Searching for novel regression functions

The objective function is the core element in most search algorithms that are used to solve engineering and scientific problems, referred to as the fitness function in evolutionary computation. Some researchers have attempted to bridge this difference by reducing the need for an explicit fitness function. A noteworthy example is the novelty search (NS) algorithm, that substitutes fitness with a measure of uniqueness, or novelty, that each individual introduces into the search. NS employs the concept of behavioral space, where each individual is described by a domain-specific descriptor that captures the main features of an individual's performance. However, defining a behavioral descriptor is not trivial, and most works with NS have focused on robotics. This paper is an extension of recent attempts to expand the application domain of NS. In particular, it represents the first attempt to apply NS on symbolic regression with genetic programming (GP). The relationship between the proposed NS algorithm and recent semantics-based GP algorithms is explored. Results are encouraging and consistent with recent findings, where NS achieves below average performance on easy problems, and achieves very good performance on hard problems. In summary, this paper presents the first attempt to apply NS on symbolic regression, a continuation of recent research devoted at extending the domain of competence for behavior-based search.