Coevolution has been used as optimization technique both successfully and unsuccessfully. Successful optimization shows integration of information at the individual level over many fitness evaluation events and over many generations. Alternative outcomes of the evolutionary process, e.g. red queen dynamics or speciation, prevent such integration. Why coevolution leads to integration of information or to alternative evolutionary outcomes is generally unclear. We study coevolutionary optimization of the density classification task in cellular automata in a spatially explicit, two-species model. We find optimization at the individual level, i.e. evolution of cellular automata that are good density classifiers. However, when we globally mix the populations, which prevents the formation of spatial patterns, we find typical red queen dynamics in which cellular automata classify all cases to a single density class regardless their actual density. Thus, we get different outcomes of the evolutionary process dependent on a small change in the model. We compare the two processes leading to the different outcomes in terms of the diversity of the two populations at the level of the genotype and at the level of the phenotype.

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We investigate the results of coevolution of spatially distributed populations. In particular, we describe work in which a simple function approximation problem is used to compare different spatial evolutionary methods. Our work shows that, on this problem, spatial coevolution is dramatically more successful than any other spatial evolutionary scheme we tested. Our results support two hypotheses about the source of spatial coevolution’s superior performance: (1) spatial coevolution allows population diversity to persist over many generations; and (2) spatial coevolution produces training examples (“parasites”) that specifically target weaknesses in models (“hosts”). The precise mechanisms by which the combination of spatial embedding and coevolution produces these results are still not well understood. 1.

Abstract—Location management is a very important and complex problem in mobile computing. There is a need to develop algorithms that could capture this complexity yet can be easily implemented and used to solve a wide range of location management scenarios. This paper investigates the use of cellular automata (CA) combined with genetic algorithms to create an evolving parallel reporting cells planning algorithm. In the reporting cell location management scheme, some cells in the network are designated as reporting cells; mobile terminals update their positions (location update) upon entering one of these reporting cells. To create such an evolving CA system, cells in the network are mapped to cellular units of the CA and neighborhoods for the CA is selected. GA is then used to discover efficient CA transition rules. The effectiveness of the GA and of the discovered CA rules is shown for a number of test problems. Index Terms—Cellular automata, genetic algorithms, mobile computing, mobility management. 1

Co-evolutionary learning involves a training process where training samples are instances of solutions that interact strategically to guide the evolutionary (learning) process. One main research issue is with the generalization performance, i.e., the search for solutions (e.g., input-output mappings) that best predict the required output for any new input that has not been seen during the evolutionary process. However, there is currently no such framework for determining the generalization performance in co-evolutionary learning even though the notion of generalization is well-understood in machine learning. In this paper, we introduce a theoretical framework to address this research issue. We present the framework in terms of game-playing although our results are more general. Here, a strategy’s generalization performance is its average performance against all test strategies. Given that the true value may not be determined by solving analytically a closed-form formula and is computationally prohibitive, we propose an estimation procedure that computes the average performance against a small sample of random test strategies instead. We perform a mathematical analysis to provide a statistical claim on the accuracy of our estimation procedure, which can be further improved by performing a second estimation on the variance of the random variable. For game-playing, it is well-known that one is more interested in the generalization

One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm to the Young cellular automaton: a discrete version of the reaction-diffusion equations proposed by Turing in 1952. In the simulation experiments we searched for proper parameter values of two hypothetical proteins playing the role of activator and inhibitor morphogens. Our results show that on molecular and cellular levels recombination is the genetic mechanism that plays the key role in morphogen evolution, obtaining similar results in the presence or absence of mutation. However, spot patterns appear more often than stripe patterns on the simulated skin of zebras. Even when simulation results are consistent with the general picture of pattern modeling and simulation based on the Turing reaction-diffusion, we conclude that the stripe pattern of zebras may be a result of other biological features (i.e., genetic interactions, the Kipling hypothesis) not included in the present model.

evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1-d CA. Moreover, their randomness can be comparable to that of 2-d CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved compared with any individual CCA PRNG. Key words: cellular automata, randomness test, pseudorandom number generator, genetic algorithm

This paper describes methods for evolving 2-D cellular automata to perform global computations. This is a difficult task because global behaviors must arise from local computations of many parallel cells. We present the results of numerous tests involving different genetic algorithm methods to perform the 2-D equivalent of classic 1-D CA tasks, including density classification and synchronization, and our own 2-D CA balanced surface minimization task. The performance of the GA was improved greatly by the use of totalistic CA rule tables, increasing the fidelity of fitness functions, and with coevolutionary techniques. 1

Abstract: This paper proposes a new hierarchical twopopulation genetic algorithm (2PGA). The 2PGA scheme constitutes of two differently sized populations containing individuals of similar fitness or cost function values. The smaller population, the elite population, consists of the best individuals, whereas the larger population contains less fit individuals. These populations have different characteristics, such as size and mutation probability, based on the fitness of the candidate solutions in these populations. The performance of our 2PGA is compared to that of a single population genetic algorithm (SPGA). Because the 2PGA has multiple parameters, the significance and the effect of the parameters is also studied. Experimental results show that the 2PGA outperforms the SPGA reliably without increasing the amount of fitness function evaluations. Although genetic algorithms are used as a platform for the 2PGA scheme, the principles presented here are applicable also to other population based evolutionary optimization methods.

Cellular automata (CA) are an important modelling paradigm in the natural sciences and an extremely useful approach in the study of complex systems. Homogeneity, massive parallelism, local cellular interactions and both synchronous and asynchronous models of rule execution are some of their most prominent features, allowing scientists to model and understand a variety of phenomena in, to name but a few, the physical, chemical, biological, social and information sciences. An ubiquitous problem related with the study of complex systems by means of CA is that of parameter identification. In some cases, analytical methods are available but in many others, due to the bottom-up complexity of the underlying processes, the best route for CA identification is through design optimization by means of a metaheuristic, such as an evolutionary algorithm. In this work we report on a systematic methodology we have developed to control the spatio-temporal behavior of a CA in order to obtain a ‘designoid ’ target pattern. Four independent CA-based complex systems were used to assess our proposal which combines clustering, fitness distance correlation and evolutionary algorithms. 1.