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Generally the problem of the optimal topological design of a network is basically an integer-programming problem (EP), or a mixed-integer programming problem (MIP). In general, combinatorial problems of this kind are NP hard, which makes it difficult to obtain an optimal, or near optimal solution. Likewise, the design of a dynamic hybrid satellite and terrestrial network (DHSTN) is a restricted topology network design problem that exhibits similar difficulties in its solution. In this paper two approaches to the dynamic hybrid network design problem are proposed and examined. The first approach is a ratio assignment (AS) approach and the second a non-linear knapsack approach. The main objective is to use a Lagrange relaxation approach to reduce the transcendental relating constraints in the DHSTN design problem so as to render them solvable.