Memetic Semantic Genetic Programming

Semantic Backpropagation (SB) was introduced in GP so as to take into account the semantics of a GP tree at all intermediate states of the program execution, i.e., at each node of the tree. The idea is to compute the optimal "should-be" values each subtree should return, whilst assuming that the rest of the tree is unchanged, so as to minimize the fitness of the tree. To this end, the Random Desired Output (RDO) mutation operator, proposed in [17], uses SB in choosing, from a given library, a tree whose semantics are preferred to the semantics of a randomly selected subtree from the parent tree. Pushing this idea one step further, this paper introduces the Local Tree Improvement (LTI) operator, which selects from the parent tree the overall best subtree for applying RDO, using a small randomly drawn static library. Used within a simple Iterated Local Search framework, LTI can find the exact solution of many popular Boolean benchmarks in reasonable time whilst keeping solution trees small, thus paving the road for truly memetic GP algorithms.