The optimization of geodetic networks may be classified into five orders (Kuang, 1996), namely:
the zero-order design problem (ZOD), which is the design of the optimal reference system
(datum); the first-order design problem (FOD), which aims to optimize the configuration of the
network (that is the point locations and the types of observed quantities and its distribution all over
the network); the second-order design problem (SOD), which aims to find the optimal weights of
the observations; the combined-order design problem (COMD), where both the first-and second‌order design problems have to be optimally solved simultaneously; and finally the third-order
design problem (THOD), which is the improvement of an existing design, by densifying or
extending the existing networks, by additional points andlor observations (Grafarend and
Schaffrin, 1979).
The COMD problem is classified, according to the present study, into three types: trial and error
approach, analytical approach and semi-analytical approach (Doma (2004)). The main objective of
this paper is to introduce a new suggested approach for solving the combined order design
(COMD) problem. Also, the discussion for solving the COMD problem is given. Three computer
programs for the computation of the criterion matrix, solving the second-order design (SOD)
problem and solving the combined-order design (COMD) problem are developed. The obtained
results will be presented in order to illustrate the application and the feasibility of the suggested
approach.