Abstract
In this paper, we deal with simplification/aggregation of large-scaled optimization problems. Motivated by the reduction of data transmission and computation in distributed optimization algorithms and necessity of a criterion for clustering agents in multi-agent systems such as electric power networks, we clarify the relationship between optimal solutions of original large-scaled optimization problems and the corresponding approximated optimization problems. Based on this analysis, we propose a hierarchically distributed optimization algorithm which reduces the data transmission and computation considerably. Furthermore, we assume stochastic dispersion on profit functions of agents and analyze the stochastic characteristics of the solutions of the optimization problems.
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