MCLP_quantum_annealer_V0.5

Geospatial optimization problems are fundamental research issues in geographic information science modeling, characterized by high dimensionality, dynamics, and discreteness. These problems often involve inequality-constrained discrete optimization, such as the maximum coverage location problem. Currently, classical high-performance and parallel spatial computing architectures are commonly employed to solve geospatial optimization problems. Under Noisy Intermediate-Scale Quantum (NISQ) conditions, quantum computing has demonstrated computational advantages, such as quantum parallelism, quantum tunneling, and quantum entanglement. The application of quantum computing to solve the maximum coverage location problem presents numerous challenges in areas like problem transformation, quantum sampling solutions, and spatial relationship verification. This paper first proposes the QUBO-MCLP algorithm workflow and designs the Transformation Operator for Inequality Constraints Considering the Capacity of Accessible Providers (TOICCAP), which accounts for the scale of accessible supply points. The paper then addresses the challenge that the scale of slack variables increases significantly as the number of service facilities increases during the TOICCAP transformation process. To mitigate this, an improved Logarithm Transformation Operator for Inequality Constraints Considering the Capacity of Accessible Providers (LTOICCAP) is introduced. Finally, for spatial relationship verification, a Spatial Coverage Consistency Checking Operator for MCLP Results (SCCCOMR) is designed. Theoretical and applied experiments are conducted using four solvers: QBSolv, D-Wave Hybrid binary quadratic model 2, D-Wave Advantage system 4.1, and Gurobi. These experiments involve location optimization calculations and result analysis on the TGD and SJC datasets. The results demonstrate the effectiveness of the QUBO-MCLP algorithm workflow, with TOICCAP successfully converting slack variables in inequality-constrained functions for p>2, and LTOICCAP effectively reducing the number of linear and quadratic variables. This paper presents a quantum computing path for Transformation-to-Sampling-to-Verification of geospatial optimization problems, adaptable to the controlled qubit scale and coherence constraints under current NISQ conditions. This approach is applicable to urban service facility planning, Internet of Things (IoT) and communication facility spatial deployment, smart city governance, and resource allocation.