Document Type



Doctor of Philosophy


Applied Mathematics

Date of Defense


Graduate Advisor

Cezary Z Janikow, Ph.D.


Berit Brogaard

Uday Chakraborty

Wenjie He


The size and complexity of a GP representation space is defined by the set of functions and terminals used, the arity of those functions, and the maximal depth of candidate solution trees in the space. Practice has shown that some means to reduce the size or bias the search must be provided. Adaptable Constrained Genetic Programming (ACGP) can discover beneficial substructures and probabilistically bias the search to promote the use of these substructures. ACGP has two operating modes: a more efficient low granularity mode (1st order heuristics) and a less efficient higher granularity mode (2nd order heuristics). Both of these operating modes produce probabilistic models, or heuristics, that bias the search for the solution to the problem at hand. The higher granularity mode should produce better models and thus improve GP performance, but in reality it does not always happen. This research analyzes the two modes, identifies problems and circumstances where the higher granularity search should be advantageous but is not, and then proposes a new methodology that divides the ACGP search into two-tiers. The first tier search exploits the computational efficiency of 1st order ACGP and builds a low granularity probabilistic model. This initial model is then used to condition the higher granularity search. The combined search scheme results in better solution fitness scores and lower computational time compared to a standard GP application or either mode of ACGP alone.

Included in

Mathematics Commons