Julian F. Miller

Cartesian Genetic Programming

This paper presents a new form of Genetic Programming called Cartesian Genetic Programming in which a program is represented as an indexed graph. The graph is encoded in the form of a linear string of integers. The inputs or terminal set and node outputs are numbered sequentially. The node functions are also separately numbered. The genotype is just a list of node connections and functions. The genotype is then mapped to an indexed graph that can be executed as a program. Evolutionary algorithms are used to evolve the genotype in a symbolic regression problem (sixth order polynomial) and the Santa Fe Ant Trail. The computational effort is calculated for both cases. It is suggested that hit effort is a more reliable measure of computational efficiency. A neutral search strategy that allows the fittest genotype to be replaced by another equally fit genotype (a neutral genotype) is examined and compared with non-neutral search for the Santa Fe ant problem. The neutral search proves to be much more effective.

Cartesian genetic programming

Cartesian Genetic Programming (CGP) is a well-known form of Genetic Programming developed by Julian Miller in 1999-2000. In its classic form, it uses a very simple integer address-based genetic representation of a program in the form of a directed graph. Graphs are very useful program representations and can be applied to many domains (e.g. electronic circuits, neural networks). It can handle cyclic or acyclic graphs. In a number of studies, CGP has been shown to be comparatively efficient to other GP techniques. It is also very simple to program. The classical form of CGP has undergone a number of developments which have made it more useful, efficient and flexible in various ways. These include self-modifying CGP (SMCGP), cyclic connections (recurrent-CGP), encoding artificial neural networks and automatically defined functions (modular CGP). SMCGP uses functions that cause the evolved programs to change themselves as a function of time. This makes it possible to find general solutions to classes of problems and mathematical algorithms (e.g. arbitrary parity, n-bit binary addition, sequences that provably compute pi and e to arbitrary precision, and so on). Recurrent-CGP allows evolution to create programs which contain cyclic, as well as acyclic, connections. This enables application to tasks which require internal states or memory. It also allows CGP to create recursive equations. CGP encoded artificial neural networks represent a powerful training method for neural networks. This is because CGP is able to simultaneously evolve the networks connections weights, topology and neuron transfer functions. It is also compatible with Recurrent-CGP enabling the evolution of recurrent neural networks. The tutorial will cover the basic technique, advanced developments and applications to a variety of problem domains. It will present a live demo of how the open source cgplibrary can be used.

Principles in the Evolutionary Design of Digital Circuits—Part II

In a previous work it was argued that by studying evolved designs of gradually increasing scale, one might be able to discern new, efficient, and generalisable principles of design. These ideas are tested in the context of designing digital circuits, particularly arithmetic circuits. This process of discovery is seen as a principle extraction loop in which the evolved data is analysed both phenotypically and genotypically by processes of data mining and landscape analysis. The information extracted is then fed back into the evolutionary algorithm to enhance its search capabilities and hence increase the likelihood of identifying new principles which explain how to build systems which are too large to evolve.

Neutrality and the Evolvability of Boolean Function Landscape

This work is a study of neutrality in the context of Evolutionary Computation systems. In particular, we introduce the use of explicit neutrality with an integer string coding scheme to allow neutrality to be measured during evolution. We tested this method on a Boolean benchmark problem. The experimental results indicate that there is a positive relationship between neutrality and evolvability: neutrality improves evolvability. We also identify four characteristics of adaptive/neutral mutations that are associated with high evolvability. They may be the ingredients in designing effective Evolutionary Computation systems for the Boolean class problem.

Evolving a Self-Repairing, Self-Regulating, French Flag Organism

A method for evolving programs that construct multicellular structures (organisms) is described. The paper concentrates on the difficult problem of evolving a cell program that constructs a fixed size French flag. We obtain and analyze an organism that shows a remarkable ability to repair itself when subjected to severe damage. Its behaviour resembles the regenerative power of some living organisms.

Information Characteristics and the Structure of Landscapes

Various techniques for statistical analysis of the structure of fitness landscapes have been proposed. An important feature of these techniques is that they study the ruggedness of landscapes by measuring their correlation characteristics. This paper proposes a new information analysis of fitness landscapes. The underlying idea is to consider a fitness landscape as an ensemble of objects that are related to the fitness of neighboring points. Three information characteristics of the ensemble are defined and studied. They are termed: information content, partial information content, and information stability. The information characteristics of a range of landscapes with known correlation features are analyzed in an attempt to reveal the advantages of the information analysis. We show that the proposed analysis is an appropriate tool for investigating the structure of fitness landscapes.

The Advantages of Landscape Neutrality in Digital Circuit Evolution

The paper studies the role of neutrality in the fitness landscapes associated with the evolutionary design of digital circuits and particularly the three-bit binary multiplier. For the purpose of the study, digital circuits are evolved extrinsically on an array of logic cells. To evolve on an array of cells, a genotype-phenotype mapping has been devised by which neutrality can be embedded in the resulting fitness landscape. It is argued that landscape neutrality is beneficial for digital circuit evolution.

Evolving Developmental Programs for Adaptation, Morphogenesis, and Self-Repair

A method for evolving a developmental program inside a cell to create multicellular organisms of arbitrary size and characteristics is described. The cell genotype is evolved so that the organism will organize itself into well defined patterns of differentiated cell types (e.g. the French Flag). In addition the cell genotypes are evolved to respond appropriately to environmental signals that cause metamorphosis of the whole organism. A number of experiments are described that show that the organisms exhibit emergent properties of self-repair and adaptation.

The Automatic Acquisition, Evolution and Reuse of Modules in Cartesian Genetic Programming

This paper presents a generalization of the graph- based genetic programming (GP) technique known as Cartesian genetic programming (CGP). We have extended CGP by utilizing automatic module acquisition, evolution, and reuse. To benchmark the new technique, we have tested it on: various digital circuit problems, two symbolic regression problems, the lawnmower problem, and the hierarchical if-and-only-if problem. The results show the new modular method evolves solutions quicker than the original nonmodular method, and the speedup is more pronounced on larger problems. Also, the new modular method performs favorably when compared with other GP methods. Analysis of the evolved modules shows they often produce recognizable functions. Prospects for further improvements to the method are discussed.

Towards the automatic design of more efficient digital circuits

This paper introduces a new methodology of evolving electronic circuits by which the process of evolutionary design is guaranteed to produce a functionally correct solution. The method employs a mapping to represent an electronic circuit on an array of logic cells that is further encoded within a genotype. The mapping is many-to-one and thus there are many genotypes that have equal fitness values. Genotypes with equal fitness values define subgraphs in the resulting fitness landscapes referred to as neutral networks. This is further used in the design of a neutral network that connects the conventional with other more efficient designs. To explore such a network a navigation strategy is defined by which the space of all functionally correct circuits can be explored. The paper shows that very efficient digital circuits can be obtained by evolving from the conventional designs. Results for several binary multiplier circuits such as the three and four-bit multipliers are reported. The evolved solution for the three-bit multiplier consists of 23 two-input logic gates that in terms of number of two-input gates used is 23.3% more efficient than the most efficient known conventional design. The logic operators required to implement this circuit are 14 ANDs, 9 XORs, and 2 inversions (NOT). The evolved four-bit multiplier consists of 57 two-input logic gates that is 10.9% more efficient (in terms of number of two-input gates used) than the most efficient known conventional design. The optimal size of the target circuits is also studied by measuring the length of the neutral walks from the obtained designs.