网络Voronoi图启发的粒子群空间优化建模

Network Voronoi Diagram Heuristic-based Particle Swarm Continuous Spatial Optimization Modeling

城市化区域多设施空间优化建模是一项实用的关键技术,可为城市公共资源均衡优化配置和空间决策提供支持。本文提出了网络Voronoi图启发的多设施选址粒子群空间优化建模方法,分别给出了基于常规Voronoi图启发的p-中值选址模型和最大覆盖选址模型,以及基于网络Voronoi面启发的p-中值选址模型和最大覆盖选址模型。模型采用Voronoi图定量提取设施功能覆盖和服务范围内的需求,并通过最小化重叠覆盖启发空间优化最大化覆盖分布的需求。p-中值选址模型考虑了需求随路径距离衰减的因素,最大覆盖选址模型顾及了设施对最大覆盖半径范围以内需求的完全覆盖,以及对以外区域的部分衰减覆盖。在空间优化粒子群算法中融入遗传进化机制和常规Voronoi图模拟的粒子动态邻域结构,提高了算法的全局搜索和优化性能。通过对实验区多设施进行的p-中值选址空间优化实验和最大覆盖选址空间优化实验,验证了本文提出的模型、方法和算法的有效性,可应用于城市化区域的空间优化决策支持。

Abstract： Spatial optimization modeling for multi facilities in urbanized area is a practical and key technique, and it can provide balance configuration optimization and spatial decision support for urban public resource. A method of particle swarm spatial optimization modeling for multi facilities location based on network Voronoi di- agram heuristic is proposed in this paper, in which we presented respectively some p-median location models and maximal covering location models by using ordinary Voronoi diagram heuristic and network Voronoi dia- gram heuristic. Those models can quantitatively extract the demands coved by the function and service of facili- ties through the Voronoi diagrams, and inspire spatial optimization to maximize the coverage for distributed de- mands by minimizing overlapped coverage. The proposed p-median location model considers the factor of de- mand attenuation with path distance, and the proposed maximal covering model takes it into account that facili- ty＇ s service provides full coverage for the demands within maximal coverage radius and partial attenuation coy-erage for the demands without maximal coverage radius. The genetic evolution mechanism and the dynamic neighborhood structure of particles simulated by ordinary Voronoi diagram are integrated in the particle swarm spatial optimization to improve global search and optimization performance of the algorithm. Through the re- search of spatial optimization configuration experiments for multi facilities in experimental city, the proposed method has been verified to be the effective and practical, it can be applied for the spatial location optimization decision in urbanized area.