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Julian Miller

University of York, Electronics, Faculty Member

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Most of my papers on researchgate or the cartesian genetic programming web site. I am a physicist at heart, who is now a computer scientist. I am a part-time sculptor and occasional poet. I think of myself as a spiritual atheist. Here is a sonnet I wrote to express this:

Benedictus

What a debt we owe to Copernicus.
That ancient wonder turned to genius.
From then on we had to be curious.
As no longer was life gratuitous.
The deep mystery of its stimulus!
What made the universe a uterus?
Doesn’t this make you feel delirious?
Sometimes all I see is miraculous!
All our days should be a benedictus.
Yet there are times when it seems tedious.
As if life like us is ubiquitous.
When all the time it is anomalous.
Address: York, York, United Kingdom

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University of York

Wolfgang Banzhaf

University of York

Wolfgang Banzhaf

Memorial University of Newfoundland

Consiglio Nazionale delle Ricerche (CNR)

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Papers by Julian Miller

SMCGP2: self modifying cartesian genetic programming in two dimensions

Self Modifying Cartesian Genetic Programming is a general purpose, graph-based, developmental for... more Self Modifying Cartesian Genetic Programming is a general purpose, graph-based, developmental form of Cartesian Genetic Programming. Using a combination of computational functions and special functions that can modify the phenotype at runtime, it has been employed to find general solutions to certain Boolean circuits and mathematical problems. In the present work, a new version, of SMCGP is proposed and demonstrated. Compared to the original SMCGP both the representation and the function set have been simplified. However, the new representation is also two-dimensional and it allows evolution and development to have more ways to solve a given problem. Under most situations we show that the new method makes the evolution of solutions to even parity and binary addition faster than with previous version of SMCGP.

The alchemy of computation: designing with the unknown

Natural Computing

Modern computers allow a methodical search of possibly billions of experiments and the exploitati... more Modern computers allow a methodical search of possibly billions of experiments and the exploitation of interactions that are not known in advance. This enables a bottom-up process of design by assembling or configuring systems and testing the degree to which they fulfill the desired goal. We give two detailed examples of this process. One is referred to as Cartesian genetic programming and the other evolution-in-materio. In the former, evolutionary algorithms are used to exploit the interactions of software components representing mathematical, logical, or computational elements. In the latter, evolutionary algorithms are used to manipulate physical systems particularly at the electrical or electronic level. We compare and contrast both approaches and discuss possible new research directions by borrowing ideas from one and using them in the other.

Genetic Programming: 4th European Conference, EuroGP 2001, Lake Como, Italy, April 2001 Proceedings

A developmental model of neural computation using cartesian genetic programming

The brain has long been seen as a powerful analogy from which novel computational techniques coul... more The brain has long been seen as a powerful analogy from which novel computational techniques could be devised. However, most artificial neural network approaches have ignored the genetic basis of neural functions. In this paper we describe a radically different approach. We have devised a compartmental model of a neuron as a collection of seven chromosomes encoding distinct computational functions representing aspects of real neurons. This model allows neurons, dendrites, and axon branches to grow, die and change while solving a computational problem. This also causes the synaptic morphology to change and affect the information processing. Since the appropriate computational equivalent functions of neural computation are unknown, we have used a form of genetic programming known as Cartesian Genetic Programming (CGP) to obtain these functions. We have evaluated the learning potential of this system in the context of solving a well known agent based learning scenario, known as wumpus world and obtained promising results.

Recurrent Cartesian Genetic Programming of Artificial Neural Networks

Genetic Programming and Evolvable Machines

Cartesian Genetic Programming of Artificial Neural Networks is a NeuroEvolutionary method based o... more Cartesian Genetic Programming of Artificial Neural Networks is a NeuroEvolutionary method based on Cartesian Genetic Programming. Cartesian Genetic Programming has recently been extended to allow recurrent connections. This work investigates applying the same recurrent extension to Cartesian Genetic Programming of Artificial Neural Networks in order to allow the evolution of recurrent neural networks. The new Recurrent Cartesian Genetic Programming of Artificial Neural Networks method is applied to the domain of series forecasting where it is shown to significantly outperform all standard forecasting techniques used for comparison including autoregressive integrated moving average and multilayer perceptrons. An ablation study is also performed isolating which specific aspects of Recurrent Cartesian Genetic Programming of Artificial Neural Networks contribute to it's effectiveness for series forecasting.

An evolvable hardware approach to digital filter design

IEE Half-day Colloquium on Evolutionary Hardware Systems, 1999

Towards the Automatic Design of More Efficient Digital Circuits

This paper introduces a new methodology of evolving electronic circuits by which the process of e... more 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 ¡ two-input logic gates that in terms of number of two-input gates used is ¡ ¢¡ £ more efficient than the most efficient known conventional design. The logic operators required to implement this circuit are ¤ ¥ ANDs, ¦ XORs, and inversions (NOT). The evolved four-bit multiplier consists of § two-input logic gates that is ¤ © ¢ ¦ £ 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.

Fault tolerant control using Cartesian genetic programming

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation, 2008

The paper focuses on the evolution of algorithms for control of a machine in the presence of sens... more The paper focuses on the evolution of algorithms for control of a machine in the presence of sensor faults, using Cartesian Genetic Programming. The key challenges in creating training sets and a fitness function that encourage a general solution are discussed. The evolved algorithms are analysed and discussed. It was found that highly novel, mathematically elegant and hitherto unknown solutions were found.

An Empirical Study of the Efficiency of Learning Boolean Functions

A Developmental method for growing Graphs and

Solving Real-valued Optimisation Problems using Cartesian Genetic Programming

Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, 2007

Classical Evolutionary Programming (CEP) and Fast Evo- lutionary Programming (FEP) have been appl... more Classical Evolutionary Programming (CEP) and Fast Evo- lutionary Programming (FEP) have been applied to real- valued function optimisation. Both of these techniques di- rectly evolve the real-values that are the arguments of the real-valued function. In this paper we have applied a form of genetic programming called Cartesian Genetic Program- ming (CGP) to a number of real-valued optimisation bench- mark problems. The approach we have taken is to evolve a computer program that controls a writing-head, which moves along and interacts with a finite set of symbols that are interpreted as real numbers, instead of manipulating the real numbers directly. In other studies, CGP has already been shown to benefit from a high degree of neutrality. We hope to exploit this for real-valued function optimisation problems to avoid being trapped on local optima. We have also used an extended form of CGP called Embedded CGP (ECGP) which allows the acquisition, evolution and re-use of modules. The effectiveness of CGP and ECGP are com- pared and contrasted with CEP and FEP on the benchmark problems. Results show that the new techniques are very ef- fective.

Aspects of Digital Evolution: Evolvability and

Evolutionary Art with Cartesian Genetic Programming

Techniques from the field of Evolutionary Computation are used to evolve a wide variety of aesthe... more Techniques from the field of Evolutionary Computation are used to evolve a wide variety of aesthetically pleasing images using Cartesian Genetic Programming (CGP). The challenges that arise from employing a fitness function based on aesthetics, and the benefits that CGP can provide, are investigated and discussed. A significant piece of software was developed that places a focus on providing the user with efficient control over the evolutionary process. Several 'non-user' fitness functions that assess the phenotypes and genotypes of the chromosomes were also employed with varying success. To improve these results, methods of maintaining diversity within the population that take advantage of the neutrality of CGP are implemented and tested.

Evolutionary Approach to Design Multiple-Valued Combinational Circuits

The Role of Neutral and Adaptive Mutation in an Evolutionary Search

We investigate neutrality in the simple Genetic Algorithms (SGA) and in our neutrality-enabled ev... more We investigate neutrality in the simple Genetic Algorithms (SGA) and in our neutrality-enabled evolutionary system using the OneMax problem. The results show that with the support of limited neutrality, SGA is less effective than our system where a larger amount of neutrality is supported. In order to understand the role of neutrality in evolutionary search of this unimodal landscape, we have created a theoretical framework that gives the number of gene changes under different levels of neutrality. The interim results of this theoretical work are also presented.

Needles in haystacks are not hard to find with neutrality

Optimisation techniques based on the use of genetic algorithms (GAs) for logic implementation on FPGAs

Optimisation Techniques based on the use of Genetic Algorithms (GAS) for Logic Implementation on ... more

Restricted Evaluation Genetic Algorithms with Tabu Search for Optimising Boolean Functions als Multi-level AND-EXOR Networks

Scalability Problems of Digital Circuit Evolution

A major problem in the evolutionary design of combinational circuits is the problem of scale. Thi... more A major problem in the evolutionary design of combinational circuits is the problem of scale. This refers to the design of electronic circuits in which the numberof gates required to implementthe optimal circuit is too high to search the space of all designs in reasonable time, even by evolution. The reason is twofold: fir stly, the size of the

A comparison between developmental and direct encodings. An update of the GECCO 2006 Paper 'The Dead State

In this paper we compare the evolutionary and run time behaviours of two forms of indirect encodi... more In this paper we compare the evolutionary and run time behaviours of two forms of indirect encoding and a direct encoding. The indirect encodings are comparable to approaches used in the emerging field of developmental systems. We evolve a developmental encoding based on a cellular automaton to grow bit patterns of predefined complexities (in the Kolmogorov sense), and compare its behaviour to the evolution of a direct encoding on the same task. We find that the developmental encodings perform worse at high complexities than the direct encodings, and suggest that this is an artefact from using cell overwriting. Our findings suggest that developmental approaches may scale better for tasks that have complexities below a certain threshold. In this updated version of the paper, we also compare the difference in behaviour of the two approaches for short and long bit strings, and observe that again cell overwriting is detrimental to performance.

SMCGP2: self modifying cartesian genetic programming in two dimensions

Self Modifying Cartesian Genetic Programming is a general purpose, graph-based, developmental for... more Self Modifying Cartesian Genetic Programming is a general purpose, graph-based, developmental form of Cartesian Genetic Programming. Using a combination of computational functions and special functions that can modify the phenotype at runtime, it has been employed to find general solutions to certain Boolean circuits and mathematical problems. In the present work, a new version, of SMCGP is proposed and demonstrated. Compared to the original SMCGP both the representation and the function set have been simplified. However, the new representation is also two-dimensional and it allows evolution and development to have more ways to solve a given problem. Under most situations we show that the new method makes the evolution of solutions to even parity and binary addition faster than with previous version of SMCGP.

The alchemy of computation: designing with the unknown

Natural Computing

Modern computers allow a methodical search of possibly billions of experiments and the exploitati... more Modern computers allow a methodical search of possibly billions of experiments and the exploitation of interactions that are not known in advance. This enables a bottom-up process of design by assembling or configuring systems and testing the degree to which they fulfill the desired goal. We give two detailed examples of this process. One is referred to as Cartesian genetic programming and the other evolution-in-materio. In the former, evolutionary algorithms are used to exploit the interactions of software components representing mathematical, logical, or computational elements. In the latter, evolutionary algorithms are used to manipulate physical systems particularly at the electrical or electronic level. We compare and contrast both approaches and discuss possible new research directions by borrowing ideas from one and using them in the other.

Genetic Programming: 4th European Conference, EuroGP 2001, Lake Como, Italy, April 2001 Proceedings

A developmental model of neural computation using cartesian genetic programming

The brain has long been seen as a powerful analogy from which novel computational techniques coul... more The brain has long been seen as a powerful analogy from which novel computational techniques could be devised. However, most artificial neural network approaches have ignored the genetic basis of neural functions. In this paper we describe a radically different approach. We have devised a compartmental model of a neuron as a collection of seven chromosomes encoding distinct computational functions representing aspects of real neurons. This model allows neurons, dendrites, and axon branches to grow, die and change while solving a computational problem. This also causes the synaptic morphology to change and affect the information processing. Since the appropriate computational equivalent functions of neural computation are unknown, we have used a form of genetic programming known as Cartesian Genetic Programming (CGP) to obtain these functions. We have evaluated the learning potential of this system in the context of solving a well known agent based learning scenario, known as wumpus world and obtained promising results.

Recurrent Cartesian Genetic Programming of Artificial Neural Networks

Genetic Programming and Evolvable Machines

Cartesian Genetic Programming of Artificial Neural Networks is a NeuroEvolutionary method based o... more Cartesian Genetic Programming of Artificial Neural Networks is a NeuroEvolutionary method based on Cartesian Genetic Programming. Cartesian Genetic Programming has recently been extended to allow recurrent connections. This work investigates applying the same recurrent extension to Cartesian Genetic Programming of Artificial Neural Networks in order to allow the evolution of recurrent neural networks. The new Recurrent Cartesian Genetic Programming of Artificial Neural Networks method is applied to the domain of series forecasting where it is shown to significantly outperform all standard forecasting techniques used for comparison including autoregressive integrated moving average and multilayer perceptrons. An ablation study is also performed isolating which specific aspects of Recurrent Cartesian Genetic Programming of Artificial Neural Networks contribute to it's effectiveness for series forecasting.

An evolvable hardware approach to digital filter design

IEE Half-day Colloquium on Evolutionary Hardware Systems, 1999

Towards the Automatic Design of More Efficient Digital Circuits

This paper introduces a new methodology of evolving electronic circuits by which the process of e... more 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 ¡ two-input logic gates that in terms of number of two-input gates used is ¡ ¢¡ £ more efficient than the most efficient known conventional design. The logic operators required to implement this circuit are ¤ ¥ ANDs, ¦ XORs, and inversions (NOT). The evolved four-bit multiplier consists of § two-input logic gates that is ¤ © ¢ ¦ £ 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.

Fault tolerant control using Cartesian genetic programming

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation, 2008

The paper focuses on the evolution of algorithms for control of a machine in the presence of sens... more The paper focuses on the evolution of algorithms for control of a machine in the presence of sensor faults, using Cartesian Genetic Programming. The key challenges in creating training sets and a fitness function that encourage a general solution are discussed. The evolved algorithms are analysed and discussed. It was found that highly novel, mathematically elegant and hitherto unknown solutions were found.

An Empirical Study of the Efficiency of Learning Boolean Functions

A Developmental method for growing Graphs and

Solving Real-valued Optimisation Problems using Cartesian Genetic Programming

Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, 2007

Classical Evolutionary Programming (CEP) and Fast Evo- lutionary Programming (FEP) have been appl... more Classical Evolutionary Programming (CEP) and Fast Evo- lutionary Programming (FEP) have been applied to real- valued function optimisation. Both of these techniques di- rectly evolve the real-values that are the arguments of the real-valued function. In this paper we have applied a form of genetic programming called Cartesian Genetic Program- ming (CGP) to a number of real-valued optimisation bench- mark problems. The approach we have taken is to evolve a computer program that controls a writing-head, which moves along and interacts with a finite set of symbols that are interpreted as real numbers, instead of manipulating the real numbers directly. In other studies, CGP has already been shown to benefit from a high degree of neutrality. We hope to exploit this for real-valued function optimisation problems to avoid being trapped on local optima. We have also used an extended form of CGP called Embedded CGP (ECGP) which allows the acquisition, evolution and re-use of modules. The effectiveness of CGP and ECGP are com- pared and contrasted with CEP and FEP on the benchmark problems. Results show that the new techniques are very ef- fective.

Aspects of Digital Evolution: Evolvability and

Evolutionary Art with Cartesian Genetic Programming

Techniques from the field of Evolutionary Computation are used to evolve a wide variety of aesthe... more Techniques from the field of Evolutionary Computation are used to evolve a wide variety of aesthetically pleasing images using Cartesian Genetic Programming (CGP). The challenges that arise from employing a fitness function based on aesthetics, and the benefits that CGP can provide, are investigated and discussed. A significant piece of software was developed that places a focus on providing the user with efficient control over the evolutionary process. Several 'non-user' fitness functions that assess the phenotypes and genotypes of the chromosomes were also employed with varying success. To improve these results, methods of maintaining diversity within the population that take advantage of the neutrality of CGP are implemented and tested.

Evolutionary Approach to Design Multiple-Valued Combinational Circuits

The Role of Neutral and Adaptive Mutation in an Evolutionary Search

We investigate neutrality in the simple Genetic Algorithms (SGA) and in our neutrality-enabled ev... more We investigate neutrality in the simple Genetic Algorithms (SGA) and in our neutrality-enabled evolutionary system using the OneMax problem. The results show that with the support of limited neutrality, SGA is less effective than our system where a larger amount of neutrality is supported. In order to understand the role of neutrality in evolutionary search of this unimodal landscape, we have created a theoretical framework that gives the number of gene changes under different levels of neutrality. The interim results of this theoretical work are also presented.

Needles in haystacks are not hard to find with neutrality

Optimisation techniques based on the use of genetic algorithms (GAs) for logic implementation on FPGAs

Optimisation Techniques based on the use of Genetic Algorithms (GAS) for Logic Implementation on ... more

Restricted Evaluation Genetic Algorithms with Tabu Search for Optimising Boolean Functions als Multi-level AND-EXOR Networks

Scalability Problems of Digital Circuit Evolution

A major problem in the evolutionary design of combinational circuits is the problem of scale. Thi... more A major problem in the evolutionary design of combinational circuits is the problem of scale. This refers to the design of electronic circuits in which the numberof gates required to implementthe optimal circuit is too high to search the space of all designs in reasonable time, even by evolution. The reason is twofold: fir stly, the size of the

A comparison between developmental and direct encodings. An update of the GECCO 2006 Paper 'The Dead State

In this paper we compare the evolutionary and run time behaviours of two forms of indirect encodi... more In this paper we compare the evolutionary and run time behaviours of two forms of indirect encoding and a direct encoding. The indirect encodings are comparable to approaches used in the emerging field of developmental systems. We evolve a developmental encoding based on a cellular automaton to grow bit patterns of predefined complexities (in the Kolmogorov sense), and compare its behaviour to the evolution of a direct encoding on the same task. We find that the developmental encodings perform worse at high complexities than the direct encodings, and suggest that this is an artefact from using cell overwriting. Our findings suggest that developmental approaches may scale better for tasks that have complexities below a certain threshold. In this updated version of the paper, we also compare the difference in behaviour of the two approaches for short and long bit strings, and observe that again cell overwriting is detrimental to performance.