James Alfred Walker

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.

Evolution and Acquisition of Modules in Cartesian Genetic Programming

The paper presents for the first time automatic module acquisition and evolution within the graph based Cartesian Genetic Programming method. The method has been tested on a set of even parity problems and compared with Cartesian Genetic Programming without modules. Results are given that show that the new modular method evolves solutions up to 20 times quicker than the original non-modular method and that the speedup is more pronounced on larger problems. Analysis of some of the evolved modules shows that often they are lower order parity functions. Prospects for further improvement of the method are discussed.

Investigating the performance of module acquisition in cartesian genetic programming

Embedded Cartesian Genetic Programming (ECGP) is a form of the graph based Cartesian Genetic Programming (CGP) in which modules are automatically acquired and evolved. In this paper we compare the efficiencies of the ECGP and CGP techniques on three classes of problem: digital adders, digital multipliers and digital comparators. We show that in most cases ECGP shows a substantial improvement in performance over CGP and that the computational speedup is more pronounced on larger problems.

PAnDA: A Reconfigurable Architecture that Adapts to Physical Substrate Variations

Field programmable gate arrays (FPGAs) are widely used in applications where online reconfigurable signal processing is required. Speed and function density of FPGAs are increasing as transistor sizes shrink to the nanoscale. As these transistors reduce in size intrinsic variability becomes more of a problem and to reliably create electronic designs according to specification time consuming statistical simulations become necessary; and even with accurate models and statistical simulation, the fabrication yield will decrease as every physical instance of a design behaves differently. This paper describes an adaptive, evolvable architecture that allows for correction and optimization of circuits directly in hardware using bioinspired techniques. Similar to FPGAs, the programmable analog and digital array (PAnDA) architecture introduced provides a digital configuration layer for circuit design. Accessing additional configuration options of the underlying analog layer enables continuous adjustment of circuit characteristics at runtime, which enables dynamic optimization of the mapped designs performance. Moreover, the yield of devices can be improved postfabrication via reconfiguration of the analog layer, which can overcome faults induced due to variability and process defects. Since optimization goals are generic, i.e., not restricted to reducing stochastic variability, power consumption or increasing speed, the same mechanisms can also enhance the devices fault tolerant abilities in the case of component degradation and failures during its lifetime or when exposed to hazardous environments.

A multi-chromosome approach to standard and embedded cartesian genetic programming

Embedded Cartesian Genetic Programming (ECGP) is an extension of Cartesian Genetic Programming (CGP) that can automatically acquire, evolve and re-use partial solutions in the form of modules. In this paper, we introduce for the first time a new multi-chromosome approach to CGP and ECGP that allows difficult problems with multiple outputs to be broken down into many smaller, simpler problems with single outputs, whilst still encoding the entire solution in a single genotype. We also propose a multi-chromosome evolutionary strategy which selects the best chromosomes from the entire population to form the new fittest individual, which may not have been present in the population. The multi-chromosome approach to CGP and ECGP is tested on a number of multiple output digital circuits. Computational Effort figures are calculated for each problem and compared against those for CGP and ECGP. The results indicate that the use of multiple chromosomes in both CGP and ECGP provide a significant performance increase on all problems tested.

Parallel evolution using multi-chromosome cartesian genetic programming

Parallel and distributed methods for evolutionary algorithms have concentrated on maintaining multiple populations of genotypes, where each genotype in a population encodes a potential solution to the problem. In this paper, we investigate the parallelisation of the genotype itself into a collection of independent chromosomes which can be evaluated in parallel. We call this multi-chromosomal evolution (MCE). We test this approach using Cartesian Genetic Programming and apply MCE to a series of digital circuit design problems to compare the efficacy of MCE with a conventional single chromosome approach (SCE). MCE can be readily used for many digital circuits because they have multiple outputs. In MCE, an independent chromosome is assigned to each output. When we compare MCE with SCE we find that MCE allows us to evolve solutions much faster. In addition, in some cases we were able to evolve solutions with MCE that we unable to with SCE. In a case-study, we investigate how MCE can be applied to to a single objective problem in the domain of image classification, namely, the classification of breast X-rays for cancer. To apply MCE to this problem, we identify regions of interest (RoI) from the mammograms, divide the RoI into a collection of sub-images and use a chromosome to classify each sub-image. This problem allows us to evaluate various evolutionary mutation operators which can pairwise swap chromosomes either randomly or topographically or reuse chromosomes in place of other chromosomes.

Predicting prime numbers using cartesian genetic programming

Prime generating polynomial functions are known that can produce sequences of prime numbers (e.g. Euler polynomials). However, polynomials which produce consecutive prime numbers are much more difficult to obtain. In this paper, we propose approaches for both these problems. The first uses Cartesian Genetic Programming (CGP) to directly evolve integer based prime-prediction mathematical formulae. The second uses multi-chromosome CGP to evolve a digital circuit, which represents a polynomial. We evolved polynomials that can generate 43 primes in a row. We also found functions capable of producing the first 40 consecutive prime numbers, and a number of digital circuits capable of predicting up to 208 consecutive prime numbers, given consecutive input values. Many of the formulae have been previously unknown.

Improving the evolvability of digital multipliers using embedded cartesian genetic programming and product reduction

Embedded Cartesian Genetic Programming (ECGP) is a form of Genetic Programming based on an acyclic directed graph representation. In this paper we investigate the use of ECGP together with a technique called Product Reduction (PR) to reduce the time required to evolve a digital multiplier. The results are compared with Cartesian Genetic Programming (CGP) with and without PR and show that ECGP improves evolvability and also that PR improves the performance of both techniques by up to eight times on the digital multiplier problems tested.

Use of a multi-objective fitness function to improve cartesian genetic programming circuits

This paper describes an approach of using a multi-objective fitness function to improve the performance of digital circuits evolved using CGP. Circuits are initially evolved for correct functionality using conventional CGP before the NSGA-II algorithm is used to extract circuits which are more efficient in terms of design complexity and delay. This approach is used to evolve typical digital-system building block circuits with results compared to standard-CGP, other evolutionary methods and conventional designs.

Evolving Variability-Tolerant CMOS Designs

As the size of CMOS devices is approaching the atomic level, the increasing intrinsic device variability is leading to higher failure rates in conventional CMOS designs. In this paper, two approaches are proposed for evolving unconventional variability-tolerent CMOS designs: one uses a simple Genetic Algorithm, whilst the other uses Cartesian Genetic Programming. Both approaches successfully evolve unconventional designs for logic gates, whilst an inverter design also shows signs of variability-tolerance.