Diagnostic Assessment of Preference Constraints for Simulation Optimization in Water Resources
Publication: Journal of Water Resources Planning and Management
Volume 144, Issue 8
Abstract
Simulation-optimization frameworks, such as multiobjective evolutionary algorithms (MOEAs), are increasingly used for real-world water resources problems. Constraints in MOEA optimization commonly represent decision maker preference, which differs from their role in classical optimization. As a result, constraints are often considered an optional aspect of the problem formulation. However, the impact of including constraints on optimization search has not been rigorously examined. This study explores how constraints impact the effectiveness, efficiency, and consistency of MOEA optimization for two water resources problems. For each problem, algorithm performance metrics are compared for two cases: (1) with constraints included during search, eliminating solutions that do not meet preference requirements, and (2) with constraints applied a posteriori to filter the full set of solutions. Results show that constraints aid in the search process by favoring solutions that meet decision maker preferences, despite the increased difficulty of finding feasible solutions. This study highlights the importance of constraints in the problem formulation for simulation-optimization applications in water resources, balancing the performance of search algorithms with the decision relevance of the solution set.
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Acknowledgments
Clarkin was supported by the Science, Mathematics, and Research for Transformation (SMART) Scholarship-for-Service Program, and Raseman and Kasprzyk were supported by a grant from the US Environmental Protection Agency’s Science to Achieve Results (STAR) program. The work used the Janus supercomputer, which is supported by the National Science Foundation (Award No. CNS-0821794) and the University of Colorado Boulder, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation (Grant No. ACI-1053575). The content in this paper is solely the responsibility of the authors and does not necessarily represent the official views of the funding agencies. We also thank David Hadka, who supported MOEA implementation, as well as Patrick Reed for productive conversations on the approach.
References
Asefa, T. 2015. “Innovative systems-based decision support: Tales for the real world.” J. Water Resour. Plann. Manage. 141 (9): 01815001. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000565.
Basdekas, L. 2014. “Is multiobjective optimization ready for water resources practitioners? Utility’s drought policy investigation.” J. Water Resour. Plann. Manage. 140 (3): 275–276. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000415.
Brozović, N., and W. Schlenker. 2011. “Optimal management of an ecosystem with an unknown threshold.” Ecol. Econ. 70 (4): 627–640. https://doi.org/10.1016/j.ecolecon.2010.10.001.
Carpenter, S., and K. Cottingham. 1997. “Resilience and restoration of lakes.” Ecol. Soc. 1 (1): 2 https://doi.org/10.5751/ES-00020-010102.
Carpenter, S. R., D. Ludwig, and W. A. Brock. 1999. “Management of eutrophication for lakes subject to potentially irreversible change.” Ecol. Appl. 9 (3): 751–771. https://doi.org/10.1890/1051-0761(1999)009%5B0751:MOEFLS%5D2.0.CO;2.
Characklis, G. W., R. C. Griffin, and P. B. Bedient. 1999. “Improving the ability of a water market to efficiently manage drought.” Water Resour. Res. 35 (3): 823–831. https://doi.org/10.1029/1998WR900094.
Characklis, G. W., B. R. Kirsch, J. Ramsey, K. E. M. Dillard, and C. T. Kelley. 2006. “Developing portfolios of water supply transfers: Portfolios of water supply transfers.” Water Resour. Res. 42 (5): W05403. https://doi.org/10.1029/2005WR004424.
Coello, C. A. C. 2002. “Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art.” Comput. Meth. Appl. Mech. Eng. 191 (11–12): 1245–1287. https://doi.org/10.1016/S0045-7825(01)00323-1.
Coello, C. A. C., G. B. Lamont, and D. A. V. Veldhuizen, eds. 2007. “Evolutionary algorithms for solving multi-objective problems.” In Genetic and evolutionary computation. New York: Springer.
Coello, C. A. C., and E. M. Montes. 2002. “Constraint-handling in genetic algorithms through the use of dominance-based tournament selection.” Adv. Eng. Inf. 16 (3): 193–203. https://doi.org/10.1016/S1474-0346(02)00011-3.
Cohon, J. L., and D. H. Marks. 1975. “A review and evaluation of multiobjective programming techniques.” Water Resour. Res. 11 (2): 208–220. https://doi.org/10.1029/WR011i002p00208.
Costa, A. L. H., J. L. de Medeiros, and F. L. P. Pessoa. 2001. “Global optimization of water distribution networks through a reduced space branch-and-bound search.” Water Resour. Res. 37 (4): 1083–1090. https://doi.org/10.1029/2000WR900267.
Deb, K. 2000. “An efficient constraint handling method for genetic algorithms.” Comput. Methods Appl. Mech. Eng. 186 (2–4): 311–338. https://doi.org/10.1016/S0045-7825(99)00389-8.
Deb, K., and H. Gupta. 2006. “Introducing robustness in multi-objective optimization.” Evolut. Comput. 14 (4): 463–494. https://doi.org/10.1162/evco.2006.14.4.463.
Deb, K., A. Pratap, S. Agarwal, and T. Meyarivan. 2002. “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Trans. Evol. Comput. 6 (2): 182–197. https://doi.org/10.1109/4235.996017.
Deb, K., A. Pratap, and T. Meyarivan. 2001. “Constrained test problems for multi-objective evolutionary optimization.” In Evolutionary multi-criterion optimization, 284–298. Chichester, UK: Wiley.
Digabel, S. L., and S. M. Wild. 2015. “A taxonomy of constraints in simulation-based optimization.” Preprint, http://arxiv.org/abs/1505.07881.
Fenicia, F., H. H. G. Savenije, P. Matgen, and L. Pfister. 2007. “A comparison of alternative multiobjective calibration strategies for hydrological modeling.” Water Resour. Res. 43 (3): W03434. https://doi.org/10.1029/2006WR005098.
Gibbs, M. S., H. R. Maier, and G. C. Dandy. 2010. “Comparison of genetic algorithm parameter setting methods for chlorine injection optimization.” J. Water Resour. Plann. Manage. 136 (2): 288–291. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000033.
Hadka, D., and P. Reed. 2012. “Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization.” Evol. Comput. 20 (3): 423–452. https://doi.org/10.1162/EVCO_a_00053.
Hadka, D., and P. Reed. 2013. “Borg: An auto-adaptive many-objective evolutionary computing framework.” Evol. Comput. 21 (2): 231–259. https://doi.org/10.1162/EVCO_a_00075.
Hadka, D., and P. Reed. 2015. “Large-scale parallelization of the Borg multiobjective evolutionary algorithm to enhance the management of complex environmental systems.” Environ. Modell. Software 69: 353–369. https://doi.org/10.1016/j.envsoft.2014.10.014.
Hall, J. W., R. J. Lempert, K. Keller, A. Hackbarth, C. Mijere, and D. J. McInerney. 2012. “Robust climate policies under uncertainty: A comparison of robust decision making and info-gap methods.” Risk Anal. 32 (10): 1657–1672. https://doi.org/10.1111/j.1539-6924.2012.01802.x.
Harik, G. R. 1995. “Finding multimodal solutions using restricted tournament selection.” In Proc., 6th Int. Conf. on Genetic Algorithms, 24–31. San Francisco, CA: Morgan Kaufmann Publishers, Inc.
Hashimoto, T., J. R. Stedinger, and D. P. Loucks. 1982. “Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation.” Water Resour. Res. 18 (1): 14–20. https://doi.org/10.1029/WR018i001p00014.
Hinks, R. W. 1980. “Reliability constrained capacity expansion planning of water resource systems.” Adv. Water Resour. 3 (3): 99–105. https://doi.org/10.1016/0309-1708(80)90053-6.
Ikeda, K., H. Kita, and S. Kobayashi. 2001. “Failure of Pareto-based MOEAs: Does non-dominated really mean near to optimal?” In Proc., 2001 Congress on Evolutionary Computation, 957–962. New York: IEEE.
Inselberg, A. 1997. “Multidimensional detective.” In Proc., IEEE Symp. on Information Visualization, 100–107. New York: IEEE.
Kasprzyk, J. R., S. Nataraj, P. M. Reed, and R. J. Lempert. 2013. “Many objective robust decision making for complex environmental systems undergoing change.” Environ. Modell. Software 42: 55–71. https://doi.org/10.1016/j.envsoft.2012.12.007.
Kasprzyk, J. R., P. M. Reed, G. W. Characklis, and B. R. Kirsch. 2012. “Many-objective de Novo water supply portfolio planning under deep uncertainty.” Environ. Modell. Software 34: 87–104. https://doi.org/10.1016/j.envsoft.2011.04.003.
Kasprzyk, J. R., P. M. Reed, and D. Hadka. 2016. “Battling arrow’s paradox to discover robust water management alternatives.” J. Water Resour. Plann. Manage. 142 (2): 04015053. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000572.
Kasprzyk, J. R., P. M. Reed, B. R. Kirsch, and G. W. Characklis. 2009. “Managing population and drought risks using many-objective water portfolio planning under uncertainty: Many-objective water portfolios.” Water Resour. Res. 45 (12): 7692–7713. https://doi.org/10.1029/2009WR008121.
Kenney, D. S., R. A. Klein, and M. P. Clark. 2004. “Use and effectiveness of municipal water restrictions during drought in Colorado.” J. Am. Water Resour. Assoc. 40 (1): 77–87. https://doi.org/10.1111/j.1752-1688.2004.tb01011.x.
Kirsch, B. R., G. W. Characklis, K. E. M. Dillard, and C. T. Kelley. 2009. “More efficient optimization of long-term water supply portfolios: Optimization of long-term water supply portfolios.” Water Resour. Res. 45 (3): W03414. https://doi.org/10.1029/2008WR007018.
Kollat, J. B., and P. Reed. 2007a. “A framework for visually interactive decision-making and design using evolutionary multi-objective optimization (VIDEO).” Environ. Modell. Software 22 (12): 1691–1704. https://doi.org/10.1016/j.envsoft.2007.02.001.
Kollat, J. B., and P. M. Reed. 2006. “Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design.” Adv. Water Resour. 29 (6): 792–807. https://doi.org/10.1016/j.advwatres.2005.07.010.
Kollat, J. B., and P. M. Reed. 2007b. “A computational scaling analysis of multiobjective evolutionary algorithms in long-term groundwater monitoring applications.” Adv. Water Resour. 30 (3): 408–419. https://doi.org/10.1016/j.advwatres.2006.05.009.
Lempert, R. J., and M. T. Collins. 2007. “Managing the risk of uncertain threshold responses: Comparison of robust, optimimum, and precautionary approaches.” Risk Anal. 27 (4): 1009–1026. https://doi.org/10.1111/j.1539-6924.2007.00940.x.
Lerma, N., J. Paredes-Arquiola, J. Andreu, A. Solera, and G. M. Sechi. 2015. “Assessment of evolutionary algorithms for optimal operating rules design in real water resource systems.” Environ. Modell. Software 69: 425–436. https://doi.org/10.1016/j.envsoft.2014.09.024.
Liebman, J. C. 1976. “Some simple-minded observations on the role of optimization in public systems decision-making.” Interfaces 6 (4): 102–108. https://doi.org/10.1287/inte.6.4.102.
Maier, H. R., et al. 2014. “Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions.” Environ. Modell. Software 62: 271–299. https://doi.org/10.1016/j.envsoft.2014.09.013.
Medaglia, A. L., S. B. Graves, and J. L. Ringuest. 2007. “A multiobjective evolutionary approach for linearly constrained project selection under uncertainty.” Eur. J. Oper. Res. 179 (3): 869–894. https://doi.org/10.1016/j.ejor.2005.03.068.
Michalewicz, Z., and M. Schoenauer. 1996. “Evolutionary algorithms for constrained parameter optimization problems.” Evol. Comput. J. 4 (1): 1–32. https://doi.org/10.1162/evco.1996.4.1.1.
Nicklow, J., et al. 2010. “State of the art for genetic algorithms and beyond in water resources planning and management.” J. Water Resour. Plann. Manage. 136 (4): 412–432. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000053.
Peterson, G., S. Carpenter, and W. A. Brock. 2003. “Uncertainty and the management of multistate ecosystems: An apparently rational route to collapse.” Ecology 84 (6): 1403–1411. https://doi.org/10.1890/0012-9658(2003)084%5B1403:UATMOM%5D2.0.CO;2.
Piscopo, A. N., J. R. Kasprzyk, and R. M. Neupauer. 2015. “An iterative approach to multi-objective engineering design: Optimization of engineered injection and extraction for enhanced groundwater remediation.” Environ. Modell. Software 69: 253–261. https://doi.org/10.1016/j.envsoft.2014.08.030.
Purshouse, R. C., and P. J. Fleming. 2007. “On the evolutionary optimization of many conflicting objectives.” IEEE Trans. Evol. Comput. 11 (6): 770–784. https://doi.org/10.1109/TEVC.2007.910138.
Reed, P. M., D. Hadka, J. D. Herman, J. R. Kasprzyk, and J. B. Kollat. 2013. “Evolutionary multiobjective optimization in water resources: The past, present and future.” Adv. Water Resour. 51: 438–456. https://doi.org/10.1016/j.advwatres.2012.01.005.
Reuss, M. 2003. “Is it time to resurrect the Harvard water program?” J. Water Resour. Plann. Manage. 129 (5): 357–360. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:5(357).
Rogers, P. 1969. “A game theory approach to the problems of international river basins.” Water Resour. Res. 5 (4): 749–760. https://doi.org/10.1029/WR005i004p00749.
Rogers, P. P., and M. B. Fiering. 1986. “Use of systems analysis in water management.” Water Resour. Res. 22 (9S): 146S–158S. https://doi.org/10.1029/WR022i09Sp0146S.
Singh, R., P. M. Reed, and K. Keller. 2015. “Many-objective robust decision making for managing an ecosystem with a deeply uncertain threshold response.” Ecol. Soc. 20 (3): 1–32. https://doi.org/10.5751/ES-07687-200312.
Smith, R., J. Kasprzyk, and E. Zagona. 2016. “Many objective analysis to optimize pumping and releases in multireservoir water supply network.” J. Water Resour. Plann. Manage. 142 (2): 04015049. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000576.
Swan, R., M. Sterling, and J. Bridgeman. 2017. “Optimisation of water treatment works performance using genetic algorithms.” J. Hydroinf. 19 (5): 719–733. https://doi.org/10.2166/hydro.2017.083.
Thierens, D., D. E. Goldberg, and A. G. Pereira. 1998. “Domino convergence, drift, and the temporal-salience structure of problems.” In Proc., IEEE Int. Conf. on Evolutionary Computation, 535–540. New York: IEEE.
Ward, V. L., R. Singh, P. M. Reed, and K. Keller. 2015. “Confronting tipping points: Can multi-objective evolutionary algorithms discover pollution control tradeoffs given environmental thresholds?” Environ. Modell. Software 73: 27–43. https://doi.org/10.1016/j.envsoft.2015.07.020.
Watkins, D. W., and D. C. McKinney. 1997. “Finding robust solutions to water resources problems.” J. Water Resour. Plann. Manage. 123 (1): 49–58. https://doi.org/10.1061/(ASCE)0733-9496(1997)123:1(49).
Watson, A. A., and J. R. Kasprzyk. 2017. “Incorporating deeply uncertain factors into the many objective search process.” Environ. Modell. Software 89: 159–171. https://doi.org/10.1016/j.envsoft.2016.12.001.
Wetzel, R. G. 1983. Limnology. Philadelphia, PA: Saunders.
Wu, W., H. R. Maier, G. C. Dandy, R. Leonard, K. Bellette, S. Cuddy, and S. Maheepala. 2016. “Including stakeholder input in formulating and solving real-world optimisation problems: Generic framework and case study.” Environ. Modell. Software 79: 197–213. https://doi.org/10.1016/j.envsoft.2016.02.012.
Zatarain Salazar, J., P. M. Reed, J. D. Herman, M. Giuliani, and A. Castelletti. 2016. “A diagnostic assessment of evolutionary algorithms for multi-objective surface water reservoir control.” Adv. Water Resour. 92: 172–185. https://doi.org/10.1016/j.advwatres.2016.04.006.
Zeff, H. B., J. R. Kasprzyk, J. D. Herman, P. M. Reed, and G. W. Characklis. 2014. “Navigating financial and supply reliability tradeoffs in regional drought management portfolios.” Water Resour. Res. 50 (6): 4906–4923. https://doi.org/10.1002/2013WR015126.
Zeleny, M. 1981. “On the squandering of resources and profits via linear programming.” Interfaces 11 (5): 101–107. https://doi.org/10.1287/inte.11.5.101.
Zheng, F., A. R. Simpson, and A. C. Zecchin. 2011. “A combined NLP-differential evolution algorithm approach for the optimization of looped water distribution systems.” Water Resour. Res. 47 (8): W08531. https://doi.org/10.1029/2011WR010394.
Zheng, F., A. C. Zecchin, H. R. Maier, and A. R. Simpson. 2016. “Comparison of the searching behavior of NSGA-II, SAMODE, and Borg MOEAs applied to water distribution system design problems.” J. Water Resour. Plann. Manage. 142 (7): 04016017. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000650.
Zitzler, E., L. Thiele, M. Laumanns, C. Fonseca, and V. Grunert da Fonseca. 2003. “Performance assessment of multiobjective optimizers: An analysis and review.” IEEE Trans. Evol. Comput. 7 (2): 117–132. https://doi.org/10.1109/TEVC.2003.810758.
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Journal of Water Resources Planning and Management
Volume 144 • Issue 8 • August 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jun 9, 2017
Accepted: Jan 3, 2018
Published online: May 18, 2018
Published in print: Aug 1, 2018
Discussion open until: Oct 18, 2018
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