Graph representations in genetic programming

Léo Françoso Dal Piccol Sotto,Márcio Porto Basgalupp,Timothy Atkinson,Roman Kalkreuth,Paul Kaufmann

doi:10.1007/s10710-021-09413-9

Abstract

Graph representations promise several desirable properties for genetic programming (GP); multiple-output programs, natural representations of code reuse and, in many cases, an innate mechanism for neutral drift. Each graph GP technique provides a program representation, genetic operators and overarching evolutionary algorithm. This makes it difficult to identify the individual causes of empirical differences, both between these methods and in comparison to traditional GP. In this work, we empirically study the behaviour of Cartesian genetic programming (CGP), linear genetic programming (LGP), evolving graphs by graph programming and traditional GP. By fixing some aspects of the configurations, we study the performance of each graph GP method and GP in combination with three different EAs: generational, steady-state and (1+lambda ). In general, we find that the best choice of representation, genetic operator and evolutionary algorithm depends on the problem domain. Further, we find that graph GP methods can increase search performance on complex real-world regression problems and, particularly in combination with the (1 + lambda) EA, are significantly better on digital circuit synthesis tasks. We further show that the reuse of intermediate results by tuning LGP’s number of registers and CGP’s levels back parameter is of utmost importance and contributes significantly to better convergence of an optimization algorithm when solving complex problems that benefit from code reuse.

Highlights

Genetic programming (GP) is a well-known technique for evolving programs and has been successfully applied on several domains, like regression, control problems, and evolution of digital circuits [19, 25]
In Linear Genetic Programming (LGP), programs are represented as lists of instructions of a programming language, and the result of each instruction is assigned to a register from a predefined set of registers [6]
For the real-world datasets, the generational algorithm worked best for GP, Cartesian genetic programming (CGP), and Evolving Graphs by Graph Programming (EGGP), the only exception being the dataset yacht for CGP and EGGP

Summary

Introduction

Genetic programming (GP) is a well-known technique for evolving programs and has been successfully applied on several domains, like regression, control problems, and evolution of digital circuits [19, 25]. In Cartesian Genetic Programming (CGP), programs are grids of nodes, and each node can use the nodes of the previous layers as arguments [23]. In both of these methods, the genotype is linear, but the phenotype is interpreted as a Directed Acyclic Graph (DAG). Standard GP represents programs in a tree-based scheme [19], and uses two standard genetic operators: crossover and mutation. LGP represents programs as lists of instructions from a programming language It uses a registers vector r, where each position is initialized with the values of the input variables, in a sequential and cyclic manner [6]. In LGP, the second argument of a binary function generally has a probability of 50% of being a constant from a predefined range

Methods

Results

Conclusion