Matthew S. Gibbs

A genetic algorithm calibration method based on convergence due to genetic drift

The selection of Genetic Algorithm (GA) parameters is a difficult problem, and if not addressed adequately, solutions of good quality are unlikely to be found. A number of approaches have been developed to assist in the calibration of GAs, however there does not exist an accepted method to determine the parameter values. In this paper, a GA calibration methodology is proposed based on the convergence of the population due to genetic drift, to allow suitable GA parameter values to be determined without requiring a trial-and-error approach. The proposed GA calibration method is compared to another GA calibration method, as well as typical parameter values, and is found to regularly lead the GA to better solutions, on a wide range of test functions. The simplicity and general applicability of the proposed approach allows suitable GA parameter values to be estimated for a wide range of situations.

Investigation into the relationship between chlorine decay and water distribution parameters using data driven methods

Drinking water contaminated by micro-organisms can be a major risk to public health. Disinfection is used to destroy micro-organisms that are potentially dangerous to humans. In order to prevent bacterial regrowth, it is also desirable to maintain a disinfectant residual throughout the water distribution system. The most commonly used disinfectant is chlorine. If the dosing rate of chlorine is too low, there may be insufficient residual at the end of the distribution system, resulting in bacterial regrowth. On the other hand, the addition of too much chlorine can lead to customer complaints about taste and odour, corrosion of the pipe network and the formation of potentially carcinogenic by-products. Consequently, in order to determine the optimal chlorine dosing rate, it is necessary to be able to predict chlorine decay in the network. In this paper three different data-driven techniques are used to predict chlorine concentrations at two key locations in the Hope Valley water distribution system, located to the north of Adelaide, South Australia. The data-driven methods applied include a linear regression model and two artificial neural networks: the Multi Layer Perceptron (MLP); and the General Regression Neural Network (GRNN). A 5-year data set containing routinely measured parameters is used for model development and validation. The results indicate that data-driven techniques are relatively successful in predicting chlorine concentrations in the distribution system. This is despite the fact that there is no hydraulic model of the system, and that only data that are collected on a routine basis were used for model development.

Comparison of Genetic Algorithm Parameter Setting Methods for Chlorine Injection Optimization

The suitability of genetic algorithms (GAs) for the optimization of water distribution systems (WDSs) has been demonstrated extensively. However, despite many years of application in many different fields, the selection of the GA parameters remains a difficult and time consuming task. In this paper, two methodologies that do not require trial-and-error GA parameter calibration have been tested on a WDS optimization problem to determine their suitability for application in the water resources field and to assess their ability in locating near-optimal solutions. The results indicate that both approaches located solutions that were significantly better than a GA using typical parameter values, while the methodology based on convergence of the GA population located the best solutions overall. This method can be easily applied to assist GA users in identifying suitable GA parameters without requiring a time consuming trial-and-error approach.

A generic framework for regression regionalization in ungauged catchments

Regionalization of rainfall-runoff models is required for many catchments, where a suitable flow record is not available to enable traditional calibration methods to be used. Most recently, donor catchment approaches have been identified as the most successful at providing suitable model parameter values. However, this approach is less attractive for regions where the number of suitable catchments available to derive model parameters is low. In this case, regression approaches that consider catchment characteristics available in GIS databases may be more appropriate. Approaches such as this have been criticized due to issues associated with the ability to identify suitable parameter values, as well as the approach used to predict them from catchment information, incorporating interactions between parameters. This study proposes a generic framework to enable systematic regression regionalization for a data poor region, considering identification of model parameters using a multi-objective approach, and sensitivity analysis including consideration of parameter interactions. The approach developed has been applied to both lumped and distributed models, in order to investigate the benefits of adopting distributed models to represent catchment heterogeneity. The results indicate that a suitable regression approach can be developed for the region considered, outperforming directly calibrated parameters on a validation period, due to more accurate representation of the recharge process. However, no benefit was found for applying the approach on a distributed scale, most likely due to scale issues with the parameter values.

Relationship between problem characteristics and the optimal number of genetic algorithm generations

Genetic Algorithms (GAs) have been successfully applied to a wide range of engineering optimization problems. The success of the GA is dependent on the parameter values used, and identifying suitable values to use is a difficult task. Typically, the GA parameters must be calibrated for each application, hence it might be expected that the optimal parameter values are related to the characteristics of each problem. To aid the calibration of GAs, it is proposed that there exists an optimal number of GA generations for a given problem, where from the number of generations, the population size can be determined from the total function evaluations that are available. A number of test functions have been considered with different problem characteristics, such as salience, correlation structure, and epistasis, and statistics are proposed to quantify each of these characteristics. A large-scale parametric study has been undertaken to determine the effect of these characteristics on the optimal number of GA generations necessary in order to solve the problem most efficiently. From these results, two function classes have been identified. The function classes have been tested on two instances of an engineering optimization problem and found to classify the most appropriate population size accurately for solving each problem. Hence, the classification method developed can be used to assist in the calibration of GAs for applications where long simulation times are expected.

Minimum Number of Generations Required for Convergence of Genetic Algorithms

Genetic Algorithms (GAs) have been applied to a wide range of optimization problems, however a great deal of time and effort is required to calibrate the GA parameters to ensure that the best possible solutions are located. It is proposed that there exists a minimum number of GA generations before the members of a population will converge to a solution for a given optimization problem. This property would be useful in the calibration of a GA, as if there is a constant number of generations to solve the problem, the best population size can be determined using the desired number of function evaluations divided by the minimum number of generations. The hypothesis is tested for two versions of a test function; a commonly used separable test function, and a version of the function with epistatic interactions introduced between decision variables. Different problem sizes and convergence criteria are also considered. Two different relationships are identified. For the case where epistatic interactions are introduced into the test function the hypothesis is validated, as a constant number of generations before convergence is identified, and this increases with the size of the problem. However, for the case with no interactions between decision variables, the smallest population size produced the best results, regardless of problem size or convergence criteria.

Using characteristics of the optimisation problem to determine the Genetic Algorithm population size when the number of evaluations is limited

The Genetic Algorithm (GA) parameter values that result in the best possible solutions being found are generally problem specific, and therefore expected to be related to the characteristics of the fitness function. In this work, statistics that characterise the fitness function have been related to the convergence of a GA population due to the repetitive application of tournament selection. Assuming that this operator has the dominant influence on the variance of the population, and that the computational time available is limited, the result can be used to determine a suitable population size. The methodology developed has been compared to other GA calibration methodologies, and was found to be the best of the different methods considered across a range of stopping criteria and problem formulations. This result demonstrates the potential usefulness of fitness function characteristics to inform the configuration of GAs, and in turn find the best possible solutions.

Calibration and Optimization of the Pumping and Disinfection of a Real Water Supply System

Maintaining a disinfectant residual in water distribution systems WDSs is generally considered paramount to ensuring a safe drinking water supply. This objective can be assisted by the use of booster stations to increase disinfectant concentrations throughout the network. However, identifying the appropriate dose at each station is an optimization problem. The aim is to minimize the total mass of disinfectant dosed and reduce the cost of disinfection along with potential taste, odor, or by-product problems, while maintaining a certain minimum residual in the network. The residual present in the water at any location is not only dependent on the amount of disinfectant added to the water, but also the hydraulics of the system and the resulting detention times. A number of previous studies have tackled this optimization problem, however, a review of current literature suggests that in many cases the hydraulics of the system have been held constant, or the WDSs considered were hypothetical systems with relatively few constraints. This study considers the booster disinfection dosing problem, including daily pump scheduling, for a real system in Sydney, Australia. Before the system can be optimized, a representative model is required to ensure useful results, and the many constraints on the daily operation system must be accounted for in the fitness function considered. The results from the optimization study indicate it is necessary to consider the hydraulics as well as the dosing regime in the optimization process, as cycling reservoir levels minimizes detention times, and hence, disinfectant residuals are maintained at the extremities of the network. Also, significant energy cost savings of up to 30% can be made by scheduling the pumping in the system in line with the off-peak electricity costs.

Selection of Genetic Algorithm Parameters for Water Distribution System Optimization

Abstract The ability of Genetic Algorithm (GA) methods, to find near optimal solutions to Water Distribution System (WDS) optimization problems has been widely demonstrated. However, one of the main concerns in applying these methods is identifying suitable values for the GA parameters. The values selected for these parameters have a significant impact on the algorithm’s behavior, and therefore greatly affect the quality of the final solution found, as well as the time taken to find that solution. A considerable amount of time and effort must be dedicated to the calibration of these parameters for the GA practitioner to have any confidence that the values used are producing the desired results. The impact of each parameter will be dependent on the values of the other parameters, and it is likely that there exists different combinations that will produce the same exploration/exploitation behavior. This offers the potential to reduce the number of parameters requiring calibration, thus making the task of applying these methods much simpler. This paper describes large-scale sensitivity analyses that have been used to calibrate a real coded GA with a distributed crossover operator, for a WDS optimization problem, the Cherry Hill–Brushy Plains network, ultimately leading to the identification of a new optimal solution. Through these analyses, groups of parameter values are identified that cause the algorithm to perform very well in terms of algorithm convergence and the quality of the final solutions obtained. These results demonstrate that by understanding the parameters controlling the GA, and the relationships between them, the effort required to calibrate a GA for a given application can be reduced significantly.

Assessment of the ability to meet environmental water requirements in the Upper South East of South Australia

Often there are a number of criteria that must be considered when evaluating water resource management options, for example both water quantity and quality issues. Each criterion generally requires a separate model to assess the outcomes from different possible scenarios. Each model will have its own uncertainties and limitations, and the combination of all of these considerations can make the identification of acceptable, let alone optimal, options difficult. In this work, a resources management problem to identify the optimal operation of a large drainage network to support ecosystems at a number of key wetlands has been considered. These ecological outcomes were assessed by the ability to deliver sufficient volumes of water below important salinity thresholds. It was found that even with an unknown volume of water available, the optimal operations of the drainage network were generally constant. For the majority of wetlands considered, the ability to supply sufficient water below a given salinity threshold was mostly insensitive to uncertainty in the contributing groundwater salinity. However, in some wetlands, water of desirable salinity levels was unlikely to be available for all scenarios at one target wetland, the variability in groundwater salinity considered had a large influence on the availability of water of suitable quality. This work highlights the importance of keeping the modelling objectives in mind when considering the outputs and uncertainties involved in integrated modelling assessment.