Analysis of Semantic Modularity for Genetic Programming

In this paper we analyze the properties of functional modularity, a concept introduced in [14] for detecting and measuring modularity in problems of automatic program synthesis, in particular by means of genetic programming. The basic components of functional modularity approach are subgoals – entities that embody module’s semantic – and monotonicity, a measure for assessing subgoals’ potential utility for searching for good modules. For a given subgoal and a sample of solutions decomposed into parts and contexts according to module definition, monotonicity measures the correlation of distance between semantics of solution’s part and the fitness of the solution. The central tenet of this approach is that highly monotonous subgoals can be used to decompose the task and improve search convergence. In the experimental part we investigate the properties of functional modularity using eight instances of problems of Boolean function synthesis. The results show that monotonicity varies depending on problem’s structure of modularity and correctly identifies good subgoals, potentially enabling automatic program decomposition.