Analysis of cluster formations on planer cells based on genetic programming

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Analysis of cluster formations on planer cells based on genetic programming Jianjun Lu · Shozo Tokinaga

Published online: 21 March 2012 © Springer Science+Business Media, LLC 2012

Abstract This paper offers an analysis of cluster formations on planer cells comprised of multi-agents utilizing local interactions and state transitions based on Genetic Programming (GP) and its applications. First, we illustrate that if the states of agents are allowed to have continuous values, equilibrium is attained on the basis of the fixed-point theorem. We also show that if the agents are restricted to binary states, equilibrium is attained in an asymptotic sense. However, for agents characterized by more than one state, the attainment of equilibrium is not ensured. We examine our results by using a simulation wherein agents learn from past experiences based on GP. Finally, we demonstrate a system comprised of cluster formations on planer cells comprised of artificial agents, and apply this system to the clustering of employees in firms. Keywords Multi-agents · Cellular automaton · Genetic Programming (GP) · Local interaction · Control of agents’ behavior 1 Introduction In recent years, which have been characterized by the electronic environment and the formation of the electronic commodity market, commodity and related information have been exchanged, so-called network communities have been formed, and the significance of these developments has been analyzed (Van Alstyne and Brynjolffson 2005; McAulay 2007; König et al. 2010). Based on a subsequent diversification of individual values and occupations, similar changes have been generated J. Lu () College of Economics and Management, China Agricultural University, Beijing 100083, China e-mail: [email protected] S. Tokinaga Graduate School of Economics, Kyushu University, Fukuoka 812-8581, Japan

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in enterprises, such as schools and business organizations (Maeda and Imai 2005; Burke and Calton 2009; Zou and Yilmaz 2010; Taifi and Passiante 2010). As a methodological contrast, the research by Frantz et al. (2009) studies social network problems from the standpoint of agent-based models. Researchers have examined these events via multi-agent model analysis, which has yielded interesting results (Tesfatsion 2001; Klos and Nooteboom 2001; Raberto et al. 2008; Yang et al. 2008; Biggiero and Sevi 2009; Safarzy´nska and van den Bergh 2010; Beckenbach and Briegel 2010; Read 2010; Pitt et al. 2011). The financial support from the local government affect as the surrounding circumstance for agents who begin to operate firms. If one firm is supported by the local government and succeeds, then another agent around this firm can also enjoy the success, because the employment is established and the cluster is gradually formalized beginning from a point in the area (Topa 2001; Cheng and Nault 2007; Alcacer and Chung 2007; Grima and Wakelin 2007; Beckenbach and Briegel 2010). It is known that the membership to join a certain site