A Multi-Pathfinder for Developing
Adaptive Robust Policies in System Dynamics
Caner Hamarat’, Erik Pruyt, Erwin T. Loonen
Abstract
Adaptivity is essential for dynamically complex and uncertain systems. Adaptive
policymaking is an approach to design policies that can be adapted over time to how the
future unfolds. It is crucial for adaptive policymaking to specify under what conditions and
how to adapt the policy. The performance of adaptive policy is critically depended on the
proper timing of the actions. This paper illustrates that robust optimization can be used as
decision support aid for appropriate specification of conditions to ensure adaptivity of policy
under uncertainty. Furthermore, multiplicity of divergent objectives of different stakeholders
is also important for policy support in dynamic systems. To address this issue, multi-objective
optimization algorithms are good candidates for a proper solution. In this paper, we outline
how to use multi-objective robust optimization in System Dynamics to support adaptive
policy design. The outlined approach results, rather than a single set of conditions, in multiple
alternative conditions under which to adapt policy. Thus, better informed policy debate on
trade-offs is possible. The approach is illustrated through a SD model about the transition
toward renewable energy systems in the EU. The study aims to propose a model-based
simulation approach with multi-objective robust optimization for supporting informed
adaptive policymaking.
Keywords
Adaptive policymaking, deep uncertainty, robust optimization, multi-objective optimization
Introduction
Dynamic complexity and deep uncertainty are common characteristics of many complex
systems. Due to increasing complexity and uncertainty of today’s world, policymaking
becomes challenging. Most traditional approaches for policymaking perform unsatisfactorily.
The reason is that their reliance on predictions results in static policies, which are designed
and fixed only according to best estimates about the future. Due to their nature, static policies
are ineffective and inappropriate for dealing with complexity and uncertainty. For this reason,
there is a strong need for innovative approaches to deal with uncertainty and complexity.
Under deep uncertainty, adaptivity and flexibility are extremely important and should be
taken into consideration in policy design (Neufville and Scholtes, 2011). A possible planning
approach is to include adaptivity and flexibility into policy design for developing long-term
adaptive policies.
“ Corresponding author: Delft University of Technology, Faculty of Technology, Policy and Management
Jaffalaan 5, 2628 BX, Delft, The Netherlands, Tel: +31 15 2788080 E-mail: c.hamarat@ tudelft.nl
1
The idea of adaptivity dates back to almost a century ago. Dewey (Dewey, 1927) put forth
an argument proposing that policies be treated as experiments, with the aim of promoting
continual learning and adaptation in response to experience over time (Busenberg, 2001).
Early applications of adaptive policies can be found in the field of environmental management
(Holling, 1978; McLain and Lee, 1996). Policies are designed from the outset to test clearly
formulated hypotheses about the behavior of an ecosystem being changed by human use (Lee,
1993). A similar attitude is also advocated by (Collingridge, 1980) with respect to the
development of new technologies. Given ignorance about the possible side effects of
technologies under development, he argues that one should strive for correctability of
decisions, extensive monitoring of effects, and flexibility. More recently, Walker et al.
(Walker, Rahman, and Cave, 2001) developed a structured, stepwise approach for dynamic
adaptation which is called adaptive policymaking. This approach suggests that plans should
be adaptive: one should take only those actions that are non-regret and time-urgent and
postpone other actions to a later stage.
In order to design an adaptive and flexible policy, it is essential to make intelligent
decisions on whether and/or when to activate necessary actions. Robust optimization
(Rosenhead, Elton, and Gupta, 1972) can be of great use in order to determine whether and/or
when to activate actions. For robust adaptive policy design, it is important to take the
multiplicity of different objectives into account, instead of designing a policy based on a
single objective (Kasprzyk et al., 2013) (Haasnoot et al.) (McInemey, Lempert, and Keller,
2012). In this paper, we outline how adaptive policymaking can be supported through multi-
objective robust optimization. We apply the outlined approach to a case study of developing
an adaptive policy for steering the transition of the EU energy system towards a more
sustainable functioning.
Methodology
The Adaptive Robust Design approach
There is a growing literature on the need for adaptive planning because of deep
uncertainty. A wide variety of approaches and analytical tools are being put forward to
support the design of adaptive plans. One example is Adaptive Policymaking (Walker et al.,
2001), which is a generic approach for designing dynamic robust long-term plans under deep
uncertainty.
Exploratory Modeling and Analysis (A gusdinata, 2008; Bankes, 1993) is a computational
approach to support the design of long-term plans under deep uncertainty. EMA uses
computational experiments to combine plausible models and other uncertainties in order to
generate a large variety of scenarios that are in tum used to analyse complex uncertain
systems, support the development of long-term strategic policies under deep uncertainty, and
test policy robustness over. EMA could also be used to develop adaptive policies under deep
uncertainty since it allows for generating and exploring a multiplicity of plausible scenarios
by sweeping multi-dimensional uncertainty space. EMA could then be used to identify
vulnerabilities and opportunities present in this ensemble of scenarios, paving the way for
2
designing targeted actions that address vulnerabilities or seize opportunities. The efficacy of
the resulting policies could then be tested over the entire ensemble of scenarios. Moreover,
EMA could be used to identify conditions under which changes in a policy are required. That
is, it could help in developing a monitoring system and its associated actions. It thus appears
that EMA could be of use in all adaptive policy-making steps.
Hence, the Adaptive Robust Design approach (Hamarat, Kwakkel, and Pruyt, 2012)
consolidates EMA into the adaptive policymaking for creating a more operational approach. It
starts along the lines of the EMA methodology with: (1) the conceptualization of the problem,
(2) the identification of uncertainties (and certainties), and (3) the development of an
ensemble of models that allows generating many plausible scenarios. It then proceeds with:
(4) the generation of a large ensemble of scenarios, (5) the exploration and analysis of the
ensemble of scenarios obtained in Step 4 in order to identify troublesome and/or promising
regions across the outcomes of interest, as well as the main causes of these troublesome and
promising regions, (6) the design -informed by the analysis in Step 5- of policies for turning
troublesome regions into unproblematic regions, (7) the implementation of the candidate
policies in the models, (8) the generation of all plausible scenarios, subject to the candidate
policies, (9) the exploration and analysis of the ensemble of scenarios obtained in Step 8 in
order to identify troublesome and/or promising regions across the outcomes of interest, as
well as the main causes of densely concentrated troublesome and/or promising regions, etc.
Steps 5-8 should be iterated until an adaptive policy emerges with robust outcomes (See
Figure 1).
(5/91...)
Identification
of vulnerabilities
and/or opportunities
(2) Identification of
(Geen ov
BI...) 6/10/...
@) Problem Generation of Iteration Des ane
Conceptualization ensemble of and actions
scenarios
8) BSE ee
of mod:
cont cont
Figure 1: The Iterative Adaptive Robust Design process
(7/1...)
Implementation of
policies in models
Computerized Decision Support
Discovering Vulnerabilities and O pportunities
Vulnerabilities and opportunities are central concepts in adaptive policy making. In
order to be able to design robust policies, it is crucial to identify problematic and/or promising
regions that can be targeted more effectively. Actions that are targeted at the regions of
interest are either taken now or in the future to address vulnerability or to take advantage of an
opportunity.
In this study, Patient Rule Induction Method (PRIM) (Friedman and Fisher, 1999;
Groves and Lempert, 2007; Kwakkel, Auping, and Pruyt, 2012; Lempert et al., 2006) is used
for discovering vulnerabilities and/or opportunities. PRIM allows distilling uncertainty sub-
spaces with high positive match ratios for a pre-specified binary classification function and
with high relative masses (above a pre-specified threshold relative to the total scenario space).
An extension of PRIM by using Principal Component Analysis (PCA) (Dalal et al., 2013), an
orthogonal transformation procedure, allows a better identification of regions of interest. In
this study, the PCA PRIM is used for identifying regions of interest for designing targeted
actions.
The specification of when to activate which actions
The adaptive part of adaptive policymaking takes the form of a monitoring system that
specifies what information should be tracked, and under which pre-specified conditions
addition, pre-specified actions will be taken. These signposts and triggers is a crucial part of
the contingency planning and the efficacy of an adaptive plan hinges on the care with which
this contingency planning is done. The values used for triggers are mostly based on logical
guesses, expert opinions or historical data. However, they should be determined more
intelligently for improving the monitoring system, which means that the performance of the
policy design. The use of optimization can be a possible solution approach for such a
problem.
Optimization is widely used in every aspect of policymaking and in various fields
ranging from engineering to science and from business to daily life. Optimization is mostly
referred as finding the optimum solution among a set of plausible alternatives under certain
constraints. It is the common practice to use optimization for predictive purposes, aiming fora
single best solution. However, this predictive approach might be misleading under uncertainty
for policymaking, where often an optimum single goal is not the main aim (Bankes, 2011). A
field in optimization to overcome the difficulty of uncertainty is robust optimization. Robust
optimization methods aim at finding optimal outcomes in the presence of uncertainty about
input parameters (Ben-Tal and Nemirovski, 1998, 2000; Bertsimas and Sim, 2004). To this
purpose, robust optimization methods can be of great use for adaptive policymaking.
For complex and uncertain systems, it is treacherous to design plans that are based on
a single objective or objectives that are imprecisely merged into a single one. Multi-objective
optimization helps to grasp the multiplicity of different and possibly conflicting objectives. In
this study, a well-established multi-objective optimization technique NSGA-II is used, namely
the Nondominated Sorting Genetic Algorithm-II (Deb et al., 2002). In this study, the triggers
are used as the input parameters to be optimized. The result is a Pareto front that includes
possible Pareto solutions that each is specified by the trigger values.
Optimization methods can be utilized for improving policy design in system dynamics
models (Coyle, 1985). A possible way of using optimization in SD is through the automated
specification of parameters in the model (Yucel and Barlas, 2011). However, it is crucial to
take the multiplicity of objective into account. The use of multi-objective optimization
methods has not been investigated thoroughly in the system dynamics literature. There are
few studies that aim to combine multi-objective optimization and system dynamics (Duggan,
2005) (Duggan, 2008b) (Duggan, 2008a) (Eksin, 2008).
EU Energy Case
Background
For 2020, the European Union (EU) has certain targets for the reduction on carbon
emissions and the share of the renewable technologies in the energy system (Commission,
2007; European Commission, 2010). The main aim is to reach 20% reduction in the carbon
emission levels compared to 1990 levels and to increase the share of the renewables at least to
20% by 2020. However, the energy system includes various uncertainties related to
technology lifetimes, economic growth, costs, leaming curves, investment preferences and so
on. For instance, precise lifetimes of technologies are not known and expected values are used
in planning decisions. Furthermore, it is deeply uncertain how the economic growth, which
has a direct influence on the energy system, will evolve. Thus, it is of great importance to take
these uncertainties into consideration when analyzing the energy system.
In order to meet the goals for 2020, an Emissions Trading Scheme (ETS) for limiting the
carbon emissions in the EU was initiated (Commission, 2003). ETS imposes a cap-and-trade
principle that sets a cap on the allowed greenhouse gas emissions and an option to trade
allowances for emissions. However, the current emissions and the share of the renewables do
not give hope for the future targets. It is necessary to take more actions for steering the
transition toward a cleaner energy production. This requires a better handling of the
uncertainties in the energy system and more robust policies that can promote the renewable
technologies.
In this study, a System Dynamics model about the EU energy systems is used for
illustrative purposes. The model represents the whole power sector in the EU and considers
congestion on interconnection lines by distinguishing different regions of the EU. Nine power
generation technologies are included and these are: wind, PV solar, solid biomass, coal,
natural gas, nuclear energy, natural gas with Carbon Capture and Sequestration (CCS), coal
gasification with CCS and large scale hydro power. The model includes the main endogenous
causal relations such as technological battlefield for investment, market supply-demand
dynamics, cost mechanisms and interconnection capacity dynamics. An aggregated level
causal loop diagram is illustrated in Figure 2, which includes the main causal loops that drive
the main dynamics of the model. Not only endogenous mechanisms but also various
exogenous uncertainties do exist in the energy systems. Further details about the model can be
5
found in (Loonen, Pruyt, and Hamarat, 2013). The uncertainties to be explored will be
explained in detail in the next section.
Installed,
capacity
Generated
Average capacity electricity
Cumulative
installed capacity Fuel scarcity carbon
allowances
Capacity growth
Natural resource potential
scarci
bu Electricity from
renewable sources
y ry
ee ee Resource price D
eS
Fuel price
carbon price
B
Technological:
progress
“Marginal ~=—»
investment costs * Levelised costs of
electricity Electricity prices
Profitability
Expected future
demand gap
Figure 2: Aggregated Causal Loop Diagram of the main dynamics
Uncertainty Specification
In order to explore the uncertainty space, not only parametric but also structural
uncertainties are included in the analysis. For exploring structural uncertainties, several
possible behaviors are identified and a switch mechanism is used for switching between
different behaviors. For example, 6 different plausible economic development trends are
defined and there is a switch that helps us explore the different economic growth scenarios.
Similarly, switches are used for electrification rate and physical limits. Remaining
uncertainties have parametric characteristics and they are explored over pre-defined ranges.
Table 1 provides an overview of the uncertainties that are analyzed and their descriptions. In
total, there are 46 uncertainties to be explored in this study.
Table 1: Specification of the uncertainties to be explored
Name
Description
Economic lifetime
Learning curve
Economic growth
Electrification rate
Physical limits
Preference weights
Battery storage
Time of nuclear ban
Price - demand elasticity
Objectives
For each technology, the average lifetimes are not known
precisely. Different ranges for the economic lifetimes are explored
for each technology.
It is uncertain for different technologies how much cost will be
decreased by increasing experience. Different progress ratios are
explored for each technology.
It is deeply uncertain how the economy will develop over time. 6
possible growth behaviors are considered.
The rate of the electrification of the economy is explored by
including 6 different electrification trends in the uncertainty
exploration.
The effect of the physical limits on the penetration rate of a
technology is unknown. 2 different behaviors are considered in the
analysis.
Different investor's perspectives on technology investments are
deeply uncertain. Growth potential, technological familiarity,
marginal investment costs and carbon abatement are possible
decision criteria.
For wind and PV solar, the availability of the battery storage is
difficult to predict. A parametric range is explored for this
uncertainty.
A forced ban for nuclear energy in the EU is expected between
2013 and 2050. The time of nuclear ban is ranged between 2013
and 2050.
A parametric range is considered for price - demand elasticity
factors.
For the multi-objective optimization, it is necessary to identify the objectives to be used
for the optimization. In this study, we use three objectives that are as follows: (1) the fraction
of the renewable technologies over the total energy system, (2) the fraction of carbon
emissions reduction in 2050 compared to 2010 levels and (3) average total costs of electricity
production. The EU has specific targets for the share of renewable technologies and the
reduction fraction of carbon emissions by 2020. To that purpose, the first two objectives are
chosen to be included in the optimization. It is obvious that these two objectives have similar
trends. So, another objective, which is thee average total costs of electricity generation, is
included for the multi-objective optimization. While the first two objectives are to be
maximized, this last cost related objective is to be minimized.
7
Analysis
From ETS toward an adaptive policy
The ETS is currently in practice around Europe for reducing the carbon emissions. It
introduces an annual cap on the maximum amount of emissions and the option for trading
these carbon emissions. The ETS policy does not reveal promising results so far and it needs
further analysis to explore the plausible futures under this policy. Using a workbench that is
written in Python (Van Rossum, 1995) which controls Vensim (Ventana Systems Inc., 2010,
2011), an ensemble of 10,000 simulations by Latin Hypercube Sampling (Pilger, Costa, and
Koppe, 2005; Seaholm, Ackerman, and Wu, 1988) is generated which consists of 46 different
uncertainties. The results indicate that it is almost impossible to meet the 2020 targets by only
using ETS policy. For most possible futures, the fraction of renewables remains around 40%
and the carbon emissions reduction fraction is around 30%. It is obvious that there is a need
for further actions to take in order to achieve a sustainable energy future. By using PCA
PRIM, the opportunities and vulnerabilities of the ETS policy can be used for designing
targeted adaptive actions to improve the policy design. Although PCA PRIM does not reveal
useful vulnerability information, there are useful findings related to opportunities to take
advantage of. PCA PRIM is used to identify the opportunities that can lead to futures where
the fraction of renewables is higher than 40%. These opportunities are mainly related with the
technology lifetimes and the learning curves of the technologies. To be more precise; longer
lifetimes of renewables, shorter lifetimes of non-renewables (especially coal and gas) and
better learning curves for renewables are the opportunities that can help promote the
sustainability.
In order to improve the policy design, some adaptive actions are added to the current ETS
policy. The first adaptive action is related with accelerating the phasing out of the old non-
renewable technologies. A desired renewable fraction level of 80% and the gap between the
desired and the current level is tracked. An additional decommissioning flow which is
factored by this gap is introduced for the non-renewable technologies. The second action aims
to make the renewable technologies more cost-attractive by introducing a subsidy fraction on
the marginal investment costs of renewable technologies. This action introduces a subsidy of
25% for a period of 10 years when the costs of renewable technologies are close to the most
expensive non-renewable with proximity of 125%. The last adaptive action is about
introducing an additional decommissioning. A forecast of the renewables fraction for 10 years
ahead is made and if the gap between the desired fraction and this forecast is bigger than a
certain trigger value of 10%, then 25% additional decommissioning is introduced.
The resulting policy with these adaptive actions is called as the adaptive policy. For
testing the performance of the adaptive policy, it is also run for the same ensemble of 10,000
simulations. There is a remarkable improvement in the policy performance with the
introduction of the adaptive policy design. Figure 3 shows a comparison of the ETS policy (in
blue) and the adaptive policy (in green) for the carbon emissions reduction fraction, average
total costs and the renewables fraction. The figures represent the envelopes which spans the
upper and lower limits for 10,000 simulations over time and the density estimates of the end
states of all runs in the respective ensembles. It can be observed that the adaptive policy
8
improves the fraction of renewables dramatically from 40% on average to 70%. Similarly,
there are clear improvements in terms of the carbon emissions reduction fraction and the
average total costs.
HS “Adapive Policy ETS
BS
re
13
el
: ——-
°
4 35 . :
fraction emesis
Mine aT ar By a wi aT Bis
Figure 3: Comparison of ETS and Adaptive policies
Fine-tuning the trigger values
In order to design an adaptive policy, signposts and triggers are used for ensuring the
adaptivity and flexibility of the policy. The specification of the triggers has a crucial
importance for the performance of the adaptive policy. To specify these triggers more
intelligently, optimization could be of great use. To this purpose, multi-objective robust
optimization is used in this study, more specifically NSGA-II algorithm is used (Deb et al.,
2002). In our adaptive policy design, there are 8 different triggers to be used as the input
parameters of the optimization algorithm. The triggers and their associated ranges can be
found in Table 2.
Table 2: Triggers and their ranges for the optimization
Name Range
Desired F raction 0.5 - 1.0
| Additional Decommissioning 0.0 - 0.75
Subsidy F actor 0.0- 0.5
| Subsidy Duration 0- 40
Proximity 1-2
Decommissioning F actor 0.0- 1.0
Time Ahead 10 - 40
Trigger 0.0- 1.0
It is crucial to decide on how to characterize robustness for the multi-objective robust
optimization. In this paper, we define the robustness in a manner similar to signal-to-noise
ratio, which is the mean divided by the standard deviation. This robustness metric enables us
to increase the mean while minimizing the perturbations. However, this can only work for
maximization, not for minimization. Instead of mean divided by the deviation, the mean
multiplied by the standard deviation is used for minimization purposes. In order to
operationalize such robustness metric, each candidate needs to be evaluated using many
simulations.
The NSGA-II algorithm is executed for a pre-defined number of 25 generations with a
population size of 100. The three objectives are as follows: (1) Maximize the fraction of
renewables, (2) maximize the fraction of carbon emissions reduction and (3) minimize the
average total costs of electricity. For the objectives to be maximized, the robustness score is
computed as the average divided by the standard deviation for 500 cases that will be used for
the optimization. For the minimization objectives, the robustness score equals the average
times the standard deviation.
Figure 4 shows the number of changes to the set of Pareto front solutions, including both
additions and removals. For the first 10 generations, there is a considerable change in the
number of Pareto solutions. After 15 generations, no change is observed which can be
interpreted that the Pareto front is stabilized and converged to a solution.
10
Figure 4: Changes to the Pareto front over the generations
In Figure 5, a 3D representation of the scores of the three objectives that are normalized
between 0 and 1 is provided. The blue dots represent the dominated solutions and the red ones
are the solutions on the Pareto front. As can be seen from the figure, the solutions converge
toward a front where the renewables fraction and the carbon emissions reduction fraction have
higher scores by trading off the score of the average total costs. There are 27 solutions on the
Pareto front. As expected, it is easy to see the tradeoff between the renewables and emissions
objectives and the cost objective (Appendix A). The figure illustrates that there is a minimum
cost limit that cannot be beaten.
06
"action reneuy
SbIeS robustness
‘average total costs robustness
Figure 5: Non-Pareto solutions in blue and Pareto Solutions in red (normalized btw. 0-1)
11
In order to have a better understanding, it is useful to see the input parameters for the
Pareto front. Figure 6 illustrates the parallel coordinates for the 28 Pareto solutions and their
corresponding values for the eight triggers. To have better visualization, the values are scaled
between 0 and 1 and their original values can be found on Table 3. The figures show that
when the amount of additional decommissioning is too small, it is mostly in combination with
smaller trigger values. This means that if there is less additional decommissioning of the non-
renewable technologies, then there must be as little as possible deviation from the desired
fraction of renewables.
coor
Proxy ‘rmeahead seeommeonfocor subsidy duration subse factor wecer
Figure 6: Parallel Coordinates for the Pareto front of the first optimization (normalized)
Discussions
This study illustrates how multiobjective robust optimization could of great use for
supporting policy design in dynamic systems. In the presence of multiple, possibly,
conflicting objectives, it is hard to design policies that satisfy all of the objectives and
tradeoffs are inevitable. This approach helps identify multiple alternative policies, instead of a
single “best” policy suggestion. Thus, it creates room for a better informed policy debate on
tradeoffs.
An essential contribution of using robust optimization for adaptive policymaking is the
intelligent specification of the policy levers, namely triggers. Initially, these parameters were
assigned values by using guesses according to historical data, expert opinion or common
sense. The resulting adaptive policy is more robust to uncertainty and outperforms the basic
ETS policy (See Figure 3). However, it might be possible to specify the triggers more
effectively for further improvement of the policy design. The values assigned by the
optimization algorithm shows that the trigger values can be determined more intelligently.
Figure 7 shows a comparison of the adaptive policy and one of the policy solutions on the
12
Pareto front identified by the robust optimization. It is obvious that robust optimization helps
improve the policy design by specifying the values more intelligently.
RB Adaptive Policy ETS 2 RE Optimized Adaptive Policy ETS 2
carbon emissions reduction fraction
io Bs Bw DE IT TOs a5 s
ume
total costs of electricity
Figure 7: Comparison of adaptive policy and optimized policy
The choice of robustness metric has an important influence on the Pareto solutions
identified by the multiobjective robust optimization. In this study, we have used a robustness
score based on the mean divided by the standard deviation for maximization, and the mean
multiplied by the standard deviation for minimization. However, it is possible to get different
results by using different metrics. In our study, we choose to use a robustness score that aims
to maximize the average over a certain number of cases and minimize the deviation. For
instance, a regret-based metric, where the aim is to minimize the maximum regret, can lead to
different results.
Multiobjective optimization and robust optimization are already computationally
exhaustive techniques separately. It becomes time and resource consuming when they are
merged together. This computational constraint limits the scope of the analysis. For instance,
it is essential to work with relatively small, less detailed models. However, sometimes it
might be essential to have quick results if, for instance, it is necessary to make a decision
quickly. For such conditions, it might be better to take advantage of faster and quicker
techniques such as Multi-Criteria Decision Analysis (MCDA).
13
Conclusions
Policymaking under deep uncertainty and dynamic complexity is a challenging task. A
possible approach for dealing with deep uncertainty is the adaptive policymaking. In a recent
paper (Hamarat et al., 2012), an Adaptive Robust Design approach for developing adaptive
policies under deep uncertainty is proposed. However, that approach does not explicitly
consider the multiplicity of different objectives. Most policy problems include multiple
parties/stakeholders/actors having multiple, potentially, conflicting objectives. So, there is a
need for methods dealing with multiple objectives. To this purpose, we use multiobjective
optimization together with the A daptive Robust Design approach.
The proposed approach in this paper is illustrated through a case study that deals with the
possible futures of the EU energy market. There is a strong need for more innovative policies
than the current ETS policy to promote the transition toward renewable technologies. The
results indicate that the proposed approach can be efficiently used for developing policy
suggestions and for improving the decision support for policymakers in dynamically complex
systems. Multiobjective optimization can be effectively utilized for improving the policy
design in system dynamics.
Acknowledgements
This study is part of the project “Dealing with Uncertainties in Infrastructure Planning and
Design: Exploratory Modeling, Real Options analysis and Policy Design” which is supported
by the Next Generation Infrastructures (NGI) Foundation.
14
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16
APPENDIX A
Table 3: Scores of the solutions on the Pareto front
fraction carbon emission
renewables score reduction score
average total
cost score
572.92454697
APPENDIX B
Table 4: Upper and lower limits of the triggers for the Pareto front solutions
1.65709637 1.07060308
1.65683552 1.06972597 572.31497905
1.65451022 1.06684621 571.74629060
1.64933297 1.04200385 565.49398064
1.64807981 1.04186434 563.90183745
1.64459214 1.04756461 569.70913003
1.64277368 1.04054030 562.94397605
1.64265164 1.05100700 571,14187547
1.63407105 1.01803123 562.88709162
1.63259528 1.02111486 561.42223050
1.63185500 1.02360786 553.88846551
1.62536401 1.01110391 552.72997174
1.62529785 1.01130922 552.83619609
1.01131470 552.83634577
Add Desired Proximity Time decommission subsidy subsidy trigger
Comm Fraction Ahead factor duration factor
Min 0.071 0.678 C372 14.016 0.492 31.204 0,192 0.008
Max 0.708 0.984 1.891 31.345 0.977 41.900 0.463 0.082
17
