Methods
Integrated Water Resources Management (IWRM) is inherently multi-objective.
Traditional approaches to such problems such as Cost-Benefit Analysis (CBA) relied on
the aggregation of objectives into a single, parameterized goal function (e.g. (Lahmeyer
1998)). This was achieved by valuation. Valuation establishes a common metric between
changes and therefore allows straight-forward comparison of the individual components
of such changes. The weighted sum of values finally is the measure based upon which
allocation decisions will be made by the decision makers (Heal 2004).
CBA are based most often on financial valuation, i.e. the quantification of costs and
benefits directly related to an allocation decision. Traditional CBA did neither pay
attention to external effects nor take into account non-use values of natural resources.
Clearly, this is a critical issue since not valuing some services is equivalent to assigning
those services a zero value. This shortcoming was addressed by the development of the
Total Economic Valuation Framework (TEV). TEV is the process of quantifying the
economic value of particular changes in the levels of a goods and/or services in a holistic
way (see Figure 1). Thus, it includes every accountable item as well as externalities that
affect the wider economy (Cropper and Oates 1992; Turner 1993).
Out of several reasons, values to these changes are difficult to assess. First and especially
in a context of subsistence and developing economies, many of these goods and services
are not traded in markets and a large part of the value may stem from nonuse value.
Second, catchment approaches involve large spatial scales that cut across political
boundaries. However, economic valuation techniques are difficult to carry out on such
scales when an exhaustive list of services provided by natural systems should be
incorporated and regional heterogeneities in the political/institutional realm exist
(National Research Council (United States) Committee on Valuing Ground Water 1997;
Acharya and Barbier 2002; Heal 2004).
o
Pr
du
Natural Resources
Structure & Function
io
ct
n
Natural Resources
Goods & Services
Allocation
Decision
Human Actions
(Private / Public)
Decisionmakers
Values
Use Values
Non-Use Values
Figure 1: Valuating goods and services from natural resources (Heal 2004). In the context of this study, the
notion natural resources refers to surface water, groundwater and related resources. Values consist of use
and non-use values to extent the narrow utilitarian approach.
Due to the various issues related to valuation and CBA, we suggest a novel approach to
IWRM that does not rely on the aggregation of objectives (see Figure 2). Rather, we
propose to combine methods from the fields of Multi-Criteria Decision Making Models
(MCDM) and Operations Research (OR) as well as the field of Artificial Intelligence
(AI) respectively to provide a systematic means for comparing tradeoffs and selecting
policy alternatives that best satisfy the decision maker’s objectives.
MCDM are methods that have proved successful in both, the linking of natural sciences /
engineering and social sciences research as well as bridging the gap between scientific
knowledge and the identification of commonly agreed upon compromise solutions that
lead to allocation decisions. Although variations exist, the basic steps of MCDM involve:
1) Definition of the decision problem and identification of stakeholders; 2) Identification
of objectives and attributes; 3) Identification and pre-selection of alternatives to
allocation; 4) Prediction of outcomes; 5) Quantification of preferences of stakeholders for
outcomes; 6) Ranking of alternatives; 7) Assessment of results; 8) Implementation and
Monitoring (Heathcote 1998; Reichert, Borsuk et al. 2004). The use of MCDM in natural
resources management has generated a substantial body of literature in recent years
(Steiguer, Liberti et al. 2003).
Traditional MCDM suffer from major shortcomings that are particularly relevant in the
context developing countries. First, the methods rely on early involvement of decision
makers and stakeholders. They thus work best in well structured institutional and political
setups with an established culture of negotiation. Furthermore, non-cooperative strategic
environments as well as latent conflict situations are not conducive to solution finding.
Second, a well defined set of allocation alternatives is under consideration in the process
of decision making. However, this set is not exhaustive and therefore does not cover the
whole set of feasible policies that can be of potential interest. Due to short-sightedness,
the presence of vested interests as well as the inherent complexity of the management
policies under consideration, non-obvious intelligent management policies might very
well never have been considered within step 3) of a MCDM. In other words, policies
might be under consideration for which there exist better ones in a Pareto-sense.
Both of the above issues can be dealt with by state of the art multi-objective optimization
methods. Multi-objective optimization denotes the task to find a set Q* of Pareto-optimal
allocation policies p* Î Q in the sense that an improvement in one component of the
objective vector f ( p* ) can be achieved only at the expense of another component. More
precisely,
Q * := {p* Î Q $/ pˆ Î Q : f ( pˆ )
f ( p*)}
Traditional approaches of solving such problems relied on the aggregation of the
objectives into a single, parameterized goal function. The optimizer would then
systematically vary the parameters to achieve a set of solutions that approximate the
Pareto–optimal set. These approaches however are sensitive to the shape of the Pareto–
optimal front and generally do not exploit synergies between solutions that could help to
reduce computational time of the search (Deb 2001). This is a major drawback in cases
where the search space is conceivably complex as in the case of IWRM.
Multi-objective evolutionary algorithms (MOEA) on the contrary do not rely on the
availability of a common metric which makes individual goods, services and with that
objectives commensurable. These methods perform well in difficult search spaces
(Zitzler and Thiele 1999; Zitzler, Thiele et al. 2003; Siegfried 2004). The genetic
algorithm models the evolution of a population of policies p through successive
generations using three probabilistic operators: reproduction, crossover, and mutation.
The reproduction process serves to retain those strategies with high fitness i.e. favorable
objective f ( p ) , the cross over operator seeks to improve the design by combining the
high-fitness strategies, and the mutation operator protects against convergence to a local
minimum by adding random noise. The effect of these operators is that designs with high
fitness will persist as the management policies evolve from one generation to the next to
the final set of Pareto-optimal solutions.
Groundwater
Soil
Natural Resources
Structure & Function
Allocation Decision
Human Actions
(Private / Public)
Identification of
Suitable Compromise
Solution
Ecosystems
Pr
Fu odu
n c ct
tio ion
ns
Strategic Environment
Institutions / Political System
Natural Resources
Goods & Services
on
ati
fic eoffs
i
t
an d
Qu f Tra
O
Set of Pareto-Optimal
Allocation Policies
Identification of
Objectives
Surface
Water
Decisionmakers
Tradeoff Analysis
Preferences
Figure 2: Identification and quantification of policy options. Boxes denote spatially distributed system
models and their outcomes. The blue curved lines denote linkages by fluxes between system components.
Figure 2 shows a sketch of our approach to IWRM. Step 3 and 4 of the traditional
MCDM are replaced by multi-objective optimization. Converse to the MCDM, our
approach therefore carries out search before decision making. That is, optimization is
performed without any preference information by the decision-makers given (Hwang and
Masud 1979; Horn 1997)1. The set of Pareto-optimal solutions then provides the
necessary input for the subsequent decision-making process that is further support by the
methods from MCDM.
The impacts of a given allocation policy on goods and services from natural resources
and the objectives under consideration are difficult to assess since the natural resources
are complex, dynamic, variable, interconnected and show nonlinear response. Therefore,
the individual systems within the investigated catchment and their linkages shall be
approached by a component-based modeling approach (see Error! Reference source not
found. for an example of a set of relevant hydrological system components of a particular
catchment). Such top-down modeling has major advantages such as quick identification
of relevant processes on the catchment scale, modular component updating once more
detailed system models become available during the research project and ease of
coordination between individual work packages and across disciplines.
Zambezi River
Kafue River
Itezhitezhi
Dam
Lake Malawi
Kafue Flat
Wetland
Luangwa
River
Kafue
Dam
Shire River
700 m3/s
700 m3/s
Zambezi Delta
320 m3/s
1060 m3/s
2100 m3/s
Kariba Dam
3500 m3/s
Cahora Bassa
Dam
Figure 3: Schematic systems representation of the major features in the Zambezi catchment. Blue triangles
denote reservoirs and lakes whereas the green triangles show wetlands. The fluxes are annual averages.
Only major tributaries to the Zambezi are shown.
As with MCDM, our approach requires first the identification of objectives by all the
stakeholders involved in policymaking and those affected by such policy or with vested
interests respectively. Without being an exhaustive list, objectives may include




1
project costs [monetary unit] (min);
Δ hydropower production [kWh] (max);
Δ extent of irrigated area [km2] (max);
Δ crop production [t/a] (max) ;
Depending on how the optimization and search process are combined, multi-objective optimization
methods can be broadly classified into: 1) Decision making before search; 2) Search before decision
making and 3) Decision making during search.







Δ extension of flooded area in existing wetlands [km2] (max);
Δ average depth to groundwater in specific locations that are sensitive to
salination [m] (max);
number of people to be resettled [-] (min);
Δ mean annual downstream runoff [m3/a] (max);
sedimentation rate in reservoir [m3/a] (min)
estimated loss in biodiversity of downstream ecosystems [# species] (min)
...
The definition of objectives can be supported by preliminary results from the componentbased model as well as a stakeholder analysis as performed in step 1). As in the case of
the economic valuation approach, failure to include essential objectives in the
optimization approach can possibly lead to unacceptable results on the basin-scale. Note
that there exists no limitation with regard to the number of objectives under
consideration. One of the major difficulties in the presence of n objectives with n ³ 2 is
the task of visualization of the results for the purpose of communication optimization
outcomes.
Due to the stochastic nature of the systems under consideration, the quantification of
uncertainty is an important task so as to identify robust management policies. To search
for such policies, evolutionary algorithms should work on an expected objective vector
function by means of Monte Carlo integration (Jin and Branke 2005). Care, however,
must be taken that the problem remains computationally tractable since the evolutionary
optimization approaches require intense computational efforts. Therefore, the inherent
parallel nature of evolutionary computation should be exploited. Furthermore, subsequent
model evaluation results can be utilized to construct systems response functions. These
functions mimic the actual system models in an approximative manner. Iterative updating
of the response functions guarantees an increased quality of the approximation of the
individual approximations to the systems. This method is very flexible and capable of
handling most complex resource management problems (Rogers and Dowla 1994; Aly
and Peralta 1999; Zheng and Wang 2002).
In an ideal decision-making process of resource utilization, i.e. in case of complete
cooperation, decisions on regional, national or even supranational scales have to be based
on local resource characteristics and the aggregate knowledge about the resource. Such
commonly shared information then is determining local policy decisions of the
distribution of economic activity throughout the catchment. In case of fragmentation
however, that is in the prevalence of non-cooperative behavior and resource utilization
policies, information on the state of resources gets a private good since only partial
knowledge on the systems state within ones own political border can be obtained.
Furthermore, the other decision makers strategies remain uncertain. Even under the truly
hypothetical assumption of complete knowledge with regard to the state of the natural
systems and their dynamics, the resources appear stochastic in the absence of full
cooperation and information sharing (Varis 1997; Varis 1998).
From the decision makers perspective, the value of information therefore becomes an
important aspect in IWRM. Decision makers not only choose between policies based on
the amount of reward they get or on how these policies change the states of the systems
but also on how much information they provide (Kaelbling, Littman et al. 1998). This
implies that there is no analytical distinction to be drawn between individual actions
taken to change the systems states (such as the installation of a groundwater supply
system to cover demand) and actions taken to gain information (such as geoexploration).
To properly account for uncertainty and, with that, the value of information. Namely,
stochastic state transition models within an agent-based optimization have to be
implemented. In other words, future states are not known by certainty to a particular
decision-maker but rather perceived as probability distributions over states. State
transitions models in the case of a great number of agents (decision makers) can be
complex. For a compact representation of the former, dynamic Bayesian networks can be
utilized (Pearl 2001). Several studies in the field of AI have shown that in case of an
agent representation that incorporates probabilities for the unobserved aspects of the
resource state and the actions of the competitors, better overall performance can be
achieved than in the case of an implementation of purely logical agents which are situated
in a deterministic environment (for a comment on that see (Russell and Norvig 2003)).
In summary, by the combination of spatially distributed systems modeling with state of
the art optimization techniques and methods from the field of AI as well as MCDM, we
aim at the development of an Assessment Toolbox for large, water related projects on the
catchment scale. In particular, it will
 serve as a means to assess and quantify the implications of different policy option
from environmental, social, economic and political viewpoints.
 allow to test working procedures for integrating scientific assessment into
stakeholder analysis and political.
 be utilized as a descriptive as well as prescriptive tool. Descriptive because it
helps to explain the emergence of likely allocation policies within a certain
institutional and political environment in the catchment. Prescriptive in the sense
of a normative tool which can identify Pareto–optimal policy designs that,
compared to a baseline, are beneficiary for the rational decision makers if
adopted and thus constitutes a indispensable input to decision making.
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