Reconstructing Dynamic Target Functions by Means of Genetic Programming Using Variable Population Size
Dynamic environments are becoming more and more popular in many applicative domains. A large amount of literature has appeared to date dealing with the problem of tracking the extrema of dynamically changing target functions, but relatively few material h
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Dipartimento di Informatica, Sistemistica e Comunicazione (D.I.S.Co.) University of Milano-Bicocca, Milan, Italy Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), Lugano, Switzerland
Abstract. Dynamic environments are becoming more and more popular in many applicative domains. A large amount of literature has appeared to date dealing with the problem of tracking the extrema of dynamically changing target functions, but relatively few material has been produced on the problem of reconstructing the shape, or more generally finding the equation, of dynamically changing target functions. Nevertheless, in many applicative domains, reaching this goal would have an extremely important impact. It is the case, for instance, of complex systems modelling, like for instance biological systems or systems of biochemical reactions, where one is generally interested in understanding what’s going on in the system over time, rather than following the extrema of some target functions. Last but not least, we also believe that being able to reach this goal would help researchers to have a useful insight on the reasons that cause the change in the system over time, or at least the pattern of this modification. This paper is intended as a first preliminary step in the attempt to fill this gap. We show that genetic programming with variable population size is able to adapt to the environment modifications much faster (i.e. using a noteworthy smaller amount of computational effort) than standard genetic programming using fixed population size. The suitability of this model is tested on a set of benchmarks based on some well known symbolic regression problems.
1 Introduction Many real-world problems are anchored in dynamic environments, where some element of the problem domain, typically the target, changes with time. For this reason, developing solid evolutionary algorithms (EAs) to reliably solve these problems is an important task. The application of evolutionary computation (EC) to dynamic environments creates challenges different to those encountered in static environments. Foremost among these, are issues of premature convergence, and the evolution of overfit solutions. In the last few years, many contributions have appeared which studied dynamic optimization environments and developped new evolutionary frameworks for solving them. Some of those contributions are discussed in Section 2. Nonetheless, the majority of those approaches are based on Genetic Algorithms (GAs) [17] or Particle Swarm Optimization (PSO) [8] and the problem objective is to find the extrema (maxima or minima) of a target function that changes with time. On the other hand, very few contributions have K. Madani et al. (Eds.): Computational Intelligence, SCI 343, pp. 121–134. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com
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L. Vanneschi and G. Cuccu
appeared to date that study the ability of Genetic Programming (GP) [22] to reconstruct target functions on dynamic optimization environments. In this paper we hypothesize that
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