Optimizing the geodetic networks based on the distances between the net points and the project border

Area of Science:

• Geodesy
• Geodetic Engineering
• Network Optimization

Background:

• Geodetic networks are crucial for engineering projects, typically designed using precision, reliability, and cost criteria.
• Existing design methods may not fully optimize point placement relative to project boundaries.

Purpose of the Study:

• To introduce and evaluate a novel Neighboring (N) criterion for geodetic network design.
• To optimize the placement of Net Points (NPs) closer to Project Borders (PBs).
• To enhance observation accuracy and reduce transportation costs in geodetic networks.

Main Methods:

• Formulation of three normalized N objective functions based on L1, L2, and L∞ norms.
• Development of corresponding N optimization models (NL1, NL2, NL∞).
• Evaluation of models against safety, precision, reliability, and cost constraints using a simulated example.

Main Results:

• The NL∞ model effectively identified the safest NP positions near the PB.
• Optimized NP placement improved network precision while maintaining reliability and observation costs.
• All N models demonstrated theoretical feasibility in enhancing observation accuracy and reducing transportation costs.

Conclusions:

• The Neighboring (N) criterion offers a viable approach to geodetic network design, particularly with the NL∞ model for safety and precision.
• Multi-objective optimization is recommended to address potential contradictions and generalize N model benefits in real-world applications.