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Automatic multiple geographical feature label placement (MGFLP) is a combinatorial optimization problem shown to be an NP-hard problem, and it is a challenge in automatic cartography. Many automatic label placement algorithms for point, line, and area features were put forward. It is a common way to use multiple candidate positions (MCP) for label placement, but the research in this way mostly focuses on point features and does not take all three types of features and all the possible candidate positions into account on the map. Therefore, in this paper, the concept of degrees of spatial freedom for feature label placement is proposed based on the idea of degrees of freedom of mechanical motion. We define the degrees of freedom (DOF) and its space for feature labels on a planar map so as the potential space, including all the optional candidate positions of each feature label, can be standardized. Based on two degrees of freedom (2-DOF) space, feature reference position (FRP), and certain buffer distance (CBD) from FRP, we studied the methods including generating, calculating, evaluating, and selecting MCP for feature label. By using and improving the discrete differential evolution genetic algorithm (DDEGA), we carried out MGFLP experiments on the same dataset used by DDEGA algorithm. The results show that: 1) although the MCP based on the 2-DOF space increase the complexity of the NP-hard problem, however, the obtained results by optimizing the performance of the algorithm and increasing the number of candidate positions are still better than the traditional 8-candidate positions model. 2) In the same 2-DOF space, increasing the candidate positions from less to more along each direction of the 2-DOF space improves the quality of label placement.

Multiple Geographical Feature Label Placement Based on Multiple Candidate Positions in Two Degrees of Freedom Space