in: Harold Fellermann et al. (Eds.), Artiﬁcial Life XII, Proceedings of the Twelfth International Conference on the Synthesis and Simulation of Living Systems, Odense, Denmark, August 2010. c  MIT Press, 2010. Available at http://www.alifexii.org/proceedings/ Catalytic Search in Dynamic Environments Lidia Yamamoto 1 and Wolfgang Banzhaf 2 1 LSIIT-FDBT, University of Strasbourg, France 2 Memorial University of Newfoundland, St. John’s, NL, Canada Lidia.Yamamoto@unistra.fr, banzhaf@cs.mun.ca Abstract Catalytic Search is an optimization algorithm inspired by ran- dom catalytic reaction networks and their pre-evolutionary dynamics. It runs within an Artiﬁcial Chemistry in which reactions can be reversible, and replication is not taken for granted. In previous work one of us had shown that although inherently slower than Evolutionary Algorithms, Catalytic Search is able to solve simple problems while naturally main- taining diversity in the population. This is a useful property when the environment may change. In this paper, we compare the performance of Catalytic Search and a Genetic Algorithm in a dynamic environment represented by a periodically changing objective function. We investigate the impact of parameters such as tempera- ture, inﬂow/outﬂow rate, and amount of catalysts. We show that Catalytic Search is generally more stable in the face of changes, although still slower in achieving the absolute best ﬁtness. Our results also offer some indications on how cat- alytic search could either degenerate into random search, or progress towards evolutionary search, although the latter tran- sition has not been fully demonstrated yet. Introduction Artiﬁcial chemistries have been used to understand the ori- gin of evolution from a pre-evolutionary, random initial state (Fontana and Buss (1994); Dittrich and Banzhaf (1998)), to devise bottom-up chemical computing algorithms for emer- gent computation (Banzhaf et al. (1996); Dittrich (2005)), and to build new optimization algorithms (Banzhaf (1990); Kanada (1995); Weeks and Stepney (2005)), among other usages. The motivation for the present work lies at the intersection of these three application domains. We are interested in exploring the emergent computation proper- ties of artiﬁcial chemistries for the construction of beamed search schemes able to optimize solutions to user-deﬁned problems. Instead of a top-down, pre-designed optimiza- tion algorithm, optimization could be regarded as a compu- tation task to emerge from the bottom up, as an outcome of molecule interactions. In this context, it is worth deter- mining the conditions for the emergence of optimization, of which evolution is only one example. Bagley and Farmer (1991) showed that primitive metabolisms called autocatalytic metabolisms can emerge in an artiﬁcial chemistry where polymers undergo reversible polymerization reactions. One of the conditions for the emergence of such metabolisms is to drive the system out of equilibrium by a constant inﬂow of molecules from the food set, accompanied by a non-selective dilution ﬂow. In this case, some reactions may be boosted by catalytic focusing: starting from a random soup of molecules, the system ends up focusing most of its activity and mass into a few types of molecules, self-organizing into autocatalytic reaction net- works that consume food molecules to produce longer poly- mers. The molecules taking part in this autocatalytic core can be regarded as primitive metabolisms. In previous work, Yamamoto (2010) proposed catalytic search, an optimization scheme inspired by catalytic focus- ing. Catalytic search is based on a pre-evolutionary chem- istry (Nowak and Ohtsuki (2008)), where reactions might be reversible, and replication is not taken for granted. The reaction energy functions are assigned such that reactions towards ﬁtter products are favored. The selective pressure in catalytic search comes from the differences in reaction rates for different molecules in the reactor. These differences can be ampliﬁed selectively by catalysts: some reactions can be accelerated by catalysts that decrease the activation en- ergy barrier necessary for them to occur. Due to the absence of direct replication, the performance of such scheme lies between that of a random search, and that of an evolution- ary algorithm. In spite of such apparent weakness, catalytic search and related chemical schemes have many interesting properties, as pointed out by Weeks and Stepney (2005): the potential to undo wrong computations or to decompose bad solutions through reversible reactions; the ability to steer the reaction ﬂow towards the production of good products by shifting the equilibrium distribution of molecules; a certain robustness to noisy ﬁtness feedback; and the prevention of premature convergence through a natural tendency to gen- erate and maintain diversity in the population. This paper focuses on the latter property. 1