The Push programming language was developed for use in genetic and evolutionary computation systems, as the representation within which evolving programs are expressed. It has been used in the production of several significant results, including results that were awarded a gold medal in the Human Competitive Results competition at GECCO-2004. One of Push’s attractive features in this context is its transparent support for the expression and evolution of modular architectures and complex control structures, achieved through explicit code self-manipulation. The latest version of Push, Push3, enhances this feature by permitting explicit manipulation of an execution stack that contains the expressions that are queued for execution in the interpreter. This paper provides a brief introduction to Push and to execution stack manipulation in Push3. It then presents a series of examples in which Push3 was used with a simple genetic programming system (PushGP) to evolve programs with non-trivial control structures.

Abstract. The paper presents for the first time automatic module acquisition and evolution within the graph based Cartesian Genetic Programming method. The method has been tested on a set of even parity problems and compared with Cartesian Genetic Programming without modules. Results are given that show that the new modular method evolves solutions up to 20 times quicker than the original non-modular method and that the speedup is more pronounced on larger problems. Analysis of some of the evolved modules shows that often they are lower order parity functions. Prospects for further improvement of the method are discussed. 1

We report how breve, a simulation environment with rich 3d graphics, was used to discover significant patterns in the dynamics of a system that evolves controllers for swarms of goal-directed agents. These patterns were discovered via visualization in the sense that we had not considered their relevance or thought to look for them initially, but they became obvious upon visually observing the behavior of the system.

The growth of program size during evolution (code “bloat”) is a well-documented and well-studied problem in genetic programming. This paper examines the use of “size fair ” genetic operators to combat code bloat in the PushGP genetic programming system. Size fair operators are compared to naive operators and to operators that use “node selection” as described by Koza. The effects of the operator choices are assessed in runs on symbolic regression, parity and multiplexor problems (2,700 runs in total). The results show that the size fair operators control bloat well while producing unusually parsimonious solutions. The computational effort required to find a solution using size fair operators is about equal to, or slightly better than, the effort required using the comparison operators. 1

Geographical distribution is widely held to be a major determinant of evolutionary dynamics. Correspondingly, genetic programming theorists and practitioners have long developed, used, and studied systems in which populations are structured in quasi-geographical ways. Here we show that a remarkably simple version of this idea produces surprisingly dramatic improvements in problem-solving performance on a suite of test problems. The scheme is trivial to implement, in some cases involving little more than the addition of a modulus operation in the population access function, and yet it provides significant benefits on all of our test problems (ten symbolic regression problems and a quantum computing problem). We recommend the broader adoption of this form of “trivial geography” in genetic programming systems.

This paper discusses the evolution of diversifying reproduction.

Embedded Cartesian Genetic Programming (ECGP) is a form of the graph based Cartesian Genetic Programming (CGP) in which modules are automatically acquired and evolved. In this paper we compare the efficiencies of the ECGP and CGP techniques on three classes of problem: digital adders, digital multipliers and digital comparators. We show that in most cases ECGP shows a substantial improvement in performance over CGP and that the computational speedup is more pronounced on larger problems.

Investigates techniques designed to allow genetic programming to evolve significantly more complex, modular, and functionally expressive code. Rather then developing a system from scratch, the research in this document builds upon the PushGP system developed by Spector (2001). PushGP uses a stack-based language with multiple stacks for operating on different data types. One stack stores program code and allows for interactive construction and modification of executable functions, modules, and control structures as the main program executes. The primary question addressed is what sort of modularity and structure evolve when their very composition arises from the evolutionary modifications of program code, rather than from external parsing on the part of genetic programming systems. The secondary question is how the computational effort of this system varies in comparison to more traditional genetic programming systems, (like Koza’s GP system with automatically defined functions).

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Embedded Cartesian Genetic Programming (ECGP) is an extension of the directed graph based Cartesian Genetic Programming (CGP), which is capable of automatically acquiring, evolving and re-using partial solutions in the form of modules. In this paper, we apply for the first time, CGP and ECGP to the well known Lawnmower problem and to the Hierarchical-if-and-Only-if problem. The latter is normally associated with Genetic Algorithms. Computational effort figures are calculated from the results of both CGP and ECGP and our results compare favourably with other techniques.