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The resources allocation and task assignment in complex distributed network environment is a typical problem of multi-agent systems (MAS). Even without taking into account interactions, coordinations, and a variety of random phenomena in networks, the bandwidth allocation problem in ATM networks is also NP-complete. This paper presents a particle dynamics approach (GPDA) that transforms the MAS problem-solving into the kinematics and dynamics of particles in a force-field. As an important application for problem-solving in MAS, this paper uses GPDA to optimize the bandwidth allocation and QoS in ATM networks. The GPA has features in terms of the high-degree parallelism, multi-objective optimization, multi-type coordination, multi-granularity coalition, and easier hardware implementation. Simulations and comparisons show the effectiveness and suitability of GPDA.