Many-Objective Robust Decision Research Articles

Exploring the trade-offs among hydropower benefits, environmental flow, and surface water temperature in a large reservoir under deep uncertainty

The negative environmental impacts of large hydroelectric reservoirs have attracted wide attention. Reservoir operation alters seasonal flow patterns and reduces downstream flow during fish spawning seasons, which may lead to the loss of fish biodiversity. Meanwhile, reservoir impoundment reduces the flow velocity and raises the reservoir surface water temperature (SWT), potentially increasing the risk of algal blooms. While previous studies have designed various operation rules to balance the hydropower benefits and environmental flow or water temperature through multi-objective optimization approaches, a comprehensive analysis of trade-offs among the hydropower benefits, environmental flow, and SWT under an uncertain future remains lacking. This study contributes the many-objective robust decision-making (MORDM) framework to the multi-objective reservoir ecological operation for the first time. We quantify the trade-offs among maximizing the hydropower benefits, maximizing the reliability of environmental flow, and minimizing the number of days with high SWT; and evaluate the robustness of the operation rules under deep uncertainties from the climate conditions and electricity market. We apply MORDM to a large and deep reservoir, Nuozhadu, located in southwest China. Our results indicate that trade-offs exist between environmental flow and SWT, emphasizing the necessity to consider multiple environmental objectives in reservoir operation. Based on MORDM, we identify an operation scheme that can not only balance hydropower benefits and two environmental objectives, but also have robust performance against the uncertain future states. Scenario discovery analysis shows that air temperature is the most important uncertain factor that influences the robustness of operation rules. Our study provides a new perspective on reservoir operation planning to achieve balanced and sustainable developments in hydropower and environments under uncertain climate and electricity market conditions.

Many-objective robust decision making for efficient designs of safety instrumented systems

A robust decision making framework is proposed to support the appropriate design and use of safety instrumented systems. This framework incorporates many-objective optimization, uncertainty analysis, robustness assessment, scenario discovery and sensitivity analysis to enhance the decision maker’s confidence in selecting a suitable policy and assessing its ability to perform as required under a wide range of plausible states of the word with a clear definition of any existing limitations and vulnerabilities. For this, the probabilistic behavior of safety instrumented systems is taken into account with detailed presentations and discussions of the needed resources and impacts of employing this kind of safety measures. This included capital cost, recurring cost and many aspects of the associated side effects, which covered loss of production, environmental impacts, and ability to intensify existing risks or even trigger new accident scenarios. A detailed application is provided to illustrate the specificity and the outcomes of each involved step.

Multi-objective robust decision-making for LIDs implementation under climatic change

Decision-makers in urban water systems have long searched for robust runoff management alternatives that can resist deviations from the performance for which they were designed. In this study, with the development of a new comprehensive framework consisting of Many- Objective Robust Decision-Making (MORDM) and Storm Water Management Model (SWMM), robust alternatives for the implementation of Low Impact Development (LID) practices are presented under future climate change. The proposed methodology has been applied to District 10 of the Tehran municipality, located in the central part of Tehran, Iran. In the first step, the performances of General Circulation Models (GCMs) in predicting rainfall in the base period (1986–2005) were compared, and MPI-ESM-LR was selected as the best model for predicting rainfall in the future period (2021–2040). In the next step, by developing the SWMM hydrological model, runoff quality and quantity were simulated under RCP8.5 and RCP2.6. By coupling SWMM with the NSGA-II multi-objective evolutionary algorithm and specifying objective functions, the most optimal LIDs implementation scenarios were produced. Then, well-characterized uncertainties were changed into deep uncertainties, and the robustness of each design alternative was quantified using two robustness assessment methods. Finally, system vulnerabilities were discovered using the patient rule induction method (PRIM) and classification and regression tree (CART). This study showed that scenarios with a higher percentage of LIDs are more robust against deep uncertainties. Using different RCP scenarios also revealed that methodological selection of future climate scenarios can affect the robustness of candidate alternatives. Implementing SWMM-MORDM enables decision-makers to effectively generate runoff management scenarios and visually evaluate their robustness against deep uncertainties.

Post-MORDM: Mapping policies to synthesize optimization and robustness results for decision-maker compromise

This paper introduces post-MORDM, a decision-support framework that augments Many Objective Robust Decision Making (MORDM). MORDM often creates an intractable number of environmental management policies, characterized by decision variable, objective, and robustness values. This large number of policies inhibits decision support, causing disagreements among decision-makers. Post-MORDM addresses these challenges via the Self-Organizing Map (SOM), synthesizing MORDM data as layers organized in a map-like coordinate system. It uses the SOM to cluster policies, discover salient characteristics, and assess cause-effect relationships between decision-maker choices (i.e. decision variable values) and performance (objective and robustness values). Overall, the goal of post-MORDM is to create a structured platform that encourages negotiation and compromise. We demonstrate post-MORDM with a case study of two illustrative decision-makers for reservoir operation policy in the Colorado River Basin, USA. Post-MORDM helps communicate tradeoffs between storage and delivery objectives, relate tradeoffs to shortage policies, and identify mutually feasible policies.

Discussion of “Resolving Conflicts between Irrigation Agriculture and Ecohydrology Using Many-Objective Robust Decision Making” by Yu Li and Wolfgang Kinzelbach

Discussion of “Resolving Conflicts between Irrigation Agriculture and Ecohydrology Using Many-Objective Robust Decision Making” by Yu Li and Wolfgang Kinzelbach

Closure to “Resolving Conflicts between Irrigation Agriculture and Ecohydrology Using Many-Objective Robust Decision Making” by Yu Li and Wolfgang Kinzelbach

Closure to “Resolving Conflicts between Irrigation Agriculture and Ecohydrology Using Many-Objective Robust Decision Making” by Yu Li and Wolfgang Kinzelbach

Resolving Conflicts between Irrigation Agriculture and Ecohydrology Using Many-Objective Robust Decision Making

AbstractIn arid regions, sustainable groundwater management is crucial for the protection of vulnerable local ecosystems but often leads to conflict with the interests of economic development. Mana...

Rhodium: Python Library for Many-Objective Robust Decision Making and Exploratory Modeling

Rhodium is an open source Python library for robust decision making (RDM), many-objective robust decision making (MORDM), and exploratory modeling. These decision-support frameworks enable the identification of robust strategies for the management of complex environmental systems, by evaluating the tradeoffs among candidate strategies, and characterizing their vulnerabilities. Robust strategies refer to management options that perform sufficiently well or acceptably under a range of potential system conditions, rather than optimally in a single, nominal state of the world. Exploratory modeling allows for the simulation of the system under an ensemble of states of the world, so as to discover the ones with consequential effects on the system [1]. Rhodium facilitates rapid application of the RDM and MORDM frameworks by providing a suite of optimization, visualization, scenario discovery, and sensitivity analysis functions. Rhodium is written in Python and can interface with models written in Python, C and C++, Fortran, R, and Excel. The source code is freely available at https://github.com/Project-Platypus/Rhodium. <strong>Funding statement:</strong> This work was partially supported by the National Science Foundation under Grant No. (1639268). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Evaluating robustness of waste load allocation under climate change using multi-objective decision making

In recent years, uncertainties in climate change have made the allocation of waste load a severe challenge. This research develops a new model framework integrating a soil and water assessment tool (SWAT) for hydrological simulation of the river basin, Borg many-objective evolutionary algorithm (Borg MOEA) for optimization, and a software for many-objective robust decision making (OpenMORDM) to minimize these uncertainties and identifying the most robust waste load allocation plans resisting the impact of system uncertainties. This framework has been applied to the Golgol River basin, Iran, which is the main source of the Ilam dam water supply. In this study, first, temperature and precipitation were predicted in 2080–2099. Then, The SWAT model was used to simulate runoff and biochemical oxygen demand (BOD). Afterward, by specifying the objective functions, the Borg MOEA produced the most optimal waste load allocation scenarios in the driest month of the future (August), So that the amount of BOD in the dam reservoir remains less than 5 mg/L. In the next step, the robustness of the solutions analyzed using OpenMORDM. Then, the results were analyzed using the patient rule induction method (PRIM) and classification and regression tree (CART) methods to identify the system vulnerability domains and minimizing false positives. Through the analysis, four climate scenarios have been used to explain how the methodological selection of them affects the resulting candidate planning solutions. The results indicated that individual design selections from the water managers or researchers could influence the efficacy of the model framework, which in turn results in failure of the most robust waste-load allocation strategies under future climate change.

On considering robustness in the search phase of Robust Decision Making: A comparison of Many-Objective Robust Decision Making, multi-scenario Many-Objective Robust Decision Making, and Many Objective Robust Optimization

In recent years, a family of approaches has emerged for supporting decision-making on complex environmental problems characterized by deep uncertainties and competing priorities. Many-Objective Robust Decision Making (MORDM), Multi-scenario MORDM and. Many-Objective Robust Optimization (MORO) differ with respect to the degree to which robustness is considered during the search for promising candidate solutions. To assess the efficacy of these three methods, we compare them using three different policy formulations of the lake problem: inter-temporal, planned adaptive, and direct policy search. The more robustness is considered in the search phase, the more robust solutions are also after re-evaluation but also the lower the performance in individual reference scenarios. Adaptive policy formulations positively affect robustness, but do not reduce the price for robustness. Multi-scenario MORDM strikes a pragmatic balance between robustness considerations and optimality in individual scenarios, at reasonable computational costs.

Defining the robust operating rule for multi-purpose water reservoirs under deep uncertainties

Depending on the concept of optimality, the decision makers responsible for the planning and management of water resources seek to maximize the optimization performance. However, the optimized solutions are vulnerable to failure because decision making in water resources management usually involves factors with deep uncertainties (e.g. runoff conditions, water demand growth, climatic forces, etc.). In this study, we further contribute to the Many-Objective Robust Decision Making framework for defining the robust operating rules of a water supply system of interest. The multi-objective optimization and uncertainty analysis tools were used to reveal the trade-offs between the competing objectives and discover the sensitive factors for the plausible states of the system, respectively. The robust operating rules are demonstrated for the Han to Wei inter-basin water transfer project, which is the most important water diversion project in Shaanxi Province, China. Results show that, although the current operating rules are optimized for the water supply system over the long term, these operating rules cannot deal with the problem of performance degradation under deep uncertainties associated with runoff conditions and water demand growth. The two uncertain factors are the sensitive factors responsible for the failure or success of the system, and robustness of the system may be achieved by reducing the effect of key uncertainties (e.g. reduced water demand growth). Furthermore, there are obvious differences in the robust operating rules across different months, with the key or sensitive months providing the uncertain ranges to likely sustain the success of the system. Finally, the successful frequency of the system derived from the most robust operating rules is 18% higher than that obtained from the current operating rules for alternative states of the world. The robust operating rules offer critical insights into the challenges posed by deep uncertainties and provide a management template for decision making on climate change and complex human activities.

Including robustness considerations in the search phase of Many-Objective Robust Decision Making

Many-Objective Robust Decision Making (MORDM) is a prominent model-based approach for dealing with deep uncertainty. MORDM has four phases: a systems analytical problem formulation, a search phase to generate candidate solutions, a trade-off analysis where different strategies are compared across many objectives, and a scenario discovery phase to identify the vulnerabilities. In its original inception, the search phase identifies optimal strategies for a single reference scenario for deep uncertainties, which may result in missing locally near-optimal, but globally more robust strategies. Recent work has addressed this issue by generating candidate strategies for multiple policy-relevant scenarios. In this paper, we incorporate a systematic scenario selection procedure in the search phase to consider both policy relevance and scenario diversity. The results demonstrate an increased tradeoff variety besides higher robustness, compared to the solutions found for a reference scenario. Future research can routinize multi-scenario search in MORDM with the aid of software packages.

Many-objective robust decision making for water allocation under climate change

Water allocation is facing profound challenges due to climate change uncertainties. To identify adaptive water allocation strategies that are robust to climate change uncertainties, a model framework combining many-objective robust decision making and biophysical modeling is developed for large rivers. The framework was applied to the Pearl River basin (PRB), China where sufficient flow to the delta is required to reduce saltwater intrusion in the dry season. Before identifying and assessing robust water allocation plans for the future, the performance of ten state-of-the-art MOEAs (multi-objective evolutionary algorithms) is evaluated for the water allocation problem in the PRB. The Borg multi-objective evolutionary algorithm (Borg MOEA), which is a self-adaptive optimization algorithm, has the best performance during the historical periods. Therefore it is selected to generate new water allocation plans for the future (2079–2099). This study shows that robust decision making using carefully selected MOEAs can help limit saltwater intrusion in the Pearl River Delta. However, the framework could perform poorly due to larger than expected climate change impacts on water availability. Results also show that subjective design choices from the researchers and/or water managers could potentially affect the ability of the model framework, and cause the most robust water allocation plans to fail under future climate change. Developing robust allocation plans in a river basin suffering from increasing water shortage requires the researchers and water managers to well characterize future climate change of the study regions and vulnerabilities of their tools.

Reducing regional drought vulnerabilities and multi-city robustness conflicts using many-objective optimization under deep uncertainty

Emerging water scarcity concerns in many urban regions are associated with several deeply uncertain factors, including rapid population growth, limited coordination across adjacent municipalities and the increasing risks for sustained regional droughts. Managing these uncertainties will require that regional water utilities identify coordinated, scarcity-mitigating strategies that trigger the appropriate actions needed to avoid water shortages and financial instabilities. This research focuses on the Research Triangle area of North Carolina, seeking to engage the water utilities within Raleigh, Durham, Cary and Chapel Hill in cooperative and robust regional water portfolio planning. Prior analysis of this region through the year 2025 has identified significant regional vulnerabilities to volumetric shortfalls and financial losses. Moreover, efforts to maximize the individual robustness of any of the mentioned utilities also have the potential to strongly degrade the robustness of the others. This research advances a multi-stakeholder Many-Objective Robust Decision Making (MORDM) framework to better account for deeply uncertain factors when identifying cooperative drought management strategies. Our results show that appropriately designing adaptive risk-of-failure action triggers required stressing them with a comprehensive sample of deeply uncertain factors in the computational search phase of MORDM. Search under the new ensemble of states-of-the-world is shown to fundamentally change perceived performance tradeoffs and substantially improve the robustness of individual utilities as well as the overall region to water scarcity. Search under deep uncertainty enhanced the discovery of how cooperative water transfers, financial risk mitigation tools, and coordinated regional demand management must be employed jointly to improve regional robustness and decrease robustness conflicts between the utilities. Insights from this work have general merit for regions where adjacent municipalities can benefit from cooperative regional water portfolio planning.

Incorporating deeply uncertain factors into the many objective search process

This paper proposes an approach for including deeply uncertain factors directly into a multi-objective search procedure, to aid in incorporating divergent quantitative scenarios within the model-based decision support process. Specifically, we extend Many Objective Robust Decision Making (MORDM), a framework for finding and evaluating planning solutions under multiple objectives, to include techniques from robust optimization. Traditional MORDM first optimized a problem under a baseline scenario, then evaluated candidate solutions under an ensemble of uncertain conditions, and finally discovered scenarios under which solutions are vulnerable. In this analysis, we perform multiple multi-objective search trials that directly incorporate these discovered scenarios within the search. Through the analysis, we have created multiple problem formulations to show how methodological choices of severe scenarios affect the resulting candidate planning solutions. We demonstrate the approach through a water planning portfolio example in the Lower Rio Grande Valley of Texas.

An open source framework for many-objective robust decision making

This study introduces a new open source software framework to support bottom-up environmental systems planning under deep uncertainty with a focus on many-objective robust decision making (MORDM), called OpenMORDM. OpenMORDM contains two complementary components: (1) a software application programming interface (API) for connecting planning models to computational exploration tools for many-objective optimization and sensitivity-based discovery of critical deeply uncertain factors; and (2) a web-based visualization toolkit for exploring high-dimensional datasets to better understand system trade-offs, vulnerabilities, and dependencies. We demonstrate the OpenMORDM framework on a challenging environmental management test case termed the “lake problem”. The lake problem has been used extensively in the prior environmental decision science literature and, in this study, captures the challenges posed by conflicting economic and environmental objectives, a water quality “tipping point” beyond which the lake may become irreversibly polluted, and multiple deeply uncertain factors that may undermine the robustness of pollution management policies. The OpenMORDM software framework enables decision makers to identify policy-relevant scenarios, quantify the trade-offs between alternative strategies in different scenarios, flexibly explore alternative definitions of robustness, and identify key system factors that should be monitored as triggers for future actions or additional planning. The web-based OpenMORDM visualization toolkit allows decision makers to easily share and visualize their datasets, with the option for analysts to extend the framework with customized scripts in the R programming language. OpenMORDM provides a platform for constructive decision support, allowing analysts and decision makers to interactively discover promising alternatives and potential vulnerabilities while balancing conflicting objectives.

How Should Robustness Be Defined for Water Systems Planning under Change?

AbstractWater systems planners have long recognized the need for robust solutions capable of withstanding deviations from the conditions for which they were designed. Robustness analyses have shifted from expected utility to exploratory bottom-up approaches which identify vulnerable scenarios prior to assigning likelihoods. Examples include Robust Decision Making (RDM), Decision Scaling, Info-Gap, and Many-Objective Robust Decision Making (MORDM). We propose a taxonomy of robustness frameworks to compare and contrast these approaches based on their methods of (1) alternative generation, (2) sampling of states of the world, (3) quantification of robustness measures, and (4) sensitivity analysis to identify important uncertainties. Building from the proposed taxonomy, we use a regional urban water supply case study in the Research Triangle region of North Carolina to illustrate the decision-relevant consequences that emerge from each of these choices. Results indicate that the methodological choices in the ...

Many-objective robust decision making for managing an ecosystem with a deeply uncertain threshold response

Singh, R., P. M. Reed, and K. Keller. 2015. Many-objective robust decision making for managing an ecosystem with a deeply uncertain threshold response. Ecology and Society 20(3): 12. https://doi.org/10.5751/ES-07687-200312

Many objective robust decision making for complex environmental systems undergoing change

This paper introduces many objective robust decision making (MORDM). MORDM combines concepts and methods from many objective evolutionary optimization and robust decision making (RDM), along with extensive use of interactive visual analytics, to facilitate the management of complex environmental systems. Many objective evolutionary search is used to generate alternatives for complex planning problems, enabling the discovery of the key tradeoffs among planning objectives. RDM then determines the robustness of planning alternatives to deeply uncertain future conditions and facilitates decision makers' selection of promising candidate solutions. MORDM tests each solution under the ensemble of future extreme states of the world (SOW). Interactive visual analytics are used to explore whether solutions of interest are robust to a wide range of plausible future conditions (i.e., assessment of their Pareto satisficing behavior in alternative SOW). Scenario discovery methods that use statistical data mining algorithms are then used to identify what assumptions and system conditions strongly influence the cost-effectiveness, efficiency, and reliability of the robust alternatives. The framework is demonstrated using a case study that examines a single city's water supply in the Lower Rio Grande Valley (LRGV) in Texas, USA. Results suggest that including robustness as a decision criterion can dramatically change the formulation of complex environmental management problems as well as the negotiated selection of candidate alternatives to implement. MORDM also allows decision makers to characterize the most important vulnerabilities for their systems, which should be the focus of ex post monitoring and identification of triggers for adaptive management.