genetic programming with a norm-referenced fitness function
In this paper, we develop a new fitness function based on adjustment of the original fitness function using population performance. We call this new fitness function norm-referenced fitness function since it is motivated by the idea of norm-referenced test. Experiments performed in two benchmark problems show that, the norm-referenced fitness function developed is capable of improving the overall performance of GP system. Further analysis of the fitness function reveals that the original fitness function suffers from an implicit bias we named as implicit bias towards exploitation in later generations. This implicit bias pushes the population towards convergence. The norm-referenced fitness developed however does not inherit this bias, and we think this is the main reason why the norm-referenced fitness function is able to outperform the original fitness function. We further study the selection of the newly introduced parameter lambda in norm-referenced fitness function and give a number of advices to select the optimal value of the parameter.
population performance fitness function adjustment internal fitness measure