optimization for sustainability of integrated ecological-economic model system of planet
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Optimization for Sustainability of Integrated Ecological-Economic Model System of Planet
Megan SchwarzJohns Hopkins UniversityDr. DiwekarJuly 1, 2013
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What is Sustainability?• “The development that
meets the needs of the present without compromising the ability of future generations to meet their own needs” (Brundtland 1987)
• Goal: To design a simplified model of the planet to explore regulatory strategies to try to increase sustainability
Heriberto Cabezas, Christopher W. Pawlowski, Audrey L. Mayer, N. Theresa Hoagland Clean Techn Environ Policy 5 (2003) 167–180
Sustainability: A path through time
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Integrated Ecological-Economic Model System of Planet
Non-D
omestic
Dom
estic
Natural Resources
Primary Producers (Plants)
Herbivores
Carnivores
Human Households
Energy Source
Industrial Sector
Energy Producer
Biologically inaccessible resourcesInaccessible Resource Pool
Resource Pool
P1 P2
H1
P3
H2 H3
C1 C2
HHEnergy Source
IS EP
fence
fence
grazing
Model Adapted from Kotecha, P.; Diwekar, U.; Cabezas, H.. “Model-based approach to study the impact of biofuels on the sustainability of an ecological system” (2011).
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Basic Mathematics of the Model•Three general types of equations
▫Basic food web model equations▫Macroeconomic model equations▫All other algebraic equations
98 constant parameters 19 time dependent state variables described
by differential equations 61 model outputs About 2000 lines of code in Matlab
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Model Simulation•Looked at how economic and ecological
parameters changed over a time period of 200 years with and without the use of biofuel as a source of energy
•Two different scenarios▫Population Explosion▫Increase in Per Capita Consumption
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Population ExplosionDynamics of Human Population and Primary Producer 2
• The population is expected to peak to about twice today’s size in the next 50 t0 100 years
• A steady drop is then expected due to an aging population and a decrease in fertility rates
• Primary producer 2 was the only ecological compartment to reach extinction
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Increase in Per Capita ConsumptionDynamics of Carnivore 1 and Human Population
• Consumption of many resources is estimated to increase by approximately 50% in the next 50 years
• Most ecological compartments reached extinction
• Shows the catastrophe where limited resources cause loss of human life▫ Decrease in population
sooner with the use of biofuels because compartments reach extinction earlier
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Conclusions about Model Simulation•Sustainability of even a simple ecosystem
may not be intuitive▫Use of biomass as a source of energy
accelerates the extinction of species•Increasing per capita consumption is
more critical than population explosion▫The ecosystem can’t sustain high levels of
human consumption
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Numerical Optimization•Goal: increase the lifetime of dying
compartments▫Increase sustainability of the system
•Need a mathematical measure of sustainability▫Fisher Information (FI) ▫FI can be used as a measure of order of a
system Information is a fundamental quantity of a
system Able to incorporate the physics and economics
of the model
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Objective Function•Objective: develop policies so the system
FI is close to the FI of a stable system▫Base case scenario
•Objective Function: minimization of the FI variance:
▫ is the current FI profile▫ is the targeted FI for the stable base
case scenario▫T is the total time under consideration
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Numerical Optimization: Non-linear Programming (NLP)
• Initial values of the decision variable are known
• The model calculates the objective function and the optimizer tries to satisfy optimality conditions (Karush-Kuhn-Tucker conditions, KKT)
• Optimizer calculates a new value for the decision variable
• Iterative sequence continues until the optimization criteria (KKT) are met
Optimal Design Initial Values
Optimizer
MODEL
Decision Variables
Objective Function
Model Adapted from: Diwekar, Urmila M. Introduction to Applied Optimization. Norwell, MA: Kluwer Academic, 2003. Print.
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Design of Techno-economic Policies for Sustainability
• Policies (control variables) are used as the decision variables at each time step
• Governmental Policies:▫ Discharge fee charged to the
industrial sector (pISHH)▫ Amount of primary producer
2 consumed by herbivore 1 through grazing
• Policy related to Efficiency of Technology:
▫ Amount of primary producer 1 required to produce a unit of the industrial sector product
0-5
10-1
520
-25
30-3
540
-45
50-5
560
-65
70-7
580
-85
90-9
510
0-10
511
0-11
512
0-12
513
0-13
514
0-14
515
0-15
516
0-16
517
0-17
518
0-18
519
0-19
5
0.0E+00
2.0E-02
4.0E-02
6.0E-02
8.0E-02
1.0E-01
1.2E-01
1.4E-01
Controlled Efficiency Policy Variable (theta) for Discretized Time Period (no bioenergy)
Time, years
Thet
a
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Governmental PolicyDischarge fee charged to the industrial sector (pISHH)
0 20 40 60 80 100 120 140 160 180 2000.00E+00
2.00E-08
4.00E-08
6.00E-08
8.00E-08
1.00E-07
1.20E-07
Uncontrolled and Controlled Discharge Fee for Increase in Per Capita Consumption Scenario (no bioenergy)
Controlled Discharge Fee Uncontrolled Discharge Fee
Time, years
Disc
harg
e Fe
e
0 20 40 60 80 100 120 140 160 180 2000.00E+00
2.00E-08
4.00E-08
6.00E-08
8.00E-08
1.00E-07
1.20E-07
Uncontrolled and Controlled Discharge Fee for Increase in Per Capita Consumption Scenario (bioenergy)
Controlled Discharge Fee Uncontrolled Discharge Fee
Time, years
Disc
harg
e Fe
e
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Governmental PolicyDischarge fee charged to the industrial sector (pISHH)
No Bioenergy
Bioenergy
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Policy Related to Efficiency of TechnologyAmount of primary producer 1 to produce a unit of the industrial sector product
0 20 40 60 80 100 120 140 160 180 2000.00E+00
2.00E-02
4.00E-02
6.00E-02
8.00E-02
1.00E-01
1.20E-01
1.40E-01
Uncontrolled and Controlled Theta for Increase in Per Capita Con-sumption Scenario (no bioenergy)
Controlled Theta Uncontrolled Theta
Time, years
Thet
a
0 20 40 60 80 100 120 140 160 180 2000.00E+00
1.00E-01
2.00E-01
3.00E-01
4.00E-01
5.00E-01
6.00E-01
7.00E-01
Uncontrolled and Controlled Discharge Fee for Increase in Per Capita Consumption Scenario (bioenergy)
Controlled Theta Uncontrolled Theta
Time, years
Thet
a
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Policy Related to Efficiency of TechnologyAmount of primary producer 1 to produce a unit of the industrial sector product
No Bioenergy
Bioenergy
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0 20 40 60 80 100 120 140 160 180 2000.00E+00
2.00E-02
4.00E-02
6.00E-02
8.00E-02
1.00E-01
1.20E-01
1.40E-01
Uncontrolled and Controlled Khat for Increase in Per Capita Consumption Scenario (no bioenergy)
Controlled khat Uncontrolled khat
Time, years
Khat
Governmental PolicyThe amount of primary producer 2 consumed by herbivore 1 through grazing
0 20 40 60 80 100 120 140 160 180 2000.00E+00
2.00E-02
4.00E-02
6.00E-02
8.00E-02
1.00E-01
1.20E-01
Uncontrolled and Controlled Khat for Increase in Per Capita Consumption Scenario (bioenergy)
Controlled khat Uncontrolled khat
Time, years
Khat
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Governmental PolicyThe amount of primary producer 2 consumed by herbivore 1 through grazing
Bioenergy
No Bioenergy
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Conclusions• Fisher Information is an indicator of
sustainability of a system▫The discharge fee charged to the industrial
sector is most effective in delaying the extinction of dying compartments
▫The amount of primary producer 1 required to produce a unit of the industrial sector product leads to small delays in the extinction of dying compartments
▫does not lead to any significant improvement in the model dynamics
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Future Work•Optimization using different control
variables•Multi-variable control•Further model enhancement
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Acknowledgments•The financial support from the National
Science Foundation, EEC-NSF Grant # 1062943 is gratefully acknowledged
•Dr. Diwekar•Kirti Yenkie•Pahola Thathiana Benavides•Professor Takoudis, Professor Jursich,
REU program
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ReferencesCabezas, H., C. W. Pawlowski, A. L. Mayer, and H. W. Whitmore. "On the Sustainability of Integrated Model
Systems with Industrial, Ecological, and Macroeconomic Components." Resources, Conservation and
Recycling 50.2 (2007): 122-29. Elsevier B.V. Web.Cabezas, Heriberto, N. Theresa Hoagland, Audrey L. Mayer, and Christopher W. Pawlowski. "Simulated Experiments with
Complex Sustainable Systems: Ecology and Technology." Resources, Conservation and Recycling 44 (2005): 279-91.
Elsevier B.V. Web.Diwekar, Urmila M. Introduction to Applied Optimization. Norwell, MA: Kluwer Academic, 2003. Print. "Finite Difference Schemes." Computational Fluid Dynamics. Brown University, n.d. Web.Kotecha, Prakash, Urmila Diwekar, and Heriberto Cabezas. "Model-based Approach to Study the Impact of Biofuels on the
Sustainability of an Ecological System." Clean Technology and Environmental Policy 15.1 (2013): 21-33. Springer
Verlag. Web.Meadows, Donella H., Dennis L. Meadows, and Jørgen Randers. Beyond the Limits: Confronting Global Collapse, Envisioning
a Sustainable Future. Vermont: Chelsea Green, 1992. Print."Report of the World Commission on Environment and Development Our Common Future."Brundtland Report 1987. United
Nations, n.d. Web.Shastri, Y., and U. Diwekar. "Sustainable Ecosystem Management Using Optimal Control Theory: Part 1 (Deterministic
Systems)." Journal of Theoretical Biology 241 (2006): 506-21. Elsevier B.V. Web.Shastri, Yogendra, Urmila Diwekar, and Heriberto Cabezas. "Optimal Control Theory for Sustainable Environmental
Management." Environmental Science and Technology 42.14 (2008): 5322-328. American Chemical Society. Web.Shastri, Yogendra, Urmila Diwekar, Heriberto Cabezas, and James Williamson. "Is Sustainability Achievable? Exploring the
Limits of Sustainability with Model Systems." Environmental Science and Technology 42.17 (2008): 6710-716. American
Chemical Society. Web.United States Census Bureau. U.S. Department of Commerce, n.d. Web. 01 July 2013.
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Questions?
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•Time average FI for a system with n species:
• = cycle time•
• and are the velocity and acceleration terms of the ecosystem
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