Declarative and Preferential Bias in GP-based Scientific Discovery

This work examines two methods for evolving dimensionally correct equations on the basis of data. It is demonstrated that the use of units of measurement aids in evolving equations that are amenable to interpretation by domain specialists. One method uses a strong typing approach that implements a declarative bias towards correct equations, the other method uses a coercion mechanism in order to implement a preferential bias towards the same objective. Four experiments using real-world, unsolved scientific problems were performed in order to examine the differences between the approaches and to judge the worth of the induction methods.Not only does the coercion approach perform significantly better on two out of the four problems when compared to the strongly typed approach, but it also regularizes the expressions it induces, resulting in a more reliable search process.A trade-off between type correctness and ability to solve the problem is identified. Due to the preferential bias implemented in the coercion approach, this trade-off does not lead to sub-optimal performance. No evidence is found that the reduction of the search space achieved through declarative bias helps in finding better solutions faster. In fact, for the class of scientific discovery problems the opposite seems to be the case.