In recent years, numerous studies have drawn the success of estimation of distribution algorithms (EDAs) to avoid the frequent breakage of building blocks of the conventional stochastic genetic operators-based evolutionary algorithms (EAs). In this paper, a novel graph-based EDA called probabilistic model building genetic network programming (PMBGNP) is proposed. Using the distinguished graph (network) structure of a graph-based EA called genetic network programming (GNP), PMBGNP ensures higher expression ability than the conventional EDAs to solve some specific problems. Furthermore, an extended algorithm called reinforced PMBGNP is proposed to combine PMBGNP and reinforcement learning to enhance the performance in terms of fitness values, search speed, and reliability. The proposed algorithms are applied to solve the problems of controlling the agents' behavior. Two problems are selected to demonstrate the effectiveness of the proposed algorithms, including the benchmark one, i.e., the Tileworld system, and a real mobile robot control.
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