Functional genetic programming and exhaustive program search with combinator expressions

Abstract

Using a strongly typed functional programming language for genetic programming has many advantages, but evolving functional programs with variables requires complex genetic operators with special cases to avoid creating ill-formed programs. We introduce combinator expressions as an alternative program representation for genetic programming, providing the same expressive power as strongly typed functional programs, but in a simpler format that avoids variables and other syntactic clutter. We outline a complete genetic-programming system based on combinator expressions, including a novel generalized genetic operator, and also show how it is possible to exhaustively enumerate all well-typed combinator expressions up to a given size. Our experimental evidence shows that combinator expressions compare favorably with prior representations for functional genetic programming and also offers insight into situations where exhaustive enumeration outperforms genetic programming and vice versa.

Utilization of reductions and abstraction elimination in typed genetic programming

“…This problem has been used by many researchers as a benchmark for GP. We compare our results with that presented in [11,4]. We use very similar set of building symbols as in [11].…”

“…Briggs and O'Neill present a technique utilizing typed GP with combinators [4]. The difference between the approach presented in their work and our approach is that they generate terms in a straightforward way directly from the library of combinators, without any use of lambda abstractions.…”

“…We call this approach to lambda term crossover hybrid, because it can be understood as hybrid of the lambda calculus representation and the purely combinator representation used in [4]. The advantage of generating terms as lnf lambda terms instead of generating them directly as combinator terms is that it reduces the search space, because there is more than one way to represent a lnf lambda term as a combinator term (this can be seen considering that lnf term (λ x .…”

“…Compared to the approach to typed GP over lambda calculus proposed by Yu [11], it uses more general term representation which is not restricting the use of outer local variables in the body of an anonymous function. Compared to the purely combinator approach by Briggs and O'Neill [4], it has the advantage of reducing the size of the search space in the term generation phase.…”

Evolving Workflow Graphs Using Typed Genetic Programming

“…There are several works [6], [7], [8] using typed GP with parametric polymorphism. All those works, as far as we know, evaluate their systems on rather simple benchmark problems in means of time needed to evaluate one individual (e.g.…”