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Key words: Nonlinear Model, Spatial Analysis, Least-Squares Method
The placement is not a new problem. The placement of some subjects with respect to given constraints frequently takes place in urban planning, agriculture, network design in geodesy, and so on. If relative relations between subjects are given, we call it relative placement. Consequently, we define "best relative placement" (BRP) as: Non-precise relative relations, like near, far, etc., are given for n subjects. There are n(n+1)/2 independent relations in addition to requested some spatial constraints. BRP is a procedure to find the best location of each subject with respect to a given region such that all constraints and relations are fulfilled.
In this paper, a new spatial function called "best relative placement" is developed. Two different approaches for solving a BRP problem are discussed which are based on the least-squares method and interval mathematics. It will be shown that interval mathematics behaves well even for nonlinear programming tasks. The least-squares and interval methods are examined using real data.