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This chapter applies linear GP to the evolution of cooperative teams to several prediction problems. Different linear methods for combining outputs of the team programs are compared. These include hybrid approaches where [1] a neural network is used to optimize the weights of programs in a team for a common decision and [2] a real-numbered vector (the representation of evolution strategies) of weights is evolved in tandem with each team. The cooperative team approach results in an improved training and generalization performance compared to the standard GP method.

What have we achieved and where do we go from here?

This book has discussed linear genetic programming, a variant of GP that employs sequences of imperative instructions as genetic material. We focused on properties and behaviors of the linear representation and argued that it has a number of advantages over tree-based GP. We also pointed out extended similarities with its biological counterpart — the DNA sequence — that have so far not been appreciated sufficiently in the literature. For example, the fact that non-coding subsequences can be kept in the code and manipulated silently, i.e., without being activated, is pretty much analogous to what happens in real genomes.

Thinking in terms of data flow and register connections allowed us to accelerate artificial evolution in linear GP by considerable factors, on the basis of both absolute runtime and number of generations. It also allowed us to considerably increase the efficiency of evolutionary search operators. This led to an induction of more powerful solutions while at the same time keeping solution size and code growth under control.

We used a variety of benchmark problems to produce empirical results that were able to shed light on fundamental questions in GP and linear GP, in particular. We ventured to explain non-trivial phenomena and to develop powerful techniques, all with an eye to their implications on the practice of GP. As an empirical text, the book is heavily based on experimental data. These were generated through thousands of GP runs, comprising millions of program evaluations done with billions of CPU cycles.

Naturally, this book cannot have the last word on linear GP. If it has helped to promote the popularity of the approach and has opened avenues for further inquiry, it has served a good purpose. We sincerely hope to have conveyed the message and convinced the reader to give this method a try.