Multi-Representation Genetic Programming: A Case Study on Tree-based and Linear Representations

TL;DR

This paper introduces a multi-representation genetic programming approach that evolves both tree-based and linear representations simultaneously, leveraging their interplay to improve solutions in symbolic regression and scheduling tasks.

Contribution

It proposes a novel multi-representation GP algorithm with a cross-representation crossover operator, addressing the gap of combining multiple representations effectively.

Findings

Multi-representation GP outperforms single-representation methods.

The cross-representation crossover enhances search effectiveness.

Improved solutions in symbolic regression and scheduling problems.

Abstract

Existing genetic programming (GP) methods are typically designed based on a certain representation, such as tree-based or linear representations. These representations show various pros and cons in different domains. However, due to the complicated relationships among representation and fitness landscapes of GP, it is hard to intuitively determine which GP representation is the most suitable for solving a certain problem. Evolving programs (or models) with multiple representations simultaneously can alternatively search on different fitness landscapes since representations are highly related to the search space that essentially defines the fitness landscape. Fully using the latent synergies among different GP individual representations might be helpful for GP to search for better solutions. However, existing GP literature rarely investigates the simultaneous effective use of evolving multiple representations. To fill this gap, this paper proposes a multi-representation GP algorithm based on tree-based and linear representations, which are two commonly used GP representations. In addition, we develop a new cross-representation crossover operator to harness the interplay between tree-based and linear representations. Empirical results show that navigating the learned knowledge between basic tree-based and linear representations successfully improves the effectiveness of GP with solely tree-based or linear representation in solving symbolic regression and dynamic job shop scheduling problems.