Constraints in Genetic Programming

Genetic programming refers to a class of genetic algorithms utilizing generic representation in the form of program trees. For a particular application, one needs to provide the set of functions, whose compositions determine the space of program structures being evolved, and the set of terminals, which determine the space of specific instances of those programs. The algorithm searches the space for the best program for a given problem, applying evolutionary mechanisms borrowed from nature. Genetic algorithms have shown great capabilities in approximately solving optimization problems which could not be approximated or solved with other methods. Genetic programming extends their capabilities to deal with a broader variety of problems. However, it also extends the size of the search space, which often becomes too large to be effectively searched even by evolutionary methods. Therefore, our objective is to utilize problem constraints, if such can be identified, to restrict this space. In this publication, we propose a generic constraint specification language, powerful enough for a broad class of problem constraints. This language has two elements -- one reduces only the number of program instances, the other reduces both the space of program structures as well as their instances. With this language, we define the minimal set of complete constraints, and a set of operators guaranteeing offspring validity from valid parents. We also show that these operators are not less efficient than the standard genetic programming operators if one preprocesses the constraints - the necessary mechanisms are identified

Adaptable Constrained Genetic Programming: Extensions and Applications

An evolutionary algorithm applies evolution-based principles to problem solving. To solve a problem, the user defines the space of potential solutions, the representation space. Sample solutions are encoded in a chromosome-like structure. The algorithm maintains a population of such samples, which undergo simulated evolution by means of mutation, crossover, and survival of the fittest principles. Genetic Programming (GP) uses tree-like chromosomes, providing very rich representation suitable for many problems of interest. GP has been successfully applied to a number of practical problems such as learning Boolean functions and designing hardware circuits. To apply GP to a problem, the user needs to define the actual representation space, by defining the atomic functions and terminals labeling the actual trees. The sufficiency principle requires that the label set be sufficient to build the desired solution trees. The closure principle allows the labels to mix in any arity-consistent manner. To satisfy both principles, the user is often forced to provide a large label set, with ad hoc interpretations or penalties to deal with undesired local contexts. This unfortunately enlarges the actual representation space, and thus usually slows down the search. In the past few years, three different methodologies have been proposed to allow the user to alleviate the closure principle by providing means to define, and to process, constraints on mixing the labels in the trees. Last summer we proposed a new methodology to further alleviate the problem by discovering local heuristics for building quality solution trees. A pilot system was implemented last summer and tested throughout the year. This summer we have implemented a new revision, and produced a User's Manual so that the pilot system can be made available to other practitioners and researchers. We have also designed, and partly implemented, a larger system capable of dealing with much more powerful heuristics

CGP lil-gp 2.1;1.02 User's Manual

This document describes extensions provided to lil-gp facilitating dealing with constraints. This document deals specifically with lil-gp 1.02, and the resulting extension is referred to as CGP lil-gp 2.1; 1.02 (the first version is for the extension, the second for the utilized lil-gp version). Unless explicitly needed to avoid confusion, version numbers are omitted

Fuzzy Decision Forest”,

Abstract I

Evolving Representation in Genetic Programming.

Abstract. Genetic Programming uses trees to represent chromosomes. The user defines the representation space by defining the set of functions and terminals to label the nodes in the trees. The sufficiency principle requires that the set be sufficient to label the desired solution trees. To satisfy this principle, the user is often forced to provide a large set, which unfortunately also enlarges the representation space and thus, the search space. Structure-preserving crossover, STGP, CGP, and CFG-based GP, give the user the power to reduce the space by specifying rules for valid tree construction. However, the user often may not be aware of the best representation space, including heuristics, to solve a particular problem. In this paper, we present a methodology, which extracts and utilizes local heuristics aiming at improving search efficiency. The methodology uses a specific technique for extracting the heuristics, based on tracing firstorder (parent-child) distributions of functions and terminals. We illustrate these distributions, and then we present a number of experimental results. . .

Evolving Problem Heuristics with On-line ACGP

Genetic Programming uses trees to represent chromosomes. The user defines the representation space by defining the set of functions and terminals to label the nodes in the trees. The sufficiency principle requires that the set be sufficient to label the desired solution trees, often forcing the user to enlarge the set, thus also enlarging the search space. Structure-preserving crossover, STGP, CGP, and CFG-based GP give the user the power to reduce the space by specifying rules for valid tree construction: types, syntax, and heuristics. However, in general the user may not be aware of the best representation space, including heuristics, to solve a particular problem. Recently, the ACGP methodology for extracting problem-specific heuristics, and thus for learning model of the problem domain, was introduced with preliminary off-line results. This paper overviews ACGP, pointing out its strength and limitations in the off-line mode. It then introduces a new on-line model, for learning while solving a problem, illustrated with experiments involving the multiplexer and the Santa Fe trail