Many forms of unconventional computing, i.e., massively parallel computers which exploit the non-linear material properties of their substrate, can be realised through simulated evolution. That is, the behaviour of non-linear media can be controlled automatically and the structural design of the media optimized through the nature-inspired machine learning approach. This chapter describes work using the Belousov-Zhabotinsky reaction as a non-linear chemical medium in which to realise computation. Firstly, aspects of the basic structure of an experimental chemical computer are evolved to implement two Boolean logic functions through a collision-based scheme. Secondly, a controller is evolved to dynamically affect the rich spatio-temporal chemical wave behaviour to implement three Boolean functions, in both simulation and experimentation.

Many forms of unconventional computing, i.e., massively parallel non-linear computers, can be realised through simulated evolution. That is, the behaviour of non-linear media can be controlled automatically and the structural design of the media optimized through the nature-inspired machine learning approach. This chapter describes work using the Belousov-Zhabotinsky reaction as a non-linear chemical medium in which to realise computation. A checkerboard image comprising of varying light intensity cells is projected onto the surface of a catalyst-loaded gel resulting in rich spatio-temporal chemical wave behaviour. Cellular automata are evolved to control the chemical activity through dynamic adjustment of the light intensity, implementing a number of Boolean functions in both simulation and experimentation.

Surrogate-assisted Optimisation has proven success in the continuous domain, but only recently begun to be explored for other representations, in particular permutations. The use of Gaussian kernel-based models has been proposed, but only tested on small problems. This case study considers much larger instances, in the experimental setting of a real-world ordering problem. We also investigate whether creating models using different distance metrics generates a diverse ensemble. Results demonstrate the following effects of use to other researchers: (i) Numerical instability in matrix inversion is a factor across all metrics, regardless of algorithm used. The likelihoood increases significantly once the models are parameterised using evolved solutions as well as the initial random population; (ii) This phase transition is also observed in different indicators of model quality. For example, predictive accuracy typically decreases once models start to include data from evolved samples. We explain this transition in terms of the distribution of samples and Gaussian kernel basis of the models; (iii) Measures of how well models predict rank-orderings are less affected; (iv) Benchmark comparisons show that using surrogate models decreases the number of evaluations required to find good solutions, without affecting quality.

The Density Classification Task is a well known test problem for two-state discrete dynamical systems. For many years researchers have used a variety of evolutionary computation approaches to evolve solutions to this problem. In this paper, we investigate the evolvability of solutions when the underlying Cellular Automaton is augmented with a type of memory based on the Least Mean Square algorithm. To obtain high performance solutions using a simple non-hybrid genetic algorithm, we design a novel representation based on the ternary representation used for Learning Classifier Systems. The new representation is found able to produce superior performance to the bit string traditionally used for representing Cellular automata. Moreover, memory is shown to improve evolvability of solutions and appropriate memory settings are able to be evolved as a component part of these solutions.

In this paper we investigate the performance and operation of a Learning Classifier System on problems with real-valued states and a Boolean action space. Specifically, we study aspects of the algorithm and parameter set of the simple strength-based Learning Classifier System used, ZCS. Increased performance is found to result from the use of an update algorithm based on that of NewBoole, an earlier strength-based Learning Classifier System and a new operator, specialize, is introduced and found to be effective in ...

Spontaneous spiral formation occurs when an excitation wave is input to a heterogeneous network of low- and high-light-intensity cells projected onto a light-sensitive Belousov-Zhabotinsky reaction. The range of network conditions where spirals form is increased if two waves are input at critical time intervals. Spirals degenerate to form multiple spirals and spirals trapped within excitable cells. Spiral formation and degeneration is dependent on network excitability, cell size, and network size. Results exhibit parallels with spiral formation in excitable biological systems such as the heart.

We present a method that is capable of implementing information transfer without any rigidly controlled architecture using the light-sensitive Belousov-Zhabotinsky (BZ) reaction system. Chemical wave fragments are injected into a subexcitable area and their collisions result in annihilation, fusion or quasi-elastic interactions depending on their initial positions. The fragments of excitation both pre and post collision possess a considerable freedom of movement when compared to previous implementations of information transfer in chemical systems. We propose that the collision of such wave fragments can be controlled automatically through adaptive computing. By extension, forms of unconventional computing, i.e., massively parallel non-linear computers, can be realised by such an approach. In this study we present initial results from using a simple evolutionary algorithm to design Boolean logic gates within the BZ system.

A type of memory based on the least mean square algorithm is explored on the density classification task, which is a well-known test problem for two-state discrete dynamical systems. In the absence of memory, there is no elementary cellular automaton that can solve this task. However, when augmented with memory, the performance of elementary cellular automaton 184 approaches that of the best-known radius three cellular automata found in the literature. It is found that rule 184 transforms spatial information about the neighborhood into temporal information that memory is able to retain and present to the rule’s transition function. This causes the cell to transition to a different state compared to the case when no memory is present, which extends blocks of cells having a common state to facilitate a solution of the task.

In cellular automata models a glider gun is an oscillating pattern of nonquiescent states that periodically emits traveling localizations (gliders). The glider streams can be combined to construct functionally complete systems of logical gates and thus realize universal computation. The glider gun is the only means of ensuring the negation operation without additional external input and therefore is an essential component of a collision-based computing circuit. We demonstrate the existence of glider-gun-like structures in both experimental and numerical studies of an excitable chemical system-the light-sensitive Belousov-Zhabotinsky reaction. These discoveries could provide the basis for future designs of collision-based reaction-diffusion computers.

The behaviour of pulses of Belousov-Zhabotinski (BZ) reaction diffusion waves can be controlled automatically through machine learning. By extension, a form of chemical network computing, i.e., a massively parallel non-linear Computer, can be realised by Such an approach. In this initial study a light-sensitive sub-excitable BZ reaction in which a checkerboard image comprising of varying light intensity cells is projected onto the Surface of a thin silica gel impregnated with tris(bipyridyl) ruthenium (II) catalyst and indicator is used to make the network. As a catalyst free BZ solution is swept past the gel, Pulses of wave fragments are injected into the checkerboard grid resulting in rich spatio-temporal behaviour. An evolutionary computing machine learning approach, a learning classifier system, is then shown able to direct the fragments through dynamic control of the light intensity within each cell in both simulated and real chemical systems.

We propose that the behavior of nonlinear media can be controlled dynamically through coevolutionary systems. In this study, a light-sensitive subexcitable Belousov-Zhabotinsky reaction is controlled using a heterogeneous cellular automaton. A checkerboard image comprising of varying light intensity cells is projected onto the surface of a catalyst-loaded gel resulting in rich spatiotemporal chemical wave behavior. The coevolved cellular automaton is shown to be able to either increase or decrease chemical activity through dynamic control of the light intensity within each cell in both simulated and real chemical systems. The approach is then extended to construct a number of simple logical functions.

We propose that the behavior of nonlinear media can be controlled automatically through evolutionary learning. By extension, forms of unconventional computing (viz., massively parallel nonlinear computers) can be realized by such an approach. In this initial study a light-sensitive subexcitable Belousov-Zhabotinsky reaction in which a checkerboard image, composed of cells of varying light intensity projected onto the surface of a thin silica gel impregnated with a catalyst and indicator, is controlled using a learning classifier system. Pulses of wave fragments are injected into the checkerboard grid, resulting in rich spatiotemporal behavior, and a learning classifier system is shown to be able to direct the fragments to an arbitrary position through dynamic control of the light intensity within each cell in both simulated and real chemical systems. Similarly, a learning classifier system is shown to be able to control the electrical stimulation of cultured neuronal networks so that they display elementary learning. Results indicate that the learned stimulation protocols identify seemingly fundamental properties of in vitro neuronal networks. Use of another learning scheme presented in the literature confirms that such fundamental behavioral characteristics of a given network must be considered in training experiments.

We apply a simple Learning Classifier System to a foreign exchange trading problem. The performance of the Learning Classifier System is compared to that of a Genetic Programming approach from the literature. The simple Learning Classifier System is able to achieve a positive excess return in simulated trading, but results are not yet fully competitive because the Learning Classifier System trades too frequently. However, the Learning Classifier System approach shows potential because returns are obtained with no offline training and the technique is inherently adaptive, unlike many of the machine learning methods currently employed for financial trading.

We propose that the behaviour of non-linear media can be controlled automatically through coevolutionary systems. By extension, forms of unconventional computing, i.e., massively parallel non-linear computers, can be realised by such an approach. In this study a light-sensitive sub-excitable Belousov-Zhabotinsky reaction is controlled using various heterogeneous cellular automata. A checkerboard image comprising of varying light intensity cells is projected onto the surface of a catalyst-loaded gel resulting in rich spatio-temporal chemical wave behaviour. The coevolved cellular automata are shown to be able to control chemical activity through dynamic control of the light intensity. The approach is demonstrated through the creation of a number of simple Boolean logic gates.

We present experimental verification of wave fragment collisions in the sub-excitable Belousov–Zhabotinsky medium observed previously in simulation [Adamatzky A, De Lacy Costello B. Binary collisions between wave fragments in a sub-excitable Belousov–Zhabotinsky medium. Chaos, Solitons & Fractals 2007;34:307–15]. We have reproduced in chemical experiments the majority of the collisions observed in simulation including annihilation, fusion and quasi-elastic types. The method we present is capable of implementing information transfer without any rigidly controlled architecture – fragments are simply introduced into an “arena” which consists of a large area of gel illuminated with a uniform light level – controlled at a level close to the sub-excitable threshold. Therefore, the fragments of excitation both pre and post collision possess a considerable freedom of movement when compared to previous implementations of information transfer in chemical systems. This chemical verification of previous theoretical results brings closer the possibility of utilising this phenomenon for implementing collision-based gates, signal tuning and programming of collision-based computers based upon excitable chemical reactions.

We propose that the behaviour of non-linear media can be controlled automatically through coevolutionary systems. By extension, forms of unconventional computing, i.e., massively parallel non-linear computers, can be realised by such an approach. In this study a light-sensitive sub-excitable Belousov-Zhabotinsky reaction in which a checkerboard image comprised of varying light intensity cells projected onto the surface of a catalyst loaded gel is controlled using a heterogeneous cellular automaton. Pulses of wave fragments are injected onto the gel resulting in rich spatio-temporal behaviour and a coevolved cellular automaton is shown able to either increase or decrease the chemical activity through dynamic control of the light intensity within each cell in both simulated and real chemical systems.

The behaviour of pulses of Belousov-Zhabotinski (BZ) reaction-diffusion waves can be controlled automatically through machine learning. By extension, a form of chemical network computing, i.e., a massively parallel non-linear computer, can be realised by such an approach. In this initial study a light-sensitive sub-excitable BZ reaction in which a checkerboard image comprising of varying light intensity cells is projected onto the surface of a thin silica gel impregnated with tris(bipyridyl) ruthenium (II) catalyst and indicator is used to make the network. As a catalyst BZ solution is swept past the gel, pulses of wave fragments are injected into the checkerboard grid resulting in rich spatio-temporal behaviour. This behaviour is shown experimentally to be repeatable under the same light projections. A machine learning approach, a learning classifier system, is then shown able to direct the fragments to an arbitrary position through dynamic control of the light intensity within each cell in both simulated and real chemical systems.

We investigate Learning Classifler Systems for online envi- ronments that consist of real-valued states and which require every ac- tion made by the agent to count towards its performance. Two Learning Classifler System architectures are considered, ZCS and XCS. We use an interval representation with these Learning Classifler Systems for the rule conditions together with roulette wheel action selection. We investigate the performance of these two Learning Classifler System architectures on a set of abstract environments with both deterministic and stochas- tic reward functions. We brie∞y review related work and relate this to the experiments performed in this paper. Although XCS clearly deliv- ers superior performance in deterministic environments, we flnd that the simple ZCS architecture is robust and able to equal or exceed the per- formance of XCS in stochastic environments, especially those with more demanding characteristics.