Enhancing Local Decisions in Agent-Based Cartesian Genetic Programming by CMA-ES

Abstract

Cartesian genetic programming is a popular version of classical genetic programming, and it has now demonstrated a very good performance in solving various use cases. Originally, programs evolved by using a centralized optimization approach. Recently, an algorithmic level decomposition of program evolution has been introduced that can be solved by a multi-agent system in a fully distributed manner. A heuristic for distributed combinatorial problem-solving was adapted to evolve these programs. The applicability of the approach and the effectiveness of the used multi-agent protocol as well as of the evolved genetic programs for the case of full enumeration in local agent decisions has already been successfully demonstrated. Symbolic regression, n-parity, and classification problems were used for this purpose. As is typical of decentralized systems, agents have to solve local sub-problems for decision-making and for determining the best local contribution to solving program evolution. So far, only a full enumeration of the solution candidates has been used, which is not sufficient for larger problem sizes. We extend this approach by using CMA-ES as an algorithm for local decisions. The superior performance of CMA-ES is demonstrated using Koza’s computational effort statistic when compared with the original approach. In addition, the distributed modality of the local optimization is scrutinized by a fitness landscape analysis.