In this paper, we focus on an aggregative optimization problem under the communication bottleneck. The aggregative optimization is to minimize the sum of local cost functions. Each cost function depends on not only local state variables but also the sum of functions of global state variables. The goal is to solve the aggregative optimization problem through distributed computation and local efficient communication over a network of agents without a central coordinator. Using the variable tracking method to seek the global state variables and the quantization scheme to reduce the communication cost spent in the optimization process, we develop a novel distributed quantized algorithm, called D-QAGT, to track the optimal variables with finite bits communication. Although quantization may lose transmitting information, our algorithm can still achieve the exact optimal solution with linear convergence rate. Simulation experiments on an optimal placement problem is carried out to verify the correctness of the theoretical results.
This study made it possible to show, using the example of Bohemia, that agrarian areas which have thus far been viewed as the “traditional” regions of emigration, also feature significant numbers of immigrants. Migration from agrarian regions not only moved in the direction of towns and urban centres. Commonly it was the case that each region was connected with other regions along multidirectional channels of exchange. In addition, in the rural environment there is clear evidence of the existence of an important system of seasonal migration. Intensive research of migration flows in the Central European rural environment, a task that still awaits international historiography, will certainly bring to light many more, thus far unknown, migration systems.