Scalability of Genetic Programming and Probabilistic Incremental Program Evolution

This paper discusses scalability of standard genetic programming (GP) and the probabilistic incremental program evolution (PIPE). To investigate the need for both effective mixing and linkage learning, two test problems are considered: ORDER problem, which is rather easy for any recombination-based GP, and TRAP or the deceptive trap problem, which requires the algorithm to learn interactions among subsets of terminals. The scalability results show that both GP and PIPE scale up polynomially with problem size on the simple ORDER problem, but they both scale up exponentially on the deceptive problem. This indicates that while standard recombination is sufficient when no interactions need to be considered, for some problems linkage learning is necessary. These results are in agreement with the lessons learned in the domain of binary-string genetic algorithms (GAs). Furthermore, the paper investigates the effects of introducing utnnecessary and irrelevant primitives on the performance of GP and PIPE.Comment: Submitted to GECCO-200

Dependency structure matrix, genetic algorithms, and effective recombination

In many different fields, researchers are often confronted by problems arising from complex systems. Simple heuristics or even enumeration works quite well on small and easy problems; however, to efficiently solve large and difficult problems, proper decomposition is the key. In this paper, investigating and analyzing interactions between components of complex systems shed some light on problem decomposition. By recognizing three bare-bones interactions-modularity, hierarchy, and overlap, facet-wise models arc developed to dissect and inspect problem decomposition in the context of genetic algorithms. The proposed genetic algorithm design utilizes a matrix representation of an interaction graph to analyze and explicitly decompose the problem. The results from this paper should benefit research both technically and scientifically. Technically, this paper develops an automated dependency structure matrix clustering technique and utilizes it to design a model-building genetic algorithm that learns and delivers the problem structure. Scientifically, the explicit interaction model describes the problem structure very well and helps researchers gain important insights through the explicitness of the procedure.This work was sponsored by Taiwan National Science Council under grant NSC97- 2218-E-002-020-MY3, U.S. Air Force Office of Scientific Research, Air Force Material Command, USAF, under grants FA9550-06-1-0370 and FA9550-06-1-0096, U.S. National Science Foundation under CAREER grant ECS-0547013, ITR grant DMR-03-25939 at Materials Computation Center, grant ISS-02-09199 at US National Center for Supercomputing Applications, UIUC, and the Portuguese Foundation for Science and Technology under grants SFRH/BD/16980/2004 and PTDC/EIA/67776/2006