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A combined genetic algorithm and fuzzy simulation approach (GAFSA) was developed through integrating fuzzy chance-constrained programming (FCCP) and genetic algorithm (GA) into a general optimization framework. The major advantage of GAFSA is that it could tackle generally-shaped fuzzy membership functions on both sides of the model constraints, rather than handle single special forms like triangular or trapezoidal. An agricultural water quality management problem that has been investigated by a number of previous studies was used to demonstrate the applicability of the proposed method. The results showed that GAFSA allowed violation of system constraints at specified possibilistic confidence levels, leading to model solutions with higher system benefits. A conservative planning scheme could bring a more reliable system, but would be less economically attractive. Conversely, planning towards a higher system benefit would lead to a higher risk of system failure. The proposed model could help agricultural water managers analyse the trade-off between the overall system benefit and the failure risk of environmental compliance. A comparison of GAFSA to FCCP was given, and the potential limitations of the proposed method were also discussed. Published version

A stochastic robust fuzzy interval linear programming (SRFILP) model was proposed for supporting municipal solid waste (MSW) management under multiple uncertainties. The method integrated stochastic robust optimization (SRO), interval linear programming (ILP) and fuzzy possibilistic programming (FPP) methods into a general framework and could simultaneously deal with uncertainties expressed as fuzzy sets, stochastic variables and discrete intervals. The SRFILP model was applied to a hypothetical problem of municipal solid waste management. The results demonstrated that flexible interval solutions under different I±-cut levels could be generated, which could help decision makers gain an in-depth insight into system complexities associated with solid waste management. The waste-management alternatives could be generated by adjusting the decision-variable values within their solution intervals. In addition, the proposed method could be used to help evaluate the trade-off between solution robustness and model robustness, and help waste managers identify desired cost-effective policies considering environmental, economic, system-feasibility and system-reliability constraints.

A factorial-design-based stochastic modeling system (FSMS) was developed in this study to systematically investigate impacts of uncertainties associated with hydrocarbon-contaminant transport in subsurface. FSMS integrated a solute transport model, factorial analysis, and Monte Carlo technique into a general framework, and effectively analyze the individual and joint effects of input parameters' uncertainties that are associated with hydrogeological conditions. Four input parameters (i.e. the mean and the variance of permeability as well as the mean and the variance of porosity) were assumed to be of uncertain nature, and the factorial design and Monte Carlo simulation algorithm were incorporated into a groundwater flow and solute transport model developed in this study. Under each factorial experiment, a number of Monte Carlo simulations were implemented. A pilot-scale physical modeling system was used to illustrate the applicability of the proposed methodology. The simulation results reveal that the uncertainties in input parameters pose considerable influences on the predicted output; especially, variations in the mean of porosity will have significant impacts on the modeling output. The results obtained from the systematic uncertainty analysis methods proposed in this study, such as mean, standard deviation, and percentile can provide useful information for further decision-making regarding the petroleum contamination problem.

An inexact two-stage stochastic quadratic programming (ITQP) model is developed for water resources management under uncertainty. The model is a hybrid of inexact quadratic programming and two-stage stochastic programming. It can deal with the uncertainties presented as both probabilities and intervals. Moreover, it can deal with nonlinearities in objective function to reflect the effects of marginal utility on the benefit and cost components. Using quadratic form in the objective function rather than linear one, the ITQP can minimize the unfair competition of water resources among multiple users under uncertain water conditions. In the modeling formulation, penalties are imposed when policies expressed as the promised water supply targets are violated. In its solution process, the ITQP model is transformed into two deterministic submodels based on an interactive algorithm and a derivative algorithm, which correspond to the lower and upper bounds of the desired objective. Interval solutions, which are feasible and stable in the given decision space, can then be obtained by solving the two submodels sequentially. The developed method is then applied to a case study of water resources management planning. The results indicate that reasonable solutions have been obtained. They can help provide bases for identifying desired water-allocation plans with maximized system benefit and minimized system-failure risk.