Optimization for Sustainability of Integrated Ecological-Economic Model System of Planet Megan Schwarz Johns Hopkins University Dr. Diwekar July 1,

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 2 Sustainability: A path through time

Integrated Ecological-Economic Model System of Planet Non-Domestic Domestic Natural Resources Primary Producers (Plants) Herbivores Carnivores Human Households Energy Source Industrial Sector Energy Producer Biologically inaccessible resources Inaccessible Resource Pool Resource Pool P1 P2 H1 P3 H2 H3 C1C2 HH Energy Source IS EP 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). 3

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 4

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 5

Population Explosion Dynamics of Human Population and Primary Producer 2 6 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

Increase in Per Capita Consumption Dynamics 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 7

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 8

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 9

Objective Function 10

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 11 Optimal Design Initial Values Optimizer MODEL Decision Variables Objective Function Model Adapted from: Diwekar, Urmila M. Introduction to Applied Optimization. Norwell, MA: Kluwer Academic, Print.

Design of Techno-economic Policies for Sustainability 12

Governmental Policy Discharge fee charged to the industrial sector (pISHH) 13

14 Governmental Policy Discharge fee charged to the industrial sector (pISHH) No BioenergyBioenergy

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16 No BioenergyBioenergy

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18 BioenergyNo Bioenergy

Conclusions 19

Future Work Optimization using different control variables Multi-variable control Further model enhancement 20

Acknowledgments The financial support from the National Science Foundation, EEC-NSF Grant # is gratefully acknowledged Dr. Diwekar Kirti Yenkie Pahola Thathiana Benavides Professor Takoudis, Professor Jursich, REU program 21

References Cabezas, 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): 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): Elsevier B.V. Web. Diwekar, Urmila M. Introduction to Applied Optimization. Norwell, MA: Kluwer Academic, 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): 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, Print. "Report of the World Commission on Environment and Development Our Common Future."Brundtland Report 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): Elsevier B.V. Web. Shastri, Yogendra, Urmila Diwekar, and Heriberto Cabezas. "Optimal Control Theory for Sustainable Environmental Management." Environmental Science and Technology (2008): 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 (2008): American Chemical Society. Web. United States Census Bureau. U.S. Department of Commerce, n.d. Web. 01 July

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