A Multitask Genetic Programming Approach with ANew Individual Representation to Symbolic Regression

Symbolic regression is a task aimed at auto-matically discovering and constructing mathematical models from data that describe the complex relationships between inputs and outputs. Evolutionary multitask methods have demonstrated powerful capabilities across various domains, but research in the field of symbolic regression remains relatively limited. To further explore the potential of evo-lutionary multi task algorithms in symbolic regression, this paper proposes a multitask Genetic Programming (GP) approach with a new individual representation (IRMTGP), which encodes shared knowledge as a shared tree, explicitly facilitating knowledge transfer between tasks. Specifically, in IRMTGP, each task's solution is composed of a shared tree and an unshared tree, where the shared tree captures common knowledge across tasks, and the unshared tree focuses on learning the characteristics of individual tasks. Furthermore, to learn the optimal shared and unshared trees, a new fitness function and evolutionary process are designed. Comparing IRMTGP with GP and Multifactorial GP on six multi task problems composed of four symbolic regression benchmarks, IRMTGP achieves smaller regression errors and better generalization capabilities in most cases.