Optimization Model for Facility Location with Maximization of a Walkability Index on a Hexagonal Grid

This work proposes the Urban Facility Augmentation Problem (UFAP), a combinatorial optimization model for allocating urban facilities to maximize walkability. The formulation integrates the Walkability Quality Index (WQI), which combines 11 dimensions related to accessibility, environmental conditions, safety, connectivity, and urban services using the CRITIC method and geospatial data on hexagonal grids. UFAP is modeled as a variant of the Facility Location Problem with budgetary, spatial feasibility, and capacity constraints, and incorporates terrain-sensitive walking times and temporal attractiveness decay. Experimental evaluations were conducted across five urban regions and three pedestrian mobility profiles, using allocation and weight-recalculation strategies. Results showed consistent positive gains in Global-WQI, with superior performance when facilities were allocated to low-WQI areas. Scenarios with fixed weights yielded larger average gains, whereas CRITIC recalculation increased sensitivity to spatial redistribution. The study establishes a computational foundation for future and metaheuristic approaches to walkability-oriented urban planning.