Chapter 11· Input Selection for an Aigal Bloom Model
221
Genetic Algorithm (GA) Selection 0/ Inputs
A genetic algorithm is a powerful optimisation technique inspired by the
principles of natural evolution and selection (Goldberg 1989). Evolutionary
algorithms have been widely used in optimising water resources variables (e.g.
Simpson et al. 1994; Dandy et al. 1996) and in ecological modelling applications
(e.g. Howard and D'Angelo 1995; Downing 1998).
To initiate the technique, a population of random solutions is generated. The
fitness of each member of the population can then be evaluated using an objective
function and the next generation is produced from the previous one using a
process of selection, crossover and mutation.
A GA can be used to select an appropriate combination of inputs to an ANN
model. GAs are weIl suited to this task as they have the ability to search through
large numbers of combinations where there may be interdependencies between
variables. For the problem of determining inputs to an ANN model, a population
of randomly selected ANNs is generated, each with a different subset of input
variables as depicted by a binary string. The models are trained and then the
output of each ANN is used to determine the predictive error, or fitness of the
solution. In this research, the root mean square error (RMSE) between the actual
and predicted values is used to determine the fitness of the model. Based on the
fitness of each member in the population, aselection scheme can then be
employed to create a new population for the next generation. In this way, fit
solutions are allowed to live and subsequently breed in the process of crossover.
In the crossover process, two parent strings are cut and part of the strings
exchanged to produce two new individuals. To maintain genetic diversity and
ensure that no important genetic material is overlooked, a mutation operation
introduces small random changes.
The process is continued in an iterative manner until the error from the ANN
model converges to an acceptable value or the maximum number of generations is
completed. Due to the selective pressure applied over the generations, the overall
trend is the evolution of higher fitness chromosomes representing optimal input
subsets.
Implementation 0/ the GA -ANN
The commercially available software package, NeuroGenetic Optimizer (NGO)
(BioComp Systems 1998) was used in this research to implement the GA-ANN.
The NGO uses GAs to evolve ANN structures while simultaneously searching for
significant input variables.
Stepwise ANN Modelling Procedure
A stepwise modelling procedure was also used in this study to determine the ANN
model inputs (see Masters 1993; Maier et al. 1998). This method involves
developing N-bivariate models, where N is the number of input variables. The
input variable that gives the smallest error (e.g. RMSE) is then included in the
model. Subsequently, N-I models are developed by combining the variable that
resulted in the best forecast with each of the remaining variables. This procedure
can then be repeated using models with three input variables, four input variables
etc., until the addition of any extra variables does not improve model performance.
221
Genetic Algorithm (GA) Selection 0/ Inputs
A genetic algorithm is a powerful optimisation technique inspired by the
principles of natural evolution and selection (Goldberg 1989). Evolutionary
algorithms have been widely used in optimising water resources variables (e.g.
Simpson et al. 1994; Dandy et al. 1996) and in ecological modelling applications
(e.g. Howard and D'Angelo 1995; Downing 1998).
To initiate the technique, a population of random solutions is generated. The
fitness of each member of the population can then be evaluated using an objective
function and the next generation is produced from the previous one using a
process of selection, crossover and mutation.
A GA can be used to select an appropriate combination of inputs to an ANN
model. GAs are weIl suited to this task as they have the ability to search through
large numbers of combinations where there may be interdependencies between
variables. For the problem of determining inputs to an ANN model, a population
of randomly selected ANNs is generated, each with a different subset of input
variables as depicted by a binary string. The models are trained and then the
output of each ANN is used to determine the predictive error, or fitness of the
solution. In this research, the root mean square error (RMSE) between the actual
and predicted values is used to determine the fitness of the model. Based on the
fitness of each member in the population, aselection scheme can then be
employed to create a new population for the next generation. In this way, fit
solutions are allowed to live and subsequently breed in the process of crossover.
In the crossover process, two parent strings are cut and part of the strings
exchanged to produce two new individuals. To maintain genetic diversity and
ensure that no important genetic material is overlooked, a mutation operation
introduces small random changes.
The process is continued in an iterative manner until the error from the ANN
model converges to an acceptable value or the maximum number of generations is
completed. Due to the selective pressure applied over the generations, the overall
trend is the evolution of higher fitness chromosomes representing optimal input
subsets.
Implementation 0/ the GA -ANN
The commercially available software package, NeuroGenetic Optimizer (NGO)
(BioComp Systems 1998) was used in this research to implement the GA-ANN.
The NGO uses GAs to evolve ANN structures while simultaneously searching for
significant input variables.
Stepwise ANN Modelling Procedure
A stepwise modelling procedure was also used in this study to determine the ANN
model inputs (see Masters 1993; Maier et al. 1998). This method involves
developing N-bivariate models, where N is the number of input variables. The
input variable that gives the smallest error (e.g. RMSE) is then included in the
model. Subsequently, N-I models are developed by combining the variable that
resulted in the best forecast with each of the remaining variables. This procedure
can then be repeated using models with three input variables, four input variables
etc., until the addition of any extra variables does not improve model performance.