Genetic programming with separability detection for symbolic regression

Genetic Programming (GP) is a popular and powerful evolutionary optimization algorithm that has a wide range of applications such as symbolic regression, classification and program synthesis. However, existing GPs often ignore the intrinsic structure of the ground truth equation of the symbolic regression problem. To improve the search efficacy of GP on symbolic regression problems by fully exploiting the intrinsic structure information, this paper proposes a genetic programming with separability detection technique (SD-GP). In the proposed SD-GP, a separability detection method is proposed to detect additive separable characteristics of input features from the observed data. Then based on the separability detection results, a chromosome representation is proposed, which utilizes multiple sub chromosomes to represent the final solution. Some sub chromosomes are used to construct separable sub functions by using separate input features, while the other sub chromosomes are used to construct sub functions by using all input features. The final solution is the weighted sum of all sub functions, and the optimal weights of sub functions are obtained by using the least squares method. In this way, the structure information can be learnt and the global search ability of GP can be maintained. Experimental results on synthetic problems with differing characteristics have demonstrated that the proposed SD-GP can perform better than several state-of-the-art GPs in terms of the success rate of finding the optimal solution and the convergence speed.