Application of genetic algorithms for the design of ozone control strategies

Designing air quality management strategies is complicated by the difficulty in simultaneously considering large amounts of relevant data, sophisticated air quality models, competing design objectives, and unquantifiable issues. For many problems, mathematical optimization can be used to simplify the design process by identifying cost-effective solutions. Optimization applications for controlling nonlinearly reactive pollutants such as tropospheric ozone, however, have been lacking because of the difficulty in representing nonlinear chemistry in mathematical programming models. We discuss the use of genetic algorithms (GAs) as an alternative optimization approach for developing ozone control strategies. A GA formulation is described and demonstrated for an urban-scale ozone control problem in which controls are considered for thousands of pollutant sources simultaneously. A simple air quality model is integrated into the GA to represent ozone transport and chemistry. Variations of the GA formulation for multiobjective and chance-constrained optimization are also presented. The paper concludes with a discussion of the practically of using more sophisticated, regulatory-scale air quality models with the GA. We anticipate that such an approach will be practical in the near term for supporting regulatory decision-making.     

A HYBRID OPTIMIZATION APPROACH TO THE ESTIMATION OF DISTRIBUTED PARAMETERS IN TWO-DIMENSIONAL CONFINED AQUIFERS1

ABSTRACT: In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is experimentally demonstrated that only one piece of prior information of the least sensitive parameter is sufficient to arrive at the global or near-global optimum solution. For hydraulic head data with measurement errors, the error in the estimation of parameters increases as the standard deviation of the errors increases. Results from our experiments show that, in general, the accuracy of the estimated parameters depends on the level of noise in the hydraulic head data and the initial values used in the truncated-Newton search technique.     

A Monitoring Network Design Procedure for Three-Dimensional (3D) Groundwater Contaminant Source Identification

Finding the location and concentration of contaminant sources is an important step in groundwater remediation and management. This discovery typically requires the solution of an inverse problem. This inverse problem can be formulated as an optimization problem where the objective function is the sum of the square of the errors between the observed and predicted values of contaminant concentration at the observation wells. Studies show that the source identification accuracy is dependent on the observation locations (i.e., network geometry) and frequency of sampling; thus, finding a set of optimal monitoring well locations is very important for characterizing the source. The objective of this study is to propose a sensitivity-based method for optimal placement of monitoring wells by incorporating two uncertainties: the source location and hydraulic conductivity. An optimality metric called D-optimality in combination with a distance metric, which tends to make monitoring locations as far apart from each other as possible, is developed for finding optimal monitoring well locations for source identification. To address uncertainty in hydraulic conductivity, an integration method of multiple well designs is proposed based on multiple hydraulic conductivity realizations. Genetic algorithm is used as a search technique for this discrete combinatorial optimization problem. This procedure was applied to a hypothetical problem based on the well-known Borden Site data in Canada. The results show that the criterion-based selection proposed in this paper provides improved source identification performance when compared to uniformly distributed placement of wells.     

Conjunctive use of models to design cost-effective ozone control strategies

The management of tropospheric ozone (O3) is particularly difficult. The formulation of emission control strategies requires considerable information including: (1) emission inventories, (2) available control technologies, (3) meteorological data for critical design episodes, and (4) computer models that simulate atmospheric transport and chemistry. The simultaneous consideration of this information during control strategy design can be exceedingly difficult for a decision-maker. Traditional management approaches do not explicitly address cost minimization. This study presents a new approach for designing air quality management strategies; a simple air quality model is used conjunctively with a complex air quality model to obtain low-cost management strategies. A simple air quality model is used to identify potentially good solutions, and two heuristic methods are used to identify cost-effective control strategies using only a small number of simple air quality model simulations. Subsequently, the resulting strategies are verified and refined using a complex air quality model. The use of this approach may greatly reduce the number of complex air quality model runs that are required. An important component of this heuristic design framework is the use of the simple air quality model as a screening and exploratory tool. To achieve similar results with the simple and complex air     

Conjunctive Use of Models to Design Cost-Effective Ozone Control Strategies

Abstract

The management of tropospheric ozone (O₃) is particularly difficult. The formulation of emission control strategies requires considerable information including: (1) emission inventories, (2) available control technologies, (3) meteorological data for critical design episodes, and (4) computer models that simulate atmospheric transport and chemistry. The simultaneous consideration of this information during control strategy design can be exceedingly difficult for a decision-maker. Traditional management approaches do not explicitly address cost minimization. This study presents a new approach for designing air quality management strategies; a simple air quality model is used conjunctively with a complex air quality model to obtain low-cost management strategies. A simple air quality model is used to identify potentially good solutions, and two heuristic methods are used to identify cost-effective control strategies using only a small number of simple air quality model simulations. Subsequently, the resulting strategies are verified and refined using a complex air quality model. The use of this approach may greatly reduce the number of complex air quality model runs that are required. An important component of this heuristic design framework is the use of the simple air quality model as a screening and exploratory tool. To achieve similar results with the simple and complex air quality models, it may be necessary to “tweak” or calibrate the simple model. A genetic algorithm-based optimization procedure is used to automate this tweaking process. These methods are demonstrated to be computationally practical using two realistic case studies, which are based on data from a metropolitan region in the United States.     

Application of Genetic Algorithms for the Design of Ozone Control Strategies

ABSTRACT

Designing air quality management strategies is complicated by the difficulty in simultaneously considering large amounts of relevant data, sophisticated air quality models, competing design objectives, and unquantifiable issues. For many problems, mathematical optimization can be used to simplify the design process by identifying cost-effective solutions. Optimization applications for controlling nonlinearly reactive pollutants such as tropospheric ozone, however, have been lacking because of the difficulty in representing nonlinear chemistry in mathematical programming models.

We discuss the use of genetic algorithms (GAs) as an alternative optimization approach for developing ozone control strategies. A GA formulation is described and demonstrated for an urban-scale ozone control problem in which controls are considered for thousands of pollutant sources simultaneously. A simple air quality model is integrated into the GA to represent ozone transport and chemistry. Variations of the GA formulation for multiobjective and chance-constrained optimization are also presented. The paper concludes with a discussion of the practicality of using more sophisticated, regulatory-scale air quality models with the GA. We anticipate that such an approach will be practical in the near term for supporting regulatory decision-making.