Single versus Multiple Tree Genetic Programming for Dynamic Decision Making

This paper considers genetic programming (GP) for dynamic decision making. Standard genetic programming only uses a single decision tree for decision making. In contrast, this paper proposes a general multiple tree framework for dynamic decision problems, where evaluation is contingent on the previous output of the program. The working hypothesis is that “recurrent” multiple trees are superior compared to conventional single trees for dynamic decision problems. To test this hypothesis, a single and a dual tree representation is considered. Both representations return Boolean values, but for the dual trees, evaluation is contingent on their previous output. Specifically, if the previous output was FALSE, the first tree is evaluated, otherwise it is the second. The single and dual trees are applied within two different domains. The first domain consists of a coevolutionary predator-prey type environment where the single and dual trees are treated as different species. The objective of a predator is to capture the phenotypic behavior of a prey. Naturally, the objective of the prey is to evade the predator. It is found that the dual trees have greater expressive capabilities, since they can capture the dynamics of the single trees when acting as predators, while evading when acting as prey. The second domain is closer related to finance. The single and dual trees are used to evolve successful trading strategies on artificial financial time series. Two different processes are constructed that exhibit some features also found in real financial data, i.e., mean-reversion and momentum effects. It is found that the single trees are unable to capture the dynamics of the mean-reverting process, but the dual trees succeed. For the trending series, both representation are capable of capturing the underlying dynamics, but the single trees have better out-of-sample performance compared to the dual trees. This is found to be a manifestation of Ockham’s razor. JEL classifications: C0, C45, C53, C63