Peter A. Whigham

Grammar-based Genetic Programming: a survey

Grammar formalisms are one of the key representation structures in Computer Science. So it is not surprising that they have also become important as a method for formalizing constraints in Genetic Programming (GP). Practical grammar-based GP systems first appeared in the mid 1990s, and have subsequently become an important strand in GP research and applications. We trace their subsequent rise, surveying the various grammar-based formalisms that have been used in GP and discussing the contributions they have made to the progress of GP. We illustrate these contributions with a range of applications of grammar-based GP, showing how grammar formalisms contributed to the solutions of these problems. We briefly discuss the likely future development of grammar-based GP systems, and conclude with a brief summary of the field.

Modelling rainfall-runoff using genetic programming

Genetic programming is an inductive form of machine learning that evolves a computer program to perform a task defined by a set of presented (training) examples and has been successfully applied to problems that are complex, nonlinear and where the size, shape, and overall form of the solution are not explicitly known in advance. This paper describes the application of a grammatically-based genetic programming system to discover rainfall-runoff relationships for two vastly different catchments. A context-free grammar is used to define the search space for the mathematical language used to express the evolving programs. A daily time series of rainfall-runoff is used to train the evolving population. A deterministic lumped parameter model, based on the unit hydrograph, is compared with the results of the evolved models on an independent data set. The favourable results of the genetic programming approach show that machine learning techniques are potentially a useful tool for developing hydrological models, especially when surface water movement and water losses are poorly understood.

A Schema Theorem for context-free grammars

The basic Schema Theorem for genetic algorithms is modified for a grammatically-based learning system. A context-free grammar is used to define a language in which each sentence is mapped to a fitness value. The derivation trees associated with these sentences are used to define the structure of schemata. The effect of crossover and mutation on schemata is described. A schema theorem is developed which describes how sentences of a language are propagated during evolution.

Neighbourhood deprivation and access to alcohol outlets: a national study

People living in poor areas suffer higher mortality than those in wealthy areas. Environmental factors partly explain this association, including exposure to pollutants and accessibility of healthcare. We sought to determine whether proximity to alcohol outlets varied by area deprivation in New Zealand. Roadway travel distance from each census unit to the nearest alcohol outlet was summarised according to socioeconomic deprivation for each area. Analyses were conducted by license type (pubs/bars, clubs, restaurants, off-licenses) and community urban-rural status. Strong associations were found between proximity to the nearest alcohol outlet and deprivation, there being greater access to outlets in more-deprived urban areas.

Modelling Microcystis aeruginosa bloom dynamics in the Nakdong River by means of evolutionary computation and statistical approach

Dynamics of a bloom-forming cyanobacteria (Microcystis aeruginosa ) in a eutrophic river � /reservoir hybrid system were modelled using a genetic programming (GP) algorithm and multivariate linear regression (MLR). The lower Nakdong River has been influenced by cultural eutrophication since construction of an estuarine barrage in 1987. During 1994 � /1998, the average concentrations of nutrients and phytoplankton were: NO3 � /N, 2.7 mg l � 1 ;N H 4 � /N, 0.6 mg l � 1 ;P O 4� � /P, 34.7 m gl � 1 ; and chlorophyll a , 50.2 m gl � 1 . Blooms of M. aeruginosa occurred in summers when there were droughts. Using data from 1995 to 1998, GP and MLR were used to construct equation models for predicting the occurrence of M. aeruginosa . Validation of the model was done using data from 1994, a year when there were severe summer blooms. GP model was very successful in predicting the temporal dynamics and magnitude of blooms while MLR resulted rather insufficient predictability. The lower Nakdong River exhibits reservoir-like ecological dynamics rather than riverine, and for this reason a previous river mechanistic model failed to describe uncertainty and complexity. Results of this study suggest that an inductive-empirical approach is more suitable for modelling the dynamics of bloom-forming algal species in a river � /reservoir transitional system. # 2002 Elsevier Science B.V. All rights reserved.

Predicting chlorophyll-a in freshwater lakes by hybridising process-based models and genetic algorithms

This paper describes the application of several machine learning techniques to modify a process-based difference equation. The original process equation was developed to model phytoplankton abundance based on measured limnological and climate variables. A genetic algorithm is shown to be capable of calibrating the constants of the process model, based on the data describing a lake environment. The resulting process model has a significantly improved performance based on unseen test data. A symbolic genetic algorithm is then applied to the process model to evolve new expressions for the grazing term of the equation. The results indicate that this approach can be used to explore new process formulations and to improve the generalisation and predictive response of process models.

An inductive approach to ecological time series modelling by evolutionary computation

Building time series models for ecological systems that can be physically interpreted is important both for understanding the dynamics of these natural systems and the development of decision support systems. This work describes the application of an evolutionary computation framework for the discovery of predictive equations and rules for phytoplankton abundance in freshwater lakes from time series data. The suggested framework evolves several different equations and rules, based on limnological and climate variables. The results demonstrate that non-linear processes in natural systems may be successfully modelled through the use of evolutionary computation techniques. Further, it shows that a grammar based genetic programming system may be used as a tool for exploring the driving processes underlying freshwater system dynamics.

Implicitly Controlling Bloat in Genetic Programming

During the evolution of solutions using genetic programming (GP) there is generally an increase in average tree size without a corresponding increase in fitness-a phenomenon commonly referred to as bloat. Although previously studied from theoretical and practical viewpoints there has been little progress in deriving controls for bloat which do not explicitly refer to tree size. Here, the use of spatial population structure in combination with local elitist replacement is shown to reduce bloat without a subsequent loss of performance. Theoretical concepts regarding inbreeding and the role of elitism are used to support the described approach. The proposed system behavior is confirmed via extensive computer simulations on benchmark problems. The main practical result is that by placing a population on a torus, with selection defined by a Moore neighborhood and local elitist replacement, bloat can be substantially reduced without compromising performance.

The dynamic geometry of geographical vector agents

This paper introduces vector agents (VA), an approach to impose a systematic framework on the geometric element of Torrens and Benenson’s Geographic Automata System (GAS). Both schemes use vector geometry as an antidote to the geographically unrealistic regular tessellation cellular automata (CA). The work reported here explores the properties of irregular and dynamic VAs in particular, a subclass of geometry not hitherto covered in detail in a spatial agent modelling context. Three realisations of vector agent geometry change are reported in this paper: the Brownian motion algorithm (through midpoint displacement); edge displacement; and vertex displacement. Through these manipulators, it is shown that vector agents offer the ability to explicitly control geometric form through the alteration of simple parameters (with the potential for further generalisation and transformation operations). 2007 Elsevier Ltd. All rights reserved.

Induction of a marsupial density model using genetic programming and spatial relationships

Machine learning techniques have been developed that allow the induction of spatial models for the prediction of habitat types and population distribution. However, most learning approaches are based on a propositional language for the development of models and therefore cannot express a wide range of possible spatial relationships that exist in the data. This paper compares the application of a functional evolutionary machine learning technique for prediction of marsupial density to some standard machine learning techniques. The ability of the learning system to express spatial relationships allows an improved predictive model to be developed, which is both parsimonious and understandable. Additionally, the maps produced from this approach have a generalised appearance of the measured glider density, suggesting that the underlying preferred habitat properties of the greater glider have been identified.