Application of Simulated Annealing in Water Resources Management: Optimal Solution of Groundwater Contamination Source Characterization Problem and Monitoring Network Design Problems

[Extract] Estimating various characteristics of an unknown groundwater pollutant source can be formulated as an optimization problem using linked simulation-optimization. Meta-heuristics based optimization algorithms such as Simulated Annealing (SA), Genetic Algorithm (GA), Tabu Search etc. are now being accepted as reliable, faster and simpler ways to solve this optimization problem. In this chapter we discuss the suitability of a variant of traditional Simulated Annealing (SA) known as the Adaptive Simulated Annealing (ASA) in solving unknown groundwater pollutant source characterization problem

Application of simulated annealing in search for efficient optimal solutions of a groundwater contamination related problem

Characterization of groundwater contamination sources is a complex inverse problem. This inverse problem becomes complicated, due to the nonlinear nature of the groundwater flow and transport processes and the associated natural uncertainties. The mathematical challenges arise due to the nonunique characteristics of this problem resulting from the nonunique response of the aquifer system to a set of stresses and the possibility of instead locating only local optimal solutions. The linked simulation‐optimization model is an efficient approach to identifying groundwater contamination source characteristics. Efficiency and accuracy of the search for optimum solutions of a linked simulation‐optimization depend on the utilized optimization algorithm. This limited study focuses on the application and efficiency of simulated annealing (SA) as the optimization algorithm for solving the source characterization problem. The advantages in using adaptive simulated algorithm (ASA) as an alternative are then evaluated. The possibility of identifying a local optimal solution rather than a global optimal solution when using SA implies failure to solve the source characterization inverse problem. The cost of such inaccurate characterization may be enormous when a remediation strategy is based on the model inferences. ASA is shown to provide a reliable and acceptable alternative for solving this challenging aquifer contamination problem

Application of Simulated Annealing and Adaptive Simulated Annealing in Search for Efficient Optimal Solutions of a Groundwater Contamination related Problem

Characterization of groundwater contamination sources is a complex inverse problem. This inverse problem becomes complicated, due to the nonlinear nature of the groundwater flow and transport processes and the associated natural uncertainties. The mathematical challenges arise due to the nonunique characteristics of this problem resulting from the nonunique response of the aquifer system to a set of stresses and the possibility of instead locating only local optimal solutions. The linked simulation‐optimization model is an efficient approach to identifying groundwater contamination source characteristics. Efficiency and accuracy of the search for optimum solutions of a linked simulation‐optimization depend on the utilized optimization algorithm. This limited study focuses on the application and efficiency of simulated annealing (SA) as the optimization algorithm for solving the source characterization problem. The advantages in using adaptive simulated algorithm (ASA) as an alternative are then evaluated. The possibility of identifying a local optimal solution rather than a global optimal solution when using SA implies failure to solve the source characterization inverse problem. The cost of such inaccurate characterization may be enormous when a remediation strategy is based on the model inferences. ASA is shown to provide a reliable and acceptable alternative for solving this challenging aquifer contamination problem

Coupled simulation-optimization model for coastal aquifer management using genetic programming-based ensemble surrogate models and multiple-realization optimization

Approximation surrogates are used to substitute the numerical simulation model within optimization algorithms in order to reduce the computational burden on the coupled simulation-optimization methodology. Practical utility of the surrogate-based simulation-optimization have been limited mainly due to the uncertainty in surrogate model simulations. We develop a surrogate-based coupled simulation-optimization methodology for deriving optimal extraction strategies for coastal aquifer management considering the predictive uncertainty of the surrogate model. Optimization models considering two conflicting objectives are solved using a multiobjective genetic algorithm. Objectives of maximizing the pumping from production wells and minimizing the barrier well pumping for hydraulic control of saltwater intrusion are considered. Density-dependent flow and transport simulation model FEMWATER is used to generate input-output patterns of groundwater extraction rates and resulting salinity levels. The nonparametric bootstrap method is used to generate different realizations of this data set. These realizations are used to train different surrogate models using genetic programming for predicting the salinity intrusion in coastal aquifers. The predictive uncertainty of these surrogate models is quantified and ensemble of surrogate models is used in the multiple-realization optimization model to derive the optimal extraction strategies. The multiple realizations refer to the salinity predictions using different surrogate models in the ensemble. Optimal solutions are obtained for different reliability levels of the surrogate models. The solutions are compared against the solutions obtained using a chance-constrained optimization formulation and single-surrogate-based model. The ensemble-based approach is found to provide reliable solutions for coastal aquifer management while retaining the advantage of surrogate models in reducing computational burden

Genetic Programming: Efficient Modeling Tool in Hydrology and Groundwater Management

[Extract] With the advent of computers a wide range of mathematical and numerical models have been developed with the intent of predicting or approximating parts of hyrdrologic cycle. Prior to the advent of conceptual process based models, physical hydraulic models, which are reduced scale representations of large hydraulic systems, were used commonly in water resources engineering. Fast development in the computational systems and numerical solutions of complex differential equations enabled development of conceptual models to represent physical systems. Thus, in the last two decades large number of mathematical models was developed to represent different processes in hydrological cycle

Reconnaissance-level alternative optimal groundwater use strategies

This study develops regionally optimal ground-water extraction strategies. Alternative explicit planning objectives arc: (1) Maximize total pumping from the underlying aquifer while causing the evolution of a steady potentiometric: surface: and (2) maintain a prespecified target potentiometric surface. Implicit objectives involve controlling stream/aquifer interflow and water flow across a state boundary, and attempting to avoid poss disruption of current cropping patterns. Models, bounds, constraints, and data arc: formulated. Alternative optimal strategies and the rationale for preferring one strategy arc: presented for a region in Arkansas. The objective of maintaining the relatively unstressed target potentiometric: surl1ce yields politically and socially unacceptable water-use strategies. The most acceptable strategy maximizes sustainable ground-water extraction, maintains recent ground-water flow to Louisiana, maintains current potentiometric surface heads It the Louisiana-Arkansas border, maintains more than minimally acceptable surface water now to Louisiana, and approximately maintains current cropping distributions. Developed planning models utilize the embedding approach, over 300 pumping variables, and 700 total variables, indicating the. utility of the embed· ding method for regional sustained yield (steady-state) planning

Optimum design of hydraulic water retaining structures incorporating uncertainty in estimating heterogeneous hydraulic conductivity utilizing stochastic ensemble surrogate models within a multi-objective multi-realisation optimisation model

In order to find optimum and reliable designs for hydraulic water retaining structures (HWRSs), a reliability based optimum design (RBOD) model was used to quantify uncertainty in estimates of seepage characteristics due to uncertainty in heterogeneous hydraulic conductivity (HHC). This included incorporating reliability measures into minimum-cost HWRS designs and utilising a multi-realisation optimisation technique based on various stochastic ensemble surrogate models. To improve the efficiency of the RBOD model and the direct search optimisation solver, a multi-objective multi-realisation optimisation (MOMRO) model was employed. Some of the stochastic optimisation constraints could be formulated as a second objective function to be minimised in the MOMRO model. This can significantly improve the search efficiency of the multi-objective non-dominated sorting genetic algorithm-II (NSGA-II) that was used, and help determine more feasible candidate solutions in the search space. Gaussian process regression was used to develop the surrogate models,which were trained on numerous datasets created from numerical seepage simulations. The effect of uncertainty was also considered for other HWRS safety factors and conditions such as overturning, flotation, sliding and eccentric loading. The results demonstrate that uncertainty in HHC estimates significantly impacts optimum HWRS design. Therefore, deterministic optimum solutions that are created based on expected values of hydraulic conductivity are not adequate for reliable HWRS design. The developed MOMRO model, which was based on an ensemble approach, addresses some of the uncertainty in HHC values that affects HWRS design. Also, the MOMRO technique improves the efficiency of the optimisation search process and facilitates a direct search process to provide many optimum alternatives

Evaluation of unknown groundwater contaminant sources characterization efficiency under hydrogeologic uncertainty in an experimental aquifer site by utilizing surrogate models

Characterization of unknown groundwater contaminant sources is an important but difficult step in effective groundwater management. The difficulties arise mainly due to the time of contaminant detection which usually happens a long time after the start of contaminant source(s) activities. Usually, limited information is available which also can be erroneous. This study utilizes Self-Organizing Map (SOM) and Gaussian Process Regression (GPR) algorithms to develop surrogate models that can approximate the complex flow and transport processes in a contaminated aquifer. The important feature of these developed surrogate models is that unlike the previous methods, they can be applied independently of any linked optimization model solution for characterizing of unknown groundwater contaminant sources. The performance of the developed surrogate models is evaluated for source characterization in an experimental contaminated aquifer site within the heterogeneous sand aquifer, located at the Botany Basin, New South Wales, Australia. In this study, the measured contaminant concentrations and hydraulic conductivity values are assumed to contain random errors. Simulated responses of the aquifer to randomly specified contamination stresses as simulated by using a three-dimensional numerical simulation model are utilized for initial training of the surrogate models. The performance evaluation results obtained by using different surrogate models are also compared. The evaluation results demonstrate the different capabilities of the developed surrogate models