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We present a method for constructing electronic circuits that uses analogues of biological multi-cellular development, genetic regulatory networks, and transcription and translation processes to build circuits. We show how small circuits may be evolved and how they may be reused to build larger circuits. We also demonstrate that the artificial `organisms' are capable of regeneration so that circuit functionality can be recovered after damage.

This paper presents a method for co-evolving neuro-inspired developmental programs for playing checkers. Each player's program is represented by seven chromosomes encoding digital circuits, using a form of genetic programming, called Cartesian Genetic Programming (CGP). The neural network that occurs by running the genetic programs has a highly dynamic morphology in which neurons grow, and die, and neurite branches together with synaptic connections form and change in response to situations encountered on the checkers board. The results show that, after a number of generations, by playing each other the agents play much better than those from earlier generations. Such learning abilities are encoded at a geneticlevel rather than at the phenotype level of neural connections.

Evolution is particularly good at finding specific solutions, which are only valid for exactly the input and environment that are presented during evolution. In most evolution experiments the input pattern order problemis not considered, even though the ability to provide a correct result for any input pattern is a prerequisite for valid circuits. Therefore, the importance of including randomness in the input pattern applied during evolution is addressed in this paper. This is shown to be mandatory--particularly in the case of unconstrained intrinsic evolution of digital circuits--in order to find valid solutions. The different ways in which unconstrained evolution and constrained evolution exploit resources of a hardware substrate are compared. It is also shown that evolution benefits from versatile input configurations. Furthermore, hierarchical fitness functions, previously introduced to improve the evolution of combinatorial circuits, are applied to the evolution of sequential circuits.

A developmental model of neural network is presented and evaluated in the game of Checkers. The network is developed using cartesian genetic programs (CGP) as genotypes. Two agents are provided with this network and allowed to co-evolve untill they start playing better. The network that occurs by running theses genetic programs has a highly dynamic morphology in which neurons grow, and die, and neurite branches together with synaptic connections form and change in response to situations encountered on the checkers board. The method has no board evaluation function, no explicit learning rules and no human expertise at playing checkers is used. The results show that, after a number of generations, by playing each other the agents begin to play much better and can easily beat agents that occur in earlier generations. Such learning abilities are encoded at a genetic level rather than at the phenotype level of neural connections.

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.

Biology presents incomparable, but desirable, characteristics compared to engineered systems. Inspired by biological development, we have devised a multi-layered design architecture that attempts to capture many of the favorable characteristics of biological mechanisms for application to design problems. In this paper we have identified and implemented essential features of Genetic Regulatory Networks (GRNs) and cell signaling so that our system exhibits self-organization which is reminiscent of aspects of biological systems.

This work is part of a project that aims to develop and operate integrated evolvable hardware systems using unconstrained evolution. Experiments are carried out on an evolvable hardware platform featuring both combinatorial and registered logic as well as sequential feedback loops. In order to be able to accurately assess the transient output of the system and at the same time speed up evolution, new fitness evaluation methods are introduced. These bitwise and hierarchical fitness evaluation methods are adapted and further developed specifically for hardware implementation. It is shown that the newly developed approaches are particularly powerful in coping with two important issues: computational ambiguities, which generally occur when evaluating binary strings, and transient effects resulting from measuring hardware output. On two combinatorial problems it is shown that the new fitness functions improve the performance of evolution and allow stable solutions to be found more reliably. The experiments are carried out with a recently developed hardware platform called reconfigurable integrated system array (RISA).

The majority of artificial neural networks are static and lifeless and do not change themselves within a learning environment. In these models learning is seen as the process of obtaining the strengths of connections between neurons (i.e. weights). We refer to this as the 'synaptic dogma'. This is in marked contrast with biological networks which have time dependent morphology and in which practically all neural aspects can change or be shaped by mutual interactions and interactions with an external environment. Inspired by this and many aspects of neuroscience, we have designed a new kind of neural network. In this model, neurons are represented by seven evolved programs that model particular components and aspects of biological neurons (dendrites, soma, axons, synapses, electrical and developmental behaviour). Each network begins as a small randomly generated network of neurons. When the seven programs are run, the neurons, dendrites, axons and synapses can increase or decrease in number and change in interaction with an external environment. Our aim is to show that it is possible to evolve programs that allow a network to learn through experience (i.e. encode the ability to learn). We report on our continuing investigations in the context of learning how to play checkers.

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.

A coevolutionary competitive learning environment for two antagonistic agents is presented. The agents are controlled by a new kind of computational network based on a compartmentalised model of neurons. We have taken the view that the genetic basis of neurons is an important [27] and neglected aspect of previous approaches. Accordingly, we have defined a collection of chromosomes representing various aspects of the neuron: soma, dendrites and axon branches, and synaptic connections. Chromosomes are represented and evolved using a form of genetic programming known as Cartesian Genetic Programming. The network formed by running the chromosomal programs has a highly dynamic morphology in which neurons grow, and die, and neurite branches together with synaptic connections form and change in response to environmental interactions. The idea of this paper is to demonstrate the importance of the genetic transfer of learned experience and life time learning. The learning is a consequence of the complex dynamics produced as a result of interaction (coevolution) between two intelligent agents. Our results show that both agents exhibit interesting learning capabilities.

Classical Evolutionary Programming (CEP) and Fast Evolutionary Programming (FEP) have been applied to real-valued function optimisation. Both of these techniques directly 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 Programming (CGP) to a number of real-valued optimisation benchmark 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 compared and contrasted with CEP and FEP on the benchmark problems. Results show that the new techniques are very effective.

Embedded Cartesian Genetic Programming (ECGP) is an extension of Cartesian Genetic Programming (CGP) capable of acquiring, evolving and re-using partial solutions. In this paper, we apply for the first time CGP and ECGP to the ones-max and order-3 deceptive problems, which are normally associated with Genetic Algorithms. Our approach uses CGP and ECGP to evolve a sequence of commands for a tape-head, which produces an arbitrary length binary string on a piece of tape. Computational effort figures are calculated for CGP and ECGP and our results compare favourably with those of Genetic Algorithms.

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.

Although intrinsic evolution has been shown to be capable of exploiting the physical properties of materials to solve problems, most researchers have chosen to limit themselves to using standard electronic components. However, it has been previously argued that because such components are human designed and intentionally have predictable responses, they may not be the most suitable medium to use when trying to get a naturally inspired search technique to solve a problem. Indeed allowing computer controlled evolution (CCE) to manipulate novel physical media can allow much greater scope for the discovery of unconventional solutions. Last year the authors demonstrated, for the first time, that CCE could manipulate liquid crystal to perform signal processing tasks (i.e frequency discrimination). In this paper we show that CCE can use liquid crystal to solve the much harder problem of controlling a robot in real time to navigate in an environment to reach an obstructed destination point.

An intrinsic evolvable hardware platform was realized to accelerate the evolutionary search process of a biologically inspired developmental model targeted at off-shelf FPGA implementation. The model has the capability of exhibiting very large transient fault-tolerance. The evolved circuits make up a digital "organism" from identical cells which only differ in internal states. Organisms implementing a 2-bit multiplier were evolved that can "recover" from almost any kinds of transient faults. This paper focuses on the design concerns and details of the evolvable hardware system, including the digital organism/cell and the intrinsic FPGA-based evolvable hardware platform.

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.

Embedded Cartesian Genetic Programming (ECGP) is an extension of the directed graph based Cartesian Genetic Programming (CGP), which is capable of automatically acquiring, evolving and re-using partial solutions in the form of modules. In this paper, we apply for the first time, CGP and ECGP to the well known Lawnmower problem and to the Hierarchical-if-and-Only-if problem. The latter is normally associated with Genetic Algorithms. Computational effort figures are calculated from the results of both CGP and ECGP and our results compare favourably with other techniques.

Structure-based virtual screening is a technology increasingly used in drug discovery. Although successful at estimating binding modes for input ligands, these technologies are less successful at ranking true hits correctly by binding free energy. This chapter presents the automated removal of false positives from virtual hit sets, by evolving a post docking filter using Cartesian Genetic Programming(CGP). We also investigate characteristics of CGP for this problem and confirm the absence of bloat and the usefulness of neutral drift.

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.

Intrinsic evolution in evolvable hardware research has hitherto been limited to using standard electronic components as the media for problem solving. However, recently it has been argued that because such components are human designed and intentionally has predictable responses; they may not be the optimal medium to use when trying to get a naturally inspired search technique to solve a problem. Evolution has been demonstrated as capable of exploiting the physical properties of material to form solutions; however, by giving evolution only conventional components, we may be placing arbitrary constraints on our ability to solve certain problems. We have shown for the first time, that liquid crystal can be used as the physical substrate for evolution. We demonstrate that it is possible to evolve various functions, including a tone discriminator, in materio.

In our previous work, we have demonstrated that evolution can be used to program liquid crystal to act as a signal processing device. In this work we discuss the stability and reconfigurability of a real time robot controller evolved in liquid crystal. We envisage these issues will be important when programming or evolving in other physical systems.

A biologically inspired developmental model targeted at hardware implementation (off-shelf FPGA) is proposed which exhibits extremely robust transient fault-tolerant capability. All cells in this model have identical genotype (physical structures), and only differ in internal states. In a 3x3 cell digital organism, some individuals which implement a 2-bit multiplier were discovered using evolution that have the ability to “recover” themselves from almost any kinds of transient faults. An intrinsic evolvable hardware platform based on FPGA was realized to speed up the evolution process.

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.

Intrinsic evolution is often limited to using standard electronic components as the media for problem solving. It has been argued that because such components are human designed and intentionally have predictable responses, they may not be the optimal medium to use when trying to get a naturally inspired search technique to solve a problem. Evolution has been demonstrated as capable of exploiting the physical properties of material to form solutions, however, by giving evolution only conventional components, we may be limiting ourselves to solving certain problems. It is hoped by allowing evolution to explore a physically rich environment, it will be able to find novel solutions to tasks presented. This paper investigates the use of liquid crystal as a novel substrate for evolution and demonstrates the feasibility of moving beyond the silicon box.

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.

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.

Prefacio.-- El pdf es la versión post-print.

In this chapter we discuss the challenge provided by the problem of evolving large amounts of computer code via Genetic Programming. We argue that the problem is analogous to what Nature had to face when moving to multi-cellular life. We propose to look at developmental processes and there mechanisms to come up with solutions for this “challenge of complexity” in Genetic Programming.

An evolvable motherboard is an intrinsic evolution platform that allows the detailed probing of internal signals of circuits that have been evolved. Several designs for an evolvable motherboard have already been demonstrated to work successfully as a platform for the evolution of electronic circuits. This paper proposes a new platform that is suitable for intrinsic evolution using a wider variety of media. The platform presents a more modular design, making it suitable for use in evolving more complex physical primitives whilst affording the possibility of performing evolution in parallel for simpler problems. The construction of the device is discussed and examples of potential experiments in silicon, liquid crystal and other media are described.

It is argued that natural evolution is, par excellence, an algorithm that exploits the physical properties of materials. Such an exploitation of the physical characteristics has already been demonstrated in intrinsic evolution of electronic circuits. This paper is an attempt to point the way toward the exciting possibility of using artificial evolution to directly exploit the properties of materials, possibly at a molecular level. It is suggested that this may be best accomplished in materials not normally associated with electronic functions. Electronic components have been prefected by human designers to construct circuits using the traditional top-down methodology. Workers in artificial intrinsic hardware evolution have with the best of motives, been abusing such components. It is a tribute to the amazing resourcefulness of a blind evolutionary process that it has been possible to evolve new circuits in this way. Artificial evolution may be much more effective when the configurable medium has a rich and complicated physics. This idea is discussed and particular examples that look extremely promising are given. Ultimately it may be possible to evolve entirely new technologies and new sorts of computational systems may be devised that confer many advantages over conventional electronic technology.

We use evolutionary search to design combinational logic circuits. The technique is based on evolving the functionality and connectivity of a rectangular array of logic cells whose dimension is defined by the circuit layout. The main idea of this approach is to improve quality of the circuits evolved by the genetic algorithm (GA) by reducing the number of active gates used. We accomplish this by combining two ideas: 1) using multi-objective fitness function; 2) evolving circuit layout. It will be shown that using these two approaches allows us to increase the quality of evolved circuits. The circuits are evolved in two phases. Initially the genome fitness is given by the percentage of output bits that are correct. Once 100% functional circuits have been evolved, the number of gates actually used in the circuit is taken into account in the fitness function. This allows us to evolve circuits with 100% functionality and minimise the number of active gates in circuit structure. The population is initialised with heterogeneous circuit layouts and the circuit layout is allowed to vary during the evolutionary process. Evolving the circuit layout together with the function is one of the distinctive features of proposed approach. The experimental results show that allowing the circuit layout to be flexible is useful when we want to evolve circuits with the smallest number of gates used. We find that it is better to use a fixed circuit layout when the objective is to achieve the highest number of 100% functional circuits. The two-fitness strategy is most effective when we allow a large number of generations.

A small gate array is evolved extrinsically to carry out a low pass filtering task defined over fifteen different frequencies. The circuit is evolved by assessing its response to digitised sine waves. Two different fitness functions are contrasted. One is based on computing the sum of the absolute differences between the actual response and that desired, the other is defined by examining characteristics of the discrete Fourier transform of the output. The gate arrays possess some linear properties, which means that they are capable of filtering composite signals which have not been encountered in training. This includes signals with noise added and with frequencies which are not in the training set.

The two-bit multiplier is a simple electronic circuit, small enough to be evolvable, and practically useful for the implementation of many digital systems. In this paper we study the structure of the two-bit multiplier fitness landscapes generated by circuit evolution on an idealised model of a field-programmable gate array. The two-bit multiplier landscapes are challenging. The difficulty in studying these landscapes stems from the genotype representation which allows us to evolve the functionality and connectivity of an array of logic cells. Here, the genotypes are simply strings defined over two completely different alphabets. This makes the study of the corresponding landscapes much more involved. We outline a model for studying the two-bit multiplier landscapes and estimate the amplitudes derived from the Fourier transform of these landscape. We show that the two-bit multiplier landscapes can be characterised in terms of subspaces, determined by the interactions between the genotype partitions.

Field programmable gate arrays (FPGAs) are a form of user-programmable logic devices that contain an array of logic gates. As there is no complete set of techniques for designing any FPGA program, researchers have been successful in evolving program designs using genetic algorithms (GAs). However, using GAs to generate software programs for FPGAs faces two main problems, namely scaling and errors. In this paper, we present our on-going research towards overcoming these problems by the integration of GAs with case-based reasoning (CBR). CBR is a problem-solving method that reuses old solutions to solve new problems. Our research work aims to apply CBR to reuse genetically evolved FPGA programs in order to develop larger programs at a reasonable computational expense. This paper describes our preliminary experiments and their results, which are encouraging.

Emergent computation refers to systems in which global information processing appears as a result of the interactions among many components, each of which may be a system that exhibits an ability for emergent computation at a different level of self-organisation. In this paper we employ a modification of cellular programming to evolve cellular machines for synchronisation. This allows global computation to occur by many local interactions among computational demes of interacting cells. The computational machine, derived from the non-uniform cellular automata model, consists of a grid of cells which are co-evolved in isolated demes. We describe experiments which show that demes can be co-evolved to perform non-trivial computation. We also analyse the mechanisms of computation within the different synchronising demes. Our results not only show that the co-evolution of demes is possible, but that they can attain high computational performance through co-operative action.

A review is given of approaches to growing neural networks and electronic circuits. A new method for growing graphs and circuits using a developmental process is discussed. The method is inspired by the view that the cell is the basic unit of biology. Programs that construct circuits are evolved to build a sequence of digital circuits at user specified iterations. The programs can be run for an arbitrary number of iterations so circuits of huge size could be created that could not be evolved. It is shown that the circuit building programs are capable of correctly predicting the next circuit in a sequence of larger even parity functions. The new method however finds building specific circuits more difficult than a non-developmental method.

In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system ({\it Partial Diffusion Operator}) to propose a quantum search algorithm runs in $O(\sqrt N/M})$ for searching unstructured list of size $N$ with $M$ matches such that, $1\le M \le N$. We will show that the performance of the algorithm is more reliable than known quantum search algorithms especially for multiple matches within the search space. A performance comparison with Grover's algorithm will be provided., Comment: 27 pages, 9 figures

The development of an entire organism from a single cell is one of the most profound and awe inspiring phenomena in the whole of the natural world. The complexity of living systems itself dwarfs anything that man has produced. This is all the more the case for the processes that lead to these intricate systems. In each phase of the development of a multi-cellular being, this living system has to survive, whether stand-alone or supported by various structures and processes provided by other living systems. Organisms construct themselves, out of humble single-celled beginnings, riding waves of interaction between the information residing in their genomes – inherited from the evolutionary past of their species via their progenitors – and the resources of their environment.

The theory of fitness landscapes has been developed to provide a suitable mathematical framework for studying the evolvability of a variety of complex systems. In evolutionary computation the notion of evolvability refers to the efficiency of evolutionary search. It has been shown that the structure of a fitness landscape affects the ability of evolutionary algorithms to search. Three characteristics specify the structure of landscapes. These are the landscape smoothness, ruggedness and neutrality. The interplay of these characteristics plays a vital role in evolutionary search. This has motivated the appearance of a variety of techniques for studying the structure of fitness landscapes. An important feature of these techniques is that they characterize the landscapes by their smoothness and ruggedness, ignoring the existence of neutrality. Perhaps, the reason for this is that the role of neutrality in evolutionary search is still poorly understood.In this chapter some recent results on the spectral properties of the algebraic structures of fitness landscapes are summarized to provide a basis for studying the landscape structure. This approach is further employed to introduce an information analysis that characterizes the structure of fitness landscapes in terms of their smoothness, ruggedness and neutrality. The findings are finally applied in a study of the fitness landscapes generated by evolving digital circuits using an idealized model of a field-programmable gate array. The landscapes of this engineering problem are quite different from many recently studied landscapes that tend to be defined over simplified combinatorial and optimization problems. The difference originates from the genotype representation that is a configuration defined over two completely different alphabets. This makes the study of the corresponding landscapes much more involved. It is shown that the circuit evolution landscapes are products of subspaces with different characteristics. They are landscapes with vast neutrality and sharply differentiated plateau.

A cell based optimization (CBO) algorithm is proposed which takes inspiration from the collective behaviour of cellular slime molds (Dictyostellium discoideum). Experiments with CBO are conducted to study the ability of simple cell-like agents to collectively manage resources across a distributed network. Cells, or agents, only have local information can signal, move, divide, and die. Heterogeneous populations of the cells are evolved using Cartesian genetic programming (CGP). Several experiments were carried out to examine the adaptation of cells to changing user demand patterns. CBO performance was compared using various methods to change demand. The experiments showed that populations consistently evolve to produce effective solutions. The populations produce better solutions when user demand patterns fluctuated over time instead of environments with static demand. This is a surprising result that shows that populations need to be challenged during the evolutionary process to produce good results.

We investigate a preliminary model of gate-like components with added random noise. We refer to these types of components as messy. The principal idea behind messy gates is that evolving circuits using messy gates may confer some beneficial properties, one being fault-tolerance. The exploitation of the physical characteristics has already been demonstrated in intrinsic evolution of electronic circuits. This provided some of the inspiration for the work reported in this paper. Here we are trying to create a simulateable world in which "physical characteristics" can be exploited. We are also trying to study the question: What kind of components are most useful in an evolutionary design scenario?.

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.

We propose building neutral networks in needle-in-haystack fitness landscapes to assist an evolutionary algorithm to perform search. The experimental results on four different problems show that this approach improves the search success rates in most cases. In situations where neutral networks do not give performance improvement, no impairment occurs either. We also tested a hypothesis proposed in our previous work. The results support the hypothesis: when the ratio of adaptive/neutral mutations during neutral walk is close to the ratio of adaptive/neutral mutations at the fitness improvement step, the evolutionary search has a high success rate. Moreover, the ratio magnitudes indicate that more neutral mutations (than adaptive mutations) are required for the algorithms to find a solution in this type of search space.

Publisher Summary This chapter puts forward the view that evolutionary algorithms together with the assemble-and-test methodology can be regarded as a discovery engine or creative machine for new designs. The chapter suggests that new principles may be discovered by examining a series of evolved designs, in this case, for arithmetic logic circuits. The chapter examines the concept of the space of all circuit representations but observes that similar ideas may well carry over to the general field of design. The human-designed algebras that form subsets of the space of all representations both for binary and multiple-valued systems are analogous to small “pools” of human principles, and by employing the blind evolutionary technique new principles may be discovered. The chapter looks at the difficult problem of principle extraction from evolved data. The chapter ends on a hopeful note that the process of learning new principles from a blind evolutionary process is just a matter of time.

The exploitation of the physical characteristics has already been demonstrated in the intrinsic evolution of electronic circuits. This paper is an initial attempt at creating a world in which "physics" can be exploited in simulation. As a starting point we investigate a model of gate-like components with added noise. We refer to this as a kind of messiness. The principal idea behind these messy gates is that artificial evolution makes a virtue of the untidiness. We are ultimately trying to study the question: What kind of components should we use in artificial evolution? Several experiments are described that show that the messy circuits have a natural robustness to noise, as well as an implicit faulttolerance. In addition, it was relatively easy for evolution to generate novel circuits that were surprisingly efficient.

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.

The two-bit multiplier is a simple electronic circuit, small enough to be feasible for evolutionary design, and practically useful as a fundamental building block used in the synthesis of many digital systems. To attain understanding of the evolvability of this digital circuit, we consider its evolutionary design as a search on a fitness landscape. We study the structure of two-bit multiplier landscapes in terms of their ruggedness and neutrality. The motivation behind this research is to attain better understanding of how these characteristics are related to the feasibility of evolving digital circuits.