees GmbH [E] makes clear
that our research  was instrumental for the creation of one of Decision
Tree's products when he states: "we were able to implement
scenario tree based stochastic optimization models for a whole variety
of practical decision making problems in the energy industry. Mainly,
our implementation has been based on your publication in the paper ... "
which refers to paper . COG's research then led to indirect impact as
suggested by the quote "we have enhanced our stochastic optimization
software towards the valuation and operational optimization of natural
gas storage and natural gas contracts. ... Amongst these customers is
Trianel (Germany), Salzburg AG (Austria), OMW (Austria), and ExxonMobil
(UK)." The direct impact COG's research has had in the acquisition
of Salzburg AG as a client is described as "We have achieved this
great success by the practical application of your original pioneering
work on scenario tree based valuation of swing options."
4. Trianel is a German utility provider. Its mission
is to coordinate and bundle the interests of municipal and communal energy
providers in order to strengthen their independence and competitiveness.
They operate a combined cycle gas turbine (CCGT) power plant in
Hamm-Uentrop in Northern Germany. Some of the shares of the plant are
operated based on deterministic optimization [F][G]. Decision
Trees was thus able to apply the stochastic optimization tool
described above (see 3) on another share to compare its
effectiveness to the standard alternative, noting that "stochastic
optimization has achieved 1,4% more profit as compared to the best
deterministic optimization. This is equivalent to approximately 2
Million Euros additional profit in 2008 yielded by stochastic
optimization" [D]. This is an indirect impact of research outputs in
5. e&t is the trading company of Energie
Allianz. e&t trades bilaterally and through brokers with all important
European power traders on the energy exchanges EEX, EXAA, OTE and IPEX as
well as on the European Climate Exchange ECX. Two important services which
e&t provides are risk management (which has to deal with uncertainty)
and energy wholesales trading (where the use of swing options and
stochastic optimization can maintain efficient trades and production). In
that context, e&t has purchased a suite of software tools based on
[3-5] for the operation of the new 750 MW unit in the coal-fired power
plant Walsum in Duisburg [H]. On a daily basis this software assesses
plans for yearly coal purchases and the associated purchase contracts.
To summarize, the underpinning research has documented impact in the
financial and energy sector, and in companies that provide services for
these sectors. That impact is also on-going and likely to persist in the
years to come.
Sources to corroborate the impact
Archived at https://www.imperial.ac.uk/ref/webarchive/nyf
on 22nd Oct2013
[B] Axioma Advisor June 2011: Minimizing Downside Risk in Axioma
Portfolio with Options. http://www.updatefrom.com/axioma/2011_q2/research_focus.asp.
This document describes the use of COG's research in Axioma's products.
Archived on 22/10/2013 https://www.imperial.ac.uk/ref/webarchive/myf
[C] Managing Director, Commerzbank describing the use of COG's research.
[D] Commerzbank iQArts Risk Parity confidential report confirming the use
of COG's research in figure 1. Available on request.
[E] General Manager, Decision Trees GmbH confirming the use of COG's
research by Decision Trees.
[F] Manager of Plant at Hamm-Uentrop confirming the use of COG's research
[G] Manager of Natural Gas Procurement Portfolio with Take-or-Pay
Contracts confirming the use of COG's research by Trianel.
[H] Analyst, e&t Energiehandelsgesellschaft confirming the use of
COG's research by e&t Energiehandelsgesellschaft.