Optimization of urban greenway route using a coverage maximization model for lines

Urban greenways enhance the social, environmental, and ecological facets of city life by offering accessible and engaging spaces for residents. Despite their significance, the route selection for these urban greenways often hinges on suitability analysis, which can be influenced by a planner's subjective judgment, thus potentially introducing bias. Spatial optimization is a potential solution for determining optimal urban greenway routes. However, urban greenway route planning poses a distinct spatial optimization challenge that is not addressed by existing models. While urban greenways are inherently linear features, there are generally no specific start or end points dictated in their planning, which contrasts with many existing line-based spatial optimization models. Moreover, the way that coverage for urban greenways is measured—by taking into account the area encompassed within a particular distance from the entire urban greenway—deviates from the method used in conventional coverage optimization models, which works through discrete point-based evaluations. To address these gaps, our study introduces the maximal covering location problem for lines (MCLP-Line) model, which is designed to determine the optimal single-line-shaped urban greenway route with maximum coverage of nearby residents. In this paper, we utilize a line graph data structure to transform the candidate road network into a graph where road segments become nodes and junctions are treated as edges. We delineate the mixed integer linear programming formulation for the MCLP-Line model and discuss approaches for eliminating subtours in the MCLP-Line model in detail. The study provides simulation tests using both randomly generated data and an empirical dataset from Lhasa to demonstrate the practicality and computational efficiency of the proposed model.