S. Wang

A multi-level Taguchi-factorial two-stage stochastic programming approach for characterization of parameter uncertainties and their interactions: An application to water resources management

This paper presents a multi-level Taguchi-factorial two-stage stochastic programming (MTTSP) approach for supporting water resources management under parameter uncertainties and their interactions. MTTSP is capable of performing uncertainty analysis, policy analysis, factor screening, and interaction detection in a comprehensive and systematic way. A water resources management problem is used to demonstrate the applicability of the proposed approach. The results indicate that interval solutions can be generated for the objective function and decision variables, and a variety of decision alternatives can be obtained under different policy scenarios. The experimental data obtained from the Taguchi’s orthogonal array design are helpful in identifying the significant factors affecting the total net benefit. Then the findings from the multi-level factorial experiment reveal the latent interactions among those important factors and their curvature effects on the model response. Such a sequential strategy of experimental designs is useful in analyzing the interactions for a large number of factors in a computationally efficient manner.

Interactive two-stage stochastic fuzzy programming for water resources management.

In this study, an interactive two-stage stochastic fuzzy programming (ITSFP) approach has been developed through incorporating an interactive fuzzy resolution (IFR) method within an inexact two-stage stochastic programming (ITSP) framework. ITSFP can not only tackle dual uncertainties presented as fuzzy boundary intervals that exist in the objective function and the left- and right-hand sides of constraints, but also permit in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated. A management problem in terms of water resources allocation has been studied to illustrate applicability of the proposed approach. The results indicate that a set of solutions under different feasibility degrees has been generated for planning the water resources allocation. They can help the decision makers (DMs) to conduct in-depth analyses of tradeoffs between economic efficiency and constraint-violation risk, as well as enable them to identify, in an interactive way, a desired compromise between satisfaction degree of the goal and feasibility of the constraints (i.e., risk of constraint violation).

An interval-parameter two-stage stochastic fuzzy program with type-2 membership functions: an application to water resources management

This paper presents an interval-parameter two-stage stochastic fuzzy programming with type-2 membership functions (ITSFP–T2MF) approach for supporting water resources management under uncertainty. ITSFP–T2MF is capable not only of dealing with a variety of uncertainties expressed as probability distributions, intervals, and type-2 fuzzy sets, but also of reflecting the complexity of uncertainty presented as the concept of a flexible fuzzy decision. A scenario-based solution method is proposed for solving ITSFP–T2MF, which takes into account different attitudes of decision makers (DMs) towards the objective-function value and constraints. Moreover, the solution method can ensure that no infeasible solutions are included in the results by means of a feasibility test and a constricting algorithm, leading to an enhanced system safety. ITSFP–T2MF is applied to a case study of water resources allocation under uncertainty. The results indicate that interval solutions can be obtained under different scenarios, which enhances the diversity of solutions for supporting the decisions of water resources allocation. Furthermore, a variety of decision alternatives can be generated under different policies for water resources management, which permits an in-depth policy analysis associated with different levels of economic penalties when the promised water-allocation targets are violated, and thus helps DMs identify desired water-allocation plans according to practical situations.

Development of a clusterwise-linear-regression-based forecasting system for characterizing DNAPL dissolution behaviors in porous media.

Groundwater contamination by dense non-aqueous phase liquids (DNAPLs) has become an issue of great concern in many industrialized countries due to their serious threat to human health. Dissolution and transport of DNAPLs in porous media are complicated, multidimensional and multiphase processes, which pose formidable challenges for investigation of their behaviors and implementation of effective remediation technologies. Numerical simulation models could help gain in-depth insight into complex mechanisms of DNAPLs dissolution and transport processes in the subsurface; however, they were computationally expensive, especially when a large number of runs were required, which was considered as a major obstacle for conducting further analysis. Therefore, proxy models that mimic key characteristics of a full simulation model were desired to save many orders of magnitude of computational cost. In this study, a clusterwise-linear-regression (CLR)-based forecasting system was developed for establishing a statistical relationship between DNAPL dissolution behaviors and system conditions under discrete and nonlinear complexities. The results indicated that the developed CLR-based forecasting system was capable not only of predicting DNAPL concentrations with acceptable error levels, but also of providing a significance level in each cutting/merging step such that the accuracies of the developed forecasting trees could be controlled. This study was a first attempt to apply the CLR model to characterize DNAPL dissolution and transport processes.

An Inexact Probabilistic–Possibilistic Optimization Framework for Flood Management in a Hybrid Uncertain Environment

Flooding is one of the leading causes of loss due to natural catastrophes, and at least one third of all losses due to natural forces can be attributed to flooding. Flood management systems involve a variety of complexities, such as multiple uncertainties, dynamic variations, and policy implications. This paper presents an inexact probabilistic-possibilistic programming with fuzzy random coefficients (IPP-FRC) model for flood management in a hybrid uncertain environment. IPP-FRC is capable not only of tackling multiple uncertainties in the form of intervals with fuzzy random boundaries but of addressing the dynamic complexity through capacity expansion planning within a multi-region, multi-flood-level, and multi-option context. The possibility and necessity measures used in IPP-FRC are suitable for risk-seeking and risk-averse decision making, respectively. A case study is used to demonstrate the applicability of the proposed methodology for facilitating flood management. The results indicate that the inexact degrees of possibility and necessity would decrease with increased probabilities of occurrence, implying a potential tradeoff between fulfillment of objectives and associated risks. A number of decision alternatives can be obtained under different policy scenarios. They are helpful for decision makers to formulate the appropriate flood management policy according to practical situations. The performance of IPP-FRC is analyzed and compared with a possibility-based fractile model.

A coupled factorial-analysis-based interval programming approach and its application to air quality management

In this study, a coupled factorial-analysis-based interval programming (CFA-IP) approach is developed through incorporating factorial analysis within an interval-parameter linear programming framework. CFA-IP can tackle uncertainties presented as intervals that exist in the objective function and the left- and right-hand sides of constraints, as well as robustly reflect interval information in the solutions for the objective-function value and decision variables. Moreover, CFA-IP has the advantage of investigating the potential interactions among input parameters and their influences on lower- and upper-bound solutions, which is meaningful for supporting an in-depth analysis of uncertainty. A regional air quality management problem is studied to demonstrate applicability of the proposed CFA-IP approach. The results indicate that useful solutions have been generated for planning the air quality management practices. They can help decision makers identify desired pollution mitigation strategies with minimized total cost and maximized environmental efficiency, as well as screen out dominant parameters and explore the valuable information that may be veiled beneath their interrelationships. Implications: The CFA-IP approach can not only tackle uncertainties presented as intervals that exist in the objective function and the left- and right-hand sides of constraints, but also investigate their interactive effects on model outputs, which is meaningful for supporting an in-depth analysis of uncertainty. Thus CFA-IP would be applicable to air quality management problems under uncertainty. The results obtained from CFA-IP can help decision makers identify desired pollution mitigation strategies, as well as investigate the potential interactions among factors and analyze their consequent effects on modeling results.

CVaR-based factorial stochastic optimization of water resources systems with correlated uncertainties

In this paper, a conditional value-at-risk based factorial stochastic programming approach is proposed to address random uncertainties and their interactions in a systematic manner. Random variables can be addressed through a risk-averse method within the two-stage stochastic programming framework. Interactions between random variables are examined through conducting a multi-level factorial analysis. The proposed approach is applied to a case study of water resources management to demonstrate its validity and applicability. A number of decision alternatives are obtained under different risk coefficients, which are useful for decision-makers to make sound water management plan and to perform an in-depth analysis of trade-offs between economic objectives and associated risks. Results obtained from the factorial experiment uncover the multi-level interactions between uncertain parameters and their contributions to the variability of net benefits. The performance of the proposed approach is compared with a factorial two-stage stochastic programming method.

Risk-based factorial probabilistic inference for optimization of flood control systems with correlated uncertainties

In this paper, a risk-based factorial probabilistic inference method is proposed to address the stochastic objective function and constraints as well as their interactions in a systematic manner. To tackle random uncertainties, decision makers’ risk preferences are taken into account in the decision process. Statistical significance for each of the linear, nonlinear, and interaction effects of risk parameters is uncovered through conducting a multi-factorial analysis. The proposed methodology is applied to a case study of flood control to demonstrate its validity and applicability. A number of decision alternatives are obtained under various combinations of risk levels associated with the objective function and chance constraints, facilitating an in-depth analysis of trade-offs between economic outcomes and associated risks. Dynamic complexities are addressed through a two-stage decision process as well as through capacity expansion planning for flood diversion within a multi-region, multi-flood-level, and multi-option context. Findings from the factorial experiment reveal the multi-level interactions between risk parameters and quantify their contributions to the variability of the total system cost. The proposed method is compared against the fractile criterion optimization model and the chance-constrained programming technique, respectively.