Battling Arrow’s Paradox to Discover Robust Water Management Alternatives
Publication: Journal of Water Resources Planning and Management
Volume 142, Issue 2
Abstract
This study demonstrates how Arrow’s Impossibility Theorem, a theory of social choice, is of direct concern when formulating water-resources systems planning problems. Traditional strategies for solving multiobjective water resources problems typically aggregate multiple performance measures into single composite objectives (e.g., a priori preference weighting or grouping-like measures by category). Arrow’s Impossibility Theorem, commonly referred to as Arrow’s Paradox, implies that a subset of performance concerns will inadvertently dictate the properties of the optimized design alternative in unpredictable ways when using aggregated objectives. This study shows how many-objective planning can aid in battling Arrow’s Paradox. Many-objective planning explicitly disaggregates measures of performance while supporting the discovery of planning tradeoffs, using tools such as multiobjective evolutionary algorithms (MOEAs). An urban water portfolio planning case study for the Lower Rio Grande Valley, Texas is used to demonstrate how aggregate, lower objective-count formulations can adversely bias risk-based decision support. Additionally, this study employs a comprehensive diagnostic assessment of the Borg MOEA’s ability to address Arrow’s Paradox by enabling users to explore problem formulations with increasing numbers of objectives and decisions. Counter to conventional assumptions, the diagnostic analysis carefully documents that for modern self-adaptive MOEA searches, increasing objective counts can lead to more effective, efficient, reliable, and controllable searches. The increased objective counts are also shown to directly reduce decision biases that can emerge from problem formulation aggregation and simplification, related to Arrow’s Paradox.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was supported in part by the Extreme Science and Engineering Discovery Environment (XSEDE) supported by the National Science Foundation, and by the University of Texas Advanced Computing Center under Grant No. TG-EAR090013. The contributions of anonymous reviewers are also graciously acknowledged.
References
Anderson, T. L., and Hill, P. J., eds. (1997). Water marketing: The next generation, Rowman and Littlefield, Lanham, MD.
Andreu, J., Capilla, J., and Sanchis, E. (1996). “AQUATOOL, a generalized decision-support system for water-resources planning and operational management.” J. Hydrol., 177(3–4), 269–291.
Arnold, J. L. (1988). “The evolution of the 1936 flood control act.” U.S. Army Corps of Engineers, Fort Belvoir, VA.
Arrow, K. J. (1950). “A difficulty in the concept of social welfare.” J. Polit. Econ., 58(4), 328–346.
Bayer, P., de Paly, M., and Burger, C. M. (2010). “Optimization of high-reliability-based hydrological design problems by robust automatic sampling of critical model realizations.” Water Resour. Res., 46(5), in press.
Borsuk, M., Clemen, R., Maguire, L., and Reckhow, K. (2001). “Stakeholder values and scientific modeling in the neuse river watershed.” Group Decis. Neg., 10(4), 355–373.
Brockhoff, D., and Zitzler, E. (2006). “Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization.” Parallel problem solving from nature IX, T. Olivier, et al., eds., Springer, Berlin, 533–542.
Brockhoff, D., and Zitzler, E. (2007). “Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods.” IEEE Congress on Evolutionary Computation, CEC 2007, IEEE, 2086–2093.
Brockhoff, D., and Zitzler, E. (2009). “Objective reduction in evolutionary multiobjective optimization: Theory and applications.” Evol. Comput., 17(2), 135–166.
Brown, C., and Carriquiry, M. (2007). “Managing hydroclimatological risk to water supply with option contracts and reservoir index insurance.” Water Resour. Res., 43, W11423.
Chankong, V., and Haimes, Y. (1983). Multiobjective decision making: Theory and methodology, North-Holland, New York.
Characklis, G., Kirsch, B. R., Ramsey, J., Dillard, K., and Kelley, C. T. (2006). “Developing portfolios of water supply transfers.” Water Resour. Res., 42(5), W0540.
Characklis, G. W., Griffin, R. C., and Bedient, P. B. (1999). “Improving the ability of a water market to efficiently manage drought.” Water Resour. Res., 35(3), 823–831.
Coello Coello, C. A., Lamont, G. B., and Van Veldhuizen, D. A., eds. (2007). “Evolutionary algorithms for solving multi-objective problems.” Genetic and evolutionary computation, 2nd Ed., Springer, New York.
Cohon, J., and Marks, D. (1975). “A review and evaluation of multiobjective programming techniques.” Water Resour. Res., 11(2), 208–220.
Deb, K., and Saxena, D. K. (2006). “Searching for Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems.” 2006 IEEE Congress on Evolutionary Computation (CEC’2006), IEEE, 3353–3360.
Franssen, M. (2005). “Arrow’s theorem, multi-criteria decision problems and multi-attribute preferences in engineering design.” Res. Eng. Des., 16(1–2), 42–56.
Fu, G., Kapelan, Z., Kasprzyk, J., and Reed, P. (2013). “Optimal design of water distribution systems using many-objective visual analytics.” J. Water Resour. Plann. Manage., 624–633.
Galelli, S., and Castelletti, A. (2013). “Tree-based iterative input variable selection for hydrological modeling.” Water Resour. Res., 49(7), 4295–4310.
Gershon, M., and Duckstein, L. (1983). “Multiobjective approaches to river basin planning.” J. Water Resour. Plann. Manage., 13–28.
Giuliani, M., Galelli, S., and Soncini-Sessa, R. (2014a). “A dimensionality reduction approach for many-objective Markov decision processes: Application to a water reservoir operation problem.” Environ. Modell. Software, 57, 101–114.
Giuliani, M., Herman, J. D., Castelletti, A., and Reed, P. (2014b). “Many-objective reservoir policy identification and refinement to reduce policy inertia and myopia in water management.” Water Resour. Res., 50, 3355–3377.
Goldberg, D. E. (2002). The design of innovation: Lessons from and for competant genetic algorithms, Kluwer Academic, Boston.
Hadka, D., and Reed, P. (2012). “Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization.” Evol. Comput., 20(3), 423–452.
Hadka, D., and Reed, P. (2013). “Borg: An auto-adaptive many-objective evolutionary computing framework.” Evol. Comput., 21(2), 231–259.
Hadka, D., and Reed, P. (2015). “Large-scale parallelization of the borg multiobjective evolutionary algorithm to enhance the management of complex environmental systems.” Environ. Modell. Softw., 69, 353–369.
Haimes, Y. Y. (1977). Hierarchical analyses of water resources systems, modeling and optimization of large scale systems, McGraw-Hill, New York.
Hashimoto, T., Stedinger, J. R., and Loucks, D. P. (1982). “Reliability, resiliency and vulnerability criteria for water resource system performance evaluation.” Water Resour. Res., 18(1), 14–20.
Heidari, M., Chow, V. T., Kokotovic, P. V., and Meredith, D. D. (1971). “Discrete differential dynamic programming approach to water resources systems optimization.” Water Resour. Res., 7(2), 273–282.
Hitch, C. J. (1960). “On the choice of objectives in systems studies.”, RAND, Santa Monica, CA.
Huang, G. H., and Loucks, D. P. (2000). “An inexact two-stage stochastic programming model for water resources management under uncertainty.” Civ. Eng. Environ. Syst., 17(2), 95–118.
Inselberg, A. (1997). “Multidimensional detective.” Proc., IEEE Symp. on Information Visualization, 1997, IEEE, 100–107.
Jaimes, A. L., Coello, C. A. C., and Barrientos, J. E. U. (2009). “Online objective reduction to deal with many-objective problems.” Evolutionary multi-criterion optimization, M. Ehrgott, C. M. Fonseca, X. Gandibleux, J.-K. Hao, and M. Sevaux, eds., Springer, Berlin, 423–437.
Kasprzyk, J. R., Nataraj, S., Reed, P. M., and Lempert, R. J. (2013). “Many objective robust decision making for complex environmental systems undergoing change.” Environ. Modell. Software, 42, 55–71.
Kasprzyk, J. R., Reed, P. M., Characklis, G. W., and Kirsch, B. R. (2012). “Many-objective de novo water supply portfolio planning under deep uncertainty.” Environ. Modell. Software, 34, 87–104.
Kasprzyk, J. R., Reed, P. M., Kirsch, B. R., and Characklis, G. W. (2009). “Managing population and drought risks using many-objective water portfolio planning under uncertainty.” Water Resour. Res., 45(12), in press.
Keim, D. A., Kohlhammer, J., Ellis, G., and Mansmann, F., eds. (2010). Mastering the information age—Solving problems with visual analytics, Eurographics Association, Goslar, Germany.
Kirsch, B. R., Characklis, G. W., Dillard, K. E. M., and Kelley, C. T. (2009). “More efficient optimization of long-term water supply portfolios.” Water Resour. Res., 45(3), W03414.
Knowles, J., and Corne, D. (2002). “On metrics for comparing non-dominated sets.” Proc., 2002 World Congress on Computational Intelligence (WCCI), IEEE, 711–716.
Kollat, J. B., and Reed, P. M. (2006). “Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design.” Adv. Water Resour., 29(6), 792–807.
Kollat, J. B., and Reed, P. M. (2007). “A framework for visually interactive decision-making and design using evolutionary multiobjective optimization (VIDEO).” Environ. Modell. Software, 22(12), 1691–1704.
Labadie, J. W. (2004). “Optimal operation of multireservoir systems: State-of-the-art review.” J. Water Resour. Plann. Manage., 93–111.
Laumanns, M. (2002). “Combining convergence and diversity in evolutionary multiobjective optimization.” Evol. Comput., 10(3), 263–282.
López Jaimes, A., Coello Coello, C. A., and Chakraborty, D. (2008). “Objective reduction using a feature selection technique.” Proc., 10th Annual Conf. on Genetic and Evolutionary Computation, Association for Computing Machinery (ACM), New York, 673–680.
Lund, J. R., and Israel, M. (1995). “Optimization of transfers in urban water supply planning.” J. Water Resour. Plann. Manage., 41–48.
Maier, H., et al. (2014). “Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions.” Environ. Modell. Software, 62, 271–299.
May, R. J., Dandy, G. C., Maier, H. R., and Nixon, J. B. (2008a). “Application of partial mutual information variable selection to ANN forecasting of water quality in water distribution systems.” Environ. Modell. Software, 23(10–11), 1289–1299.
May, R. J., Maier, H. R., Dandy, G. C., and Fernando, T. M. K. G. (2008b). “Non-linear variable selection for artificial neural networks using partial mutual information.” Environ. Modell. Software, 23(10–11), 1312–1326.
Nicklow, J. (2010). “State of the art for genetic algorithms and beyond in water resources planning and management.” J. Water Resour. Plann. Manage., 412–432.
Palmer, R. N., and Characklis, G. W. (2009). “Reducing the costs of meeting regional water demand through risk-based transfer agreements.” J. Environ. Manage., 90(5), 1703–1714.
Palmer, R. N., and Lund, J. R. (1985). “Multi-objective analysis with subjective information.” J. Water Resour. Plann. Manage., 399–416.
Reed, P., Hadka, D., Herman, J., Kasprzyk, J., and Kollat, J. (2013). “Evolutionary multiobjective optimization in water resources: The past, present and future.” Adv. Water Resour., 51, 438–456.
Reed, P. M., and Hadka, D. (2014). “Evolving many-objective water management to exploit exascale computing.” Water Resour. Res., 50(10), 8367–8373.
Reed, P. M., and Kasprzyk, J. R. (2009). “Water resources management: The myth, the wicked, and the future.” J. Water Resour. Plann. Manage., 411–413.
Reuss, M. (2005). “Ecology, planning, and river management in the United States: Some historical reflections.” Ecol. Soc., 10(1), 34.
Singh, A., and Minsker, B. S. (2008). “Uncertainty-based multiobjective optimization of groundwater remediation design.” Water Resour. Res., 44(2), W02404.
Smith, M. G., and Marin, C. M. (1993). “Analysis of short-run domestic water supply transfers under uncertainty.” Water Resour. Res., 29(8), 2909–2916.
Teytaud, O. (2007). “On the hardness of offline multi-objective optimization.” Evol. Comput., 15(4), 475–491.
Tsoukias, A. (2008). “From decision theory to decision aiding methodology.” Eur. J. Oper. Res., 187(1), 138–161.
U.S. Council on Environmental Quality. (2013). “Principles and requirements for federal investments in water resources.”.
van Veldhuizen, D. A., and Lamont, G. B. (1998). “Evolutionary computation and convergence to a Pareto front.” Proc., 3rd Annual Conf.Genetic Programming 1998, J. R. Koza, W. Banzhaf, K. Chellapilla, K. Deb, M. Dorigo, and D. B. Fogel, eds., Morgan Kaufmann, San Francisco, 22–25.
van Werkhoven, K., Wagener, T., Reed, P., and Tang, Y. (2009). “Sensitivity-guided reduction of parametric dimensionality for multi-objective calibration of watershed models.” Adv. Water Resour., 32(8), 1154–1169.
Vaux Jr., H. J., and Howitt, R. E. (1984). “Managing water scarcity: An evaluation of interregional transfers.” Water Resour. Res., 20(7), 785–792.
Vrugt, J. A., and Robinson, B. A. (2007). “Improved evolutionary optimization from genetically adaptive multimethod search.” Proc. Natl. Acad. Sci., 104(3), 708–711.
Watkins Jr., D. W., McKinney, D. C. (1997). “Finding robust solutions to water resources problems.” J. Water Resour. Plann. Manage., 49–58.
Woodruff, M., Hadka, D., Reed, P. M., and Simpson, T. W. (2012). “Auto-adaptive search capabilities of the new Borg MOEA: A detailed comparison on alternative product family design problem formulations.” 14th AIAA/ISSMO Multidisicplinary Analysis and Optimization Conf., American Institute of Aeronautics and Astronautics (AIAA), Reston, VA.
Woodruff, M. J., Reed, P. M., and Simpson, T. (2013). “Many objective visual analytics: Rethinking the design of complex engineered systems.” Struct. Multidiscip. Optim., 48(1), 201–219.
Zeff, H. B., and Characklis, G. W. (2013). “Managing water utility financial risks through third-party index insurance contracts.” Water Resour. Res., 49(8), 4939–4951.
Zeff, H. B., Kasprzyk, J. R., Herman, J. D., Reed, P. M., and Characklis, G. W. (2014). “Navigating financial and supply reliability tradeoffs in regional drought management portfolios.” Water Resour. Res., 50, 4906–4923.
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C. M., and Grunert da Fonseca, V. (2003). “Performance assessment of multiobjective optimizers: An analysis and review.” IEEE Trans. Evol. Comput., 7(2), 117–132.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 142 • Issue 2 • February 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jul 24, 2014
Accepted: Jun 3, 2015
Published online: Sep 1, 2015
Published in print: Feb 1, 2016
Discussion open until: Feb 1, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.