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

TL;DR

This work introduces MRGP-TL, a multi-representation genetic programming framework that co-evolves tree-based and linear GP populations and exchanges building blocks via a novel cross-representation adjacency-list crossover (CALX). By unifying diverse building blocks into adjacency lists, MRGP-TL enables effective knowledge sharing between representations, improving symbolic regression and dynamic job shop scheduling performance compared with single-representation baselines. Empirical results show statistically significant improvements in DJSS and competitive gains in symbolic regression, with analyses highlighting the benefits of CALX, parameter sensitivity, and budget allocation across representations. The study demonstrates that coupling heterogeneous GP representations can reduce representation risk and enhance search efficiency, suggesting broader applicability to additional GP variants and problem domains.

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.

Figures (13)

• Figure 1: An example of GP individuals with tree-based and linear representations for the same mathematical formula.
• Figure 2: Switching GP representations to jump out of local optima.
• Figure 3: Evolutionary framework of MRGP. The novel components are highlighted by the dark boxes.
• Figure 4: The schematic diagram of CALX between trees and instruction sequences
• Figure 5: An example of constructing a tree by $\texttt{GrowTreeBasedAL}(\cdot)$. The dashed tree nodes are randomly generated.