John A. Belward

Use of advanced techniques to optimize a multi-dimensional dairy model

Available methods for the optimization of agricultural systems vary widely, in terms of derivation, applicability and performance. A whole-farm dairying model with 16 separate, interacting managerial options was optimized by the hill-climbing (quasi-Newton), direct search (simplex), genetic algorithm (GENESIS) and simulated annealing (VFSR) techniques. The latter two clearly out-performed the former, with simulated annealing always identifying the global optimum.

Fractal dimensions for rainfall time series

Fractals are objects which have a similar appearance when viewed at different scales. Such objects have detail at arbitrarily small scales, making them too complex to be represented by Euclidean space. They are assigned a dimension which is non-integer. Some natural phenomena have been modelled as fractals with success; examples include geologic deposits, topographical surfaces and seismic activity. In particular, time series data has been represented as a curve with dimension between one and two. There are many different ways of defining fractal dimension. Most are equivalent in the continuous domain, but when applied in practice to discrete data sets lead to different results. Three methods for estimating fractal dimension are evaluated for accuracy. Two standard algorithms, Hursts rescaled range analysis and the box-counting method, are compared with a recently introduced method which has not yet been widely used. It will be seen that this last method offers superior efficiency and accuracy, and it is recommended for fractal dimension calculations for time series data. We have applied these fractal analysis techniques to rainfall time series data from a number of gauge locations in Queensland. The suitability of fractal analysis for rainfall time series data is discussed, as is the question of how the theory might aid our interpretation of rainfall data.

Robust parameter settings of evolutionary algorithms for the optimisation of agricultural systems models

Numerical optimisation methods are being more commonly applied to agricultural systems models, to identify the most profitable management strategies. The available optimisation algorithms are reviewed and compared, with literature and our studies identifying evolutionary algorithms (including genetic algorithms) as superior in this regard to simulated annealing, tabu search, hill-climbing, and direct-search methods. Results of a complex beef property optimisation, using a real-value genetic algorithm, are presented. The relative contributions of the range of operational options and parameters of this method are discussed, and general recommendations listed to assist practitioners applying evolutionary algorithms to the solution of agricultural systems.

Survival of the fittest--genetic algorithms versus evolution strategies in the optimization of systems models

The use of numerical optimization techniques on simulation models is a developing field. Many of the available algorithms are not well suited to the types of problems posed by models of agricultural systems. Coming from different historical and developmental backgrounds, both genetic algorithms and evolution strategies have proven to be thorough and efficient methods in identifying the global optimum of such systems. A challenging herd dynamics model is used to test and compare optimizations using binary and real-value genetic algorithms, as well as evolution strategies. All proved successful in identifying the global optimum of this model, but evolution strategies were notably slower in achieving this. As the more successful innovations of each of these methods are being commonly adopted by all, the boundaries between them are becoming less clear-cut. They are effectively merging into one general class of optimization methods now termed evolutionary algorithms.

A variational approach to the radiometric enhancement of digital imagery

In this correspondence, we present a variational approach to the problem of finding suitable radiometric image transformations that optimize desirable characteristics of the output image histogram. This variational approach can be interpreted as the minimization of the cumulative spacing between histogram bars in the least squares sense subject to some weight function. Most of the common histogram transformation procedures used in remote sensing applications can be deduced from this general variational approach with an appropriate choice of the weight function.

Optimizing simulation models of agricultural systems

Agricultural systems vary widely in terms of scale, scope and purpose. Managers of thesereal-world systems are typically faced with a multitude of alternative management optionsand strategies, and are turning more towards simulation models in an attempt to evaluatethese and identify the optimal combination. From a modelling perspective, agriculturalsystems present a range of problems which need to be addressed, and these are outlinedwith examples. General conclusions are drawn on which of the available methodologies aremost likely to be successful for users.

Derivation of L-system Models from Measurements of Biological Branching Structures Using Genetic Algorithms

L-systems are widely used in the modelling of branching structures and the growth process of biological objects such as plants, nerves and airways in lungs. The derivation of such L-system models involves a lot of hard mental work and time-consuming manual procedures. A method based on genetic algorithms for automating the derivation of L-systems is presented here. The method involves representation of branching structure, translation of L-systems to axial tree architectures, comparison of branching structure and the application of genetic algorithms. Branching structures are represented as axial trees and positional information is considered as an important attribute along with length and angle in the database configuration of branches. An algorithm is proposed for automatic L-system translation that compares randomly generated branching structures with the target structure. Edit distance, which is proposed as a measure of dissimilarity between rooted trees, is extended for the comparison of structures represented in axial trees and positional information is involved in the local cost function. Conventional genetic algorithms and repair mechanics are employed in the search for L-system models having the best fit to observational data.

Tabu search not an optimal choice for models of agricultural systems

With the increasing use of models to evaluate agricultural systems and identify the best solutions, the difficult task of economic optimisation can be performed by a number of different methods. Amongst these is the newer tabu search strategy, which initially appears well suited to this task. However, despite successes in other disciplines, it has methodological flaws when applied to multi-dimensional systems with continuous independent variables, as demonstrated in this paper. For these types of problems, typical of agricultural models, other methods such as simulated annealing or genetic algorithms appear better suited.

A Comparison of Techniques for the Reconstruction of Leaf Surfaces from Scanned Data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Performance of genetic algorithms and simulated annealing in the economic optimization of a herd dynamics model

This study focuses on replicated exploratory optimizations of a large and difficult beef herd dynamics model, using the net present value over a 10-year planning horizon as the variable of interest. Faced with a practical search-space of the order of 10100 possible management decision combinations, the thorough but slow search pattern of simulated annealing struggled, on average falling 1.2% short of the global optimum of the system. By comparison, the cross-breeding and mutating nature of the genetic algorithm searches usually produced good results, averaging 0.1% from the global optimum. Also, these were achieved with about half the computing time used by the simulated annealing optimizations. Hence, for this problem, genetic algorithms proved the superior method.