A probabilistic framework with the gradient-based method for multi-objective land use optimization

Land use planning seeks to outline the future location and type of development activity. The planning process should reconcile development with environmental conservation and other concerns pertaining to sustainability; hence multi-objective spatial optimization is considered an effective tool to serve this purpose. However, as the number of social, economic, and environmental objectives increases, especially when numerous spatial units exist, the curse of dimensionality becomes a serious problem, making previous methods unsuitable. In this paper, we formulate a probabilistic framework based on the gradient descent algorithm (GDA) to search for Pareto optimal solutions more effectively and efficiently. Under this framework, land use as decision parameter(s) in each cell is represented as a probability vector instead of an integer value. Thus, the objectives can be designed as differentiable functions such that the GDA can be used for multi-objective optimization. An initial experiment is conducted using simulation data to compare the GDA with the genetic algorithm, with the results showing that the GDA outperforms the genetic algorithm, especially for large-scale problems. Furthermore, the outcomes in a real-world case study of Shenzhen demonstrate that the proposed framework is capable of generating effective optimal scenarios more efficiently, rendering it a pragmatic tool for planning practices.