An improved quantum genetic algorithm with adaptive dynamic rotation for urban facility spatial optimization

Facility allocation plays a crucial role in modern urban planning and design. However, the allocation of various facilities in a reasonable manner is a complex problem involving high-dimensional multi-peak combination optimization. Existing heuristic methods for facility configuration, including traditional genetic algorithms and their improved variants, often suffer from premature convergence and limited search diversity when dealing with large-scale spatial optimization problems under geographical correlation and heterogeneity constraints in urban coupled environments. These limitations result in suboptimal solutions and reduced effectiveness of planning schemes. This paper proposes an improved quantum genetic algorithm with adaptive dynamic rotation angle (IQGA-ADA) for spatial optimization of facility configuration. The proposed IQGA-ADA method addresses the limitations of existing approaches through two key innovations: (1) an ADA mechanism integrated into the population renewal strategy to prevent early-stage local convergence and enhance global search capabilities; (2) the application of S-transform for processing multi-modal spatial data (including population distribution, traffic network, and facility location information) to extract characteristic quantities (root mean square and mean value) that enhance the identification degree of facility configuration patterns. By conducting a case analysis on the spatial optimization of first aid facilities, the proposed algorithm demonstrates its capability to enhance the fairness of repositioning optimization for such facilities. Quantitative results show that IQGA-ADA achieves a 68% improvement in fitness value over the real-coded genetic algorithm (RCGA), with the average fitness converging at approximately 5 iterations compared to 125 iterations for RCGA. Experimental results indicate that the proposed algorithm exhibits stronger global search capabilities and performs better in handling high-dimensional multi-peak spatial optimization problems. Moreover, the research highlights the potential application of quantum evolution mechanisms in addressing geospatial optimization problems.