Greedy Semantic Local Search for Small Solutions

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, and to choose a subtree that matches as well as possible these target values. A single tree is evolved by iteratively replacing one of its nodes with the best subtree from a static library according to this local fitness, with tree size as a secondary criterion. Previous results for standard Boolean GP benchmarks that have been obtained by the authors with another variant of SB are improved in term of tree size. SB is then applied for the first time to categorical GP benchmarks, and outperforms all known results to date for three variable finite algebras.