An active learning approach for identifying the smallest subset of informative scenarios for robust planning under deep uncertainty

Abstract Deep uncertainty in future climate, socio-economic and technological conditions poses a great challenge to medium-long term decision making. Recently, several approaches have been proposed to identify solutions that are robust with respect to a large ensemble of deeply uncertain future scenarios. In this paper, we introduce ROSS (Robust Optimal Scenario Selection), a novel algorithm that uses an active learning approach for adaptively selecting the smallest scenario subset to be included into a robust optimization process. ROSS contributes a twofold novelty in the field of robust optimization under deep uncertainty. First, it allows the computational requirements for the generation of robust solutions to be considerably reduced with respect to traditional optimization methods. Second, it allows the identification of the most informative regions of the scenario set containing the scenarios to be included in the optimization process for generating a robust solution. We test ROSS on the real case study of robust planning of an off-grid hybrid energy system, combining diesel generation with renewable energy sources and storage technologies. Results show that ROSS enables computational requirements to be reduced between 23% to 84% compared with traditional robust optimization methods, depending on the complexity of the robustness metrics considered. It is also able to identify very small regions of the scenario set containing the most informative scenarios for generating a robust solution.

[1]  G. Schneller,et al.  Decision making under uncertainty: Starr's Domain criterion , 1983 .

[2]  Patrick M. Reed,et al.  Reducing regional drought vulnerabilities and multi-city robustness conflicts using many-objective optimization under deep uncertainty , 2015 .

[3]  Joseph R. Kasprzyk,et al.  Many objective robust decision making for complex environmental systems undergoing change , 2012, Environ. Model. Softw..

[4]  Casey Brown,et al.  Robustness indicators for evaluation under climate change: Application to the upper Great Lakes , 2013 .

[5]  Casey Brown,et al.  Sustainable water management under future uncertainty with eco-engineering decision scaling , 2016 .

[6]  Jonathan D. Herman,et al.  How should robustness be defined for water systems planning under change , 2015 .

[7]  Theodor J. Stewart,et al.  Multi-objective optimisation under deep uncertainty , 2019, Operational Research.

[8]  Warren E. Walker,et al.  Developing dynamic adaptive policy pathways: a computer-assisted approach for developing adaptive strategies for a deeply uncertain world , 2015, Climatic Change.

[9]  Holger R. Maier,et al.  A systematic approach to determining metamodel scope for risk-based optimization and its application to water distribution system design , 2015, Environ. Model. Softw..

[10]  Benjamin P. Bryant,et al.  Thinking Inside the Box , 2010 .

[11]  Patrick M. Reed,et al.  Identifying Actionable Compromises: Navigating Multi‐City Robustness Conflicts to Discover Cooperative Safe Operating Spaces for Regional Water Supply Portfolios , 2019, Water Resources Research.

[12]  Jan H. Kwakkel,et al.  Including robustness considerations in the search phase of Many-Objective Robust Decision Making , 2018, Environ. Model. Softw..

[13]  Andrea Castelletti,et al.  Data-driven dynamic emulation modelling for the optimal management of environmental systems , 2012, Environ. Model. Softw..

[14]  Andrea Castelletti,et al.  Is robustness really robust? How different definitions of robustness impact decision-making under climate change , 2016, Climatic Change.

[15]  H. Maier,et al.  Including adaptation and mitigation responses to climate change in a multiobjective evolutionary algorithm framework for urban water supply systems incorporating GHG emissions , 2014 .

[16]  Joseph H. A. Guillaume,et al.  An uncertain future, deep uncertainty, scenarios, robustness and adaptation: How do they fit together? , 2016, Environ. Model. Softw..

[17]  Andrea Castelletti,et al.  Dynamic, multi-objective optimal design and operation of water-energy systems for small, off-grid islands , 2019, Applied Energy.

[18]  Joseph R. Kasprzyk,et al.  Many-objective de Novo water supply portfolio planning under deep uncertainty , 2012, Environ. Model. Softw..

[19]  Warren E. Walker,et al.  Dynamic adaptive policy pathways: A method for crafting robust decisions for a deeply uncertain world , 2013 .

[20]  Patrick M. Reed,et al.  Cooperative drought adaptation: Integrating infrastructure development, conservation, and water transfers into adaptive policy pathways , 2015 .

[21]  Myles T. Collins,et al.  Managing the Risk of Uncertain Threshold Responses: Comparison of Robust, Optimum, and Precautionary Approaches , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[22]  Robert J. Lempert,et al.  Do We Need Better Predictions to Adapt to a Changing Climate , 2009 .

[23]  Andrea Castelletti,et al.  A general framework for Dynamic Emulation Modelling in environmental problems , 2012, Environ. Model. Softw..

[24]  Laura Uusitalo,et al.  An overview of methods to evaluate uncertainty of deterministic models in decision support , 2015, Environ. Model. Softw..

[25]  Zoran Kapelan,et al.  Comparison of Robust Optimization and Info-Gap Methods for Water Resource Management under Deep Uncertainty , 2016 .

[26]  Robert J Lempert,et al.  A new decision sciences for complex systems , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Shabbir Ahmed,et al.  On robust optimization of two-stage systems , 2004, Math. Program..

[28]  M. Schlesinger,et al.  Robust Strategies for Abating Climate Change , 2000 .

[29]  Jan H. Kwakkel,et al.  How Robust is a Robust Policy? Comparing Alternative Robustness Metrics for Robust Decision-Making , 2016 .

[30]  David G. Groves,et al.  A General, Analytic Method for Generating Robust Strategies and Narrative Scenarios , 2006, Manag. Sci..

[31]  P. Laplace A Philosophical Essay On Probabilities , 1902 .

[32]  J. Harou,et al.  Selecting Portfolios of Water Supply and Demand Management Strategies Under Uncertainty—Contrasting Economic Optimisation and ‘Robust Decision Making’ Approaches , 2013, Water Resources Management.

[33]  Warren E. Walker,et al.  Comparing Robust Decision-Making and Dynamic Adaptive Policy Pathways for model-based decision support under deep uncertainty , 2016, Environ. Model. Softw..

[34]  Jan H. Kwakkel,et al.  An exploratory approach for adaptive policymaking by using multi-objective robust optimization , 2014, Simul. Model. Pract. Theory.

[35]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .

[36]  Zoran Kapelan,et al.  Flexible Water Distribution System Design under Future Demand Uncertainty , 2015 .

[37]  Thorsten Wagener,et al.  A vulnerability driven approach to identify adverse climate and land use change combinations for critical hydrologic indicator thresholds: Application to a watershed in Pennsylvania, USA , 2014 .

[38]  Andrea Castelletti,et al.  A bottom‐up approach to identifying the maximum operational adaptive capacity of water resource systems to a changing climate , 2016 .

[39]  Andrea Castelletti,et al.  Robustness Metrics: How Are They Calculated, When Should They Be Used and Why Do They Give Different Results? , 2018 .

[40]  Barbara S. Minsker,et al.  Applying Dynamic Surrogate Models in Noisy Genetic Algorithms to Optimize Groundwater Remediation Designs , 2011 .

[41]  Howard S. Wheater,et al.  Assessing the Vulnerability of Water Supply to Changing Streamflow Conditions , 2014 .

[42]  David A. Cohn,et al.  Active Learning with Statistical Models , 1996, NIPS.

[43]  Zoran Kapelan,et al.  Robust optimization of water infrastructure planning under deep uncertainty using metamodels , 2017, Environ. Model. Softw..

[44]  David G. Groves,et al.  Paleoclimate Scenarios to Inform Decision Making in Water Resource Management: Example from Southern California’s Inland Empire , 2014 .

[45]  Andrea Castelletti,et al.  Discovering Dependencies, Trade‐Offs, and Robustness in Joint Dam Design and Operation: An Ex‐Post Assessment of the Kariba Dam , 2019, Earth's Future.

[46]  Casey Brown,et al.  Decision scaling: Linking bottom‐up vulnerability analysis with climate projections in the water sector , 2012 .

[47]  Klaus Keller,et al.  Robust Climate Policies Under Uncertainty: A Comparison of Robust Decision Making and Info‐Gap Methods , 2012, Risk analysis : an official publication of the Society for Risk Analysis.

[48]  Casey Brown,et al.  Bottom-up climate risk assessment of infrastructure investment in the Niger River Basin , 2013, Climatic Change.

[49]  B. C. Trindade,et al.  Deeply uncertain pathways: Integrated multi-city regional water supply infrastructure investment and portfolio management , 2019 .

[50]  Andrea Castelletti,et al.  Many‐objective reservoir policy identification and refinement to reduce policy inertia and myopia in water management , 2014 .

[51]  J. D. Quinn,et al.  Exploring How Changing Monsoonal Dynamics and Human Pressures Challenge Multireservoir Management for Flood Protection, Hydropower Production, and Agricultural Water Supply , 2018, Water Resources Research.

[52]  David G. Groves,et al.  A New Analytic Method for Finding Policy-Relevant Scenarios: , 2007 .

[53]  Joseph R. Kasprzyk,et al.  Incorporating deeply uncertain factors into the many objective search process , 2017, Environ. Model. Softw..

[54]  Patrick A. Ray,et al.  Performance-Based Evaluation of an Improved Robust Optimization Formulation , 2014 .

[55]  P. Reed,et al.  Beyond optimality: Multistakeholder robustness tradeoffs for regional water portfolio planning under deep uncertainty , 2014 .

[56]  Julien Boé,et al.  Statistical and dynamical downscaling of the Seine basin climate for hydro‐meteorological studies , 2007 .

[57]  Andrea Castelletti,et al.  Interactive response surface approaches using computationally intensive models for multiobjective planning of lake water quality remediation , 2011 .

[58]  Rebecca A. Kelly,et al.  A formal framework for scenario development in support of environmental decision-making , 2009, Environ. Model. Softw..

[59]  R. Lempert,et al.  Shaping the Next One Hundred Years: New Methods for Quantitative Long-Term Policy Analysis , 2003 .

[60]  S. French Decision Theory: An Introduction to the Mathematics of Rationality , 1986 .

[61]  Holger R. Maier,et al.  Adaptive, multiobjective optimal sequencing approach for urban water supply augmentation under deep uncertainty , 2015 .

[62]  P. Harrison,et al.  Cross-sectoral impacts of climate change and socio-economic change for multiple, European land- and water-based sectors , 2015, Climatic Change.