The paper deals with a multi-agent-based architecture for an artificial stock market. We attempt to add more heterogeneity to agents. Specifically, in this architecture rational agents prefer forecast equation models or simple trading rules to support their decision making, and own their own individual base or just learn from a public base. Besides these rational agents, a type of irrational agent is also defined. We focus on applying the GP approach to model cognitive behavior of adaptive agents. Time series generated from this multi-agent-based artificial stock market are demonstrated to replicate some features and compared with empirical studies.