In this paper we first review the main results obtained in the theory of schemata in Genetic Programming (GP) emphasising their strengths and weaknesses. Then we propose a new, simpler definition of the concept of schema for GP which is quite close to the original concept of schema in genetic algorithms (GAs).

We review the main results obtained in the theory of schemata in Genetic Programming (GP) emphasising their strengths and weaknesses. Then we propose a new, simpler definition of the concept of schema for GP which is closer to the original concept of schema in genetic algorithms (GAs). Along with a new form of crossover, one-point crossover, and point mutation this concept of schema has been used to derive an improved schema theorem for GP which describes the propagation of schemata from one generation to the next. We discuss this result and show that our schema theorem is the natural counterpart for GP of the schema theorem for GAs, to which it asymptotically converges. 1 Introduction Genetic Programming (GP) has been applied successfully to a large number of difficult problems like automatic design, pattern recognition, robotic control, synthesis on neural architectures, symbolic regression, music and picture generation [2, 9, 10, 11, 12, 13]. However a relatively small numbe...

In this paper a new, general and exact schema theory for genetic programming is presented. The theory includes a microscopic schema theorem applicable to crossover operators which replace a subtree in one parent with a subtree from the other parent to produce the offspring. A more macroscopic schema theorem is also provided which is valid for crossover operators in which the probability of selecting any two crossover points in the parents depends only on their size and shape. The theory is based on the notions of Cartesian node reference systems and variable-arity hyperschemata both introduced here for the first time. In the paper we provide examples which show how the theory can be specialised to specific crossover operators and how it can be used to derive an exact definition of effective fitness and a size-evolution equation for GP. 1

This paper examines measures of diversity in genetic programming. The goal is to understand the importance of such measures and their relationship with fitness. Diversity methods and measures from the literature are surveyed and a selected set of measures are applied to common standard problem instances in an experimental study. Results show the varying definitions and behaviours of diversity and the varying correlation between diversity and fitness during different stages of the evolutionary process. Populations in the genetic programming algorithm are shown to become structurally similar while maintaining a high amount of behavioural differences. Conclusions describe what measures are likely to be important for understanding and improving the search process and why diversity might have different meaning for different problem domains.

expensive, and that has led the investigation to how to automate them. In particular, Software Testing can take up to half of the resources of the development of new software. Although there has been a lot of work on automating the testing phase, fixing a bug after its presence has been discovered is still a duty of the programmers. In this paper we propose an evolutionary approach to automate the task of fixing bugs. This novel evolutionary approach is based on Co-evolution, in which programs and test cases co-evolve, influencing each other with the aim of fixing the bugs of the programs. This competitive co-evolution is similar to what happens in nature for predators and prey. The user needs only to provide a buggy program and a formal specification of it. No other information is required. Hence, the approach may work for any implementable software. We show some preliminary experiments in which bugs in an implementation of a sorting algorithm are automatically fixed. I.

In recent theoretical and experimental work on schemata in genetic programming we have proposed a new simpler form of crossover in which the same crossover point is selected in both parent programs. We call this operator one-point crossover because of its similarity with the corresponding operator in genetic algorithms. One point crossover presents very interesting properties from the theory point of view. In this paper we describe this form of crossover as well as a new variant called strict one-point crossover highlighting their useful theoretical and practical features. We also present experimental evidence which shows that one-point crossover compares favourably with standard crossover.

Abstract not found

EDDIE is a genetic programming based decision support tool for financial forecasting. EDDIE itself does not replace forecasting experts. It serves to improve the productivity of experts in searching the space of decision trees, with the aim to improve the odds in its user's favour. The efficacy of EDDIE has been reported in the literature. However, discovering patterns in historical data is only the first step towards building a practical financial forecasting tool. Data preparation, rules organization and application are all important issues. This paper describes an architecture that embeds EDDIE for learning from and monitoring the stock market.

Fitness distributions (landscapes) of programs tend to a limit as they get bigger. Markov chain convergence theorems give general upper bounds on the linear program sizes needed for convergence. Tight bounds (exponential in N, N log N and smaller) are given for five computer models (any, average, cyclic, bit flip and Boolean). Mutation randomizes a genetic algorithm population in 1 4 (l + 1)(log(l) + 4) generations. Results for a genetic programming (GP) like model are confirmed by experiment. 1

Introduction It has been long noticed that there are emergent phenomena in genetic programming (GP) runs unintended by the human designer of the algorithm. Early on it was observed that code which does not change the output of the program (i.e. non-e#ective code) appears in many GP runs [34, 38, 2]. It was also noted that bloat a#ects many GP systems. Reasons for bloat and non-e#ective code have been examined in years past [25, 4, 7] and remedies have been developed more or less e#ective under particular circumstances (e.g. [29, 15, 22, 17]). Here we would like to argue that non-e#ective code and bloat are only the tip of an iceberg and that there is more to be discovered about "emergent phenomena" in GP runs. Particularly, we would like to study repetition of patterns in GP-evolved programs. These are instructions, or more interestingly, groups of instructions, that occur several times in a program. In fact long sequences of instructions which are repeated can sometimes be decompose