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Mission design of DeltaV-low-cost gravity assists tours for the Icy Moons exploration (orbiters around Io, Europa, Ganymede and probes for the detection of liquid water beneath their surfaces) is considered, taking radiation hazard into account. Limited dynamic opportunities of using flybys require multiple gravity assists. Relevance of regular creation of optimum scenarios – sequences of passing of celestial bodies with definition of conditions of their execution is obvious. This work is devoted to the description of criteria for creation of such chains