基于动态博弈与空间拓扑优化的老城更新智能决策模型及系统实现

Intelligent Decision-Making Model and System Implementation for Old City Renewal Based on Dynamic Game and Spatial Topology Optimization

摘要: 本研究针对老城街区改造中的搬迁补偿机制设计与空间资源配置优化关键问题，结合空间拓扑网络理论、行为经济学原理及动态规划方法，开展系统性理论建模与算法创新，构建多维耦合决策模型体系，有效解决了搬迁补偿方案设计、整院面积最大化利用、性价比增益拐点计算及智能决策软件框架构建等相关问题。研究构建融合物理空间属性与居民心理预期的双维度补偿决策模型，案例应用中搬迁成功率达95.58%，同时将修缮补偿案例比例控制在39.81%；通过Delaunay三角剖分算法构建空间拓扑网络优化空间重组，成功腾空34个完整院落(腾空比例94.4%)，优化面积12,890平方米，十年期净收益12297.47万元、投资回报率达538%；借助随机微分方程与动态规划结合的模型，识别出搬迁率79.3%时的性价增益拐点，此时可腾空28个完整院落并获得最高35%租金溢价；同时开发基于数字孪生技术、采用五层体系架构的智能决策支持系统，集成多目标优化求解引擎与LSTM-GAN预测模型，可为老城街区平移置换决策提供高效精准的自动化技术支持。

Abstract: This research focuses on the key issues of the relocation compensation mechanism design and spatial resource allocation optimization in the renovation of old urban blocks. By integrating the spatial topological network theory, behavioral economics principles, and dynamic programming methods, it conducts systematic theoretical modeling and algorithm innovation, establishing a multi-dimensional coupled decision-making model system. This effectively addresses related problems such as the design of relocation compensation plans, maximizing the utilization of the entire courtyard area, calculating the cost-benefit gain inflection point, and constructing the framework of an intelligent decision-making software. The research constructs a dual-dimensional compensation decision-making model that integrates physical space attributes and residents’ psychological expectations. In the case application, the relocation success rate reached 95.58%, while the proportion of renovation compensation cases was controlled at 39.81%. Through the Delaunay triangulation algorithm, a spatial topological network was constructed to optimize spatial reorganization, successfully vacating 34 complete courtyards (vacation rate 94.4%), optimizing an area of 12,890 square meters, achieving a net income of 122.9747 million yuan over a ten-year period, and an investment return rate of 538%. By using a model that combines stochastic differential equations and dynamic programming, the cost-benefit gain inflection point at a relocation rate of 79.3% was identified. At this point, 28 complete courtyards could be vacated and a maximum rental premium of 35% could be obtained. Additionally, an intelligent decision support system based on digital twin technology and adopting a five-layer architecture was developed, integrating a multi-objective optimization solver and an LSTM-GAN prediction model, which can provide efficient and precise automated technical support for the decision-making of old urban block relocation and replacement.