Grammatical Evolution: STE criterion in Symbolic Regression Task

Grammatical evolution (GE) is one of the newest among computational methods (Ryan et al., 1998), (O’Neill and Ryan, 2001). Basically, it is a tool used to automatically generate Backus-Naur-Form (BNF) computer programmes. The method's evolution mechanism may be based on a standard genetic algorithm (GA). GE is very often used to solve the problem of a symbolic regression, determining a module's own parameters (as it is also the case of other optimization problems) as well as the module structure itself. A Sum Square Error (SSE) method is usually used as the testing criterion. In this paper, however, we will present the original method, which uses a Sum Epsilon Tube Error (STE) optimizing criterion. In addition, we will draw a possible parallel between the SSE and STE criteria describing the statistical properties of this new and promising minimizing method. Index Terms — Grammatical Evolution, SSE, STE, Epsilon Tube, Laplace Distribution.