Genetic Programming uses a tree based representation to express solutions to problems. Trees are constructed from a primitive set which consists of a function set and a terminal set. An extension to GP is the ability to define modules, which are in turn tree based representations defined in terms of the primitives. The most well known of these methods is Koza's Automatically Defined Functions. In this paper it is proved that for a given problem, the minimum number of nodes in the main tree plus the nodes in any modules is independent of the primitive set (up to an additive constant) and depends only on the function being expressed. This reduces the number of user defined parameters in the run and makes the inclusion of a hypothesis in the search space independent of the primitive set.

In nature, systems with enormous numbers of components (i.e. cells) are evolved from a relatively small genotype. It has not yet been demonstrated that artificial evolution is sufficient to make such a system evolvable. Consequently researchers have been investigating forms of computational development that may allow more evolvable systems. The approaches taken have largely used re-writing, multi- cellularity, or genetic regulation. In many cases it has been difficult to produce general purpose computation from such systems. In this paper we introduce computational development using a form of Cartesian Genetic Programming that includes self-modification operations. One advantage of this approach is that ab initio the system can be used to solve computational problems. We present results on a number of problems and demonstrate the characteristics and advantages that self-modification brings.

This paper presents an empirical study of the variation of program size over time, for a form of Genetic Programming called Cartesian Genetic Programming. Two main types of Cartesian genetic programming are examined: one uses a fully connected graph, with no redundant nodes, while the other allows partial connectedness and has redundant nodes. Studies are reported here for fitness based search and for a flat fitness landscape.

Abstract. An original approach to automatic design of image operators is presented in this paper. The proposed solution employs evolvable hardware at simplified functional level and produces image operators (digital circuits), which can compete against traditional designs in terms of quality and implementation cost in Xilinx’s chips. 1

The effects of neutrality on evolutionary search have been considered in a number of interesting studies, the results of which, however, have been contradictory. Some researchers have found neutrality to be beneficial to aid evolution whereas others have argued that the presence of neutrality in the evolutionary process is useless. We believe that this confusion is due to several reasons: many studies have based their conclusions on performance statistics (e.g., on whether or not a system with neutrality could solve a particular problem faster than a system without neutrality) rather than a more in-depth analysis of population dynamics, studies often consider problems, representations and search algorithms that are relatively complex and so results represent the compositions of multiple effects (e.g., bloat or spurious attractors in genetic programming), there is not a single definition of neutrality and different studies have added neutrality to problems in radically different ways. In this paper, we try to shed some light on neutrality by addressing these problems. That is, we use the simplest possible definition of neutrality (a neutral network of constant fitness, identically distributed in the whole search space), we consider one of the simplest possible algorithms (a mutation based, binary genetic algorithm) applied to two simple problems (a unimodal landscape and a deceptive landscape), and analyse both performance figures and, critically, population flows from and to the neutral network and the basins of attraction of the optima.

This paper introduces a continuous model for Multi-cellular Developmental Design. The cells are fixed on a 2D grid and exchange ”chemicals ” with their neighbors during the growth process. The quantity of chemicals that a cell produces, as well as the differentiation value of the cell in the phenotype, are controlled by a Neural Network (the genotype) that takes as inputs the chemicals produced by the neighboring cells at the previous time step. In the proposed model, the number of iterations of the growth process is not pre-determined, but emerges during evolution: only organisms for which the growth process stabilizes give a phenotype (the stable state), others are declared nonviable. The optimization of the controller is done using the NEAT algorithm, that optimizes both the topology and the weights of the Neural Networks. Though each cell only receives local information from its neighbors, the experimental results of the proposed approach on the ’flags ’ problems (the phenotype must match a given 2D pattern) are almost as good as those of a direct regression approach using the same model with global information. Moreover, the resulting multi-cellular organisms exhibit almost perfect self-healing characteristics.

A comparison between four evolutionary techniques for solving symbolic regression problems is presented in this paper. The compared methods are multi-expression programming, gene expression programming, grammatical evolution, and linear genetic programming. The comparison includes all aspects of the considered evolutionary algorithms: individual representation, fitness assignment, genetic operators, and evolutionary scheme. Several numerical experiments using five benchmarking problems are carried out. Two test problems are taken from PROBEN1 and contain real-world data. The results reveal that multi-expression programming has the best overall behavior for the considered test problems.

We investigate neutrality in the simple Genetic Algorithms (SGA) and in our neutrality-enabled evolutionary system using the OneMax problem.

Abstract. The effects of neutrality on evolutionary search are not fully understood. In this paper we make an effort to shed some light on how and why bit-wise neutrality – an important form of neutrality induced by a genotype-phenotype map where each phenotypic bit is obtained by transforming a group of genotypic bits via an encoding function – influences the behaviour of a mutation-based GA on functions of unitation. To do so we study how the fitness distance correlation (fdc) of landscapes changes under the effect of different (neutral) encodings. We also study how phenotypic mutation rates change as a function of the genotypic mutation rate for different encodings. This allows us to formulate simple explanations for why the behaviour of a GA changes so radically with different types of neutrality and mutation rates. Finally, we corroborate these conjectures with extensive empirical experimentation. 1

A complete Genetic Programming (GP) system implemented in a single FPGA is described in this paper. The GP system is capable of solving problems that require large populations and by using parallel tness evaluations can solve problems in a much shorter time that a conventional GP system in software. A high level language to hardware compilation system called Handel-C is used for implementation.