Fundamental Issues in the Use of Genetic Programming in Agent Based Computational Economics

1 Motivation Genetic programming has been applied to agent-based computational economics for more than half a decade. This line of research is currently challenged by several non-trivial technical issues. This paper will give a full account of them, including their significance and solvability. Genetic programming is to grow (evolve) a population of evolving hierarchies of building blocks (subroutines), the basic units of learning and information, from an immense space of them. There are three key words in this brief definition, namely, building blocks, hierarchies ,a ndevolving population of hierarchies. A building block is a class of decision rules defined by some specific characteristics which can perform certain kinds of functions. In genetic programming, building blocks are initially randomly generated by a set of primitives, known as the function set and terminal set. Here comes the first issue: the choice of primitives. Once a set of primitives is given, hierarchies are derived by some production rules (grammar). Given the grammar, any hierarchy which is syntactically valid is a legitimate species. Its appearance and popularity will be crucially dependent on its fitness, which is basically driven by three genetic operators, namely, reproduction, crossover ,a ndmutation. Issues encountered at this stage are two-fold: the semantic restrictions of derived hierarchies and the use of genetic operators. Finally, those hierarchies are not static, but dynamically adapted to the environment which is either exogenously given or endogenously change with the agents. The dynamics generated by GP is a sequence of sets of programs (parse trees, subroutines, ideas, strategies). This sequence can be interpreted as the evolution of an artificial society as a whole. In other words, a society of adaptive agents has a one-to-one and onto relation to a population of programs. Alternatively, this sequence can also be interpreted as the adaptation of a single agent. In this case, a society of agents consists of many populations of programs. The first interpretation is often referred to as single-population GP (SGP), whereas the second is dubbed multi-population GP (MGP). Which interpretation is appropriate? We will address this issue at the end of the paper.

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