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

Abstract

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.

Keywords:

• Spatial optimization
• gradient-based optimizer
• planning support system
• land use planning
• multi-objective optimization

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data and codes availability statement

The data and codes that support the findings of this study are available with the identifier(s) at the private link: https://doi.org/10.6084/m9.figshare.21220019

Additional information

Funding

This work was supported by the Hong Kong Research Grants Council [CRF C4139-20G and AoE/E-603/18] and the National Key R&D Program of China [2019YFC1510400].

Notes on contributors

Haowen Luo

Haowen Luo is currently pursuing his Ph.D. degree in the Department of Geography and Resource Management, The Chinese University of Hong Kong. His recent research is focused on spatial optimization for urban planning. His main contributions to the paper include model designing and algorithm implementation, conducting case studies and experiments, writing, and revising this paper.

Bo Huang

Bo Huang is currently Wei Lun Professor of Geography and Resource Management at The Chinese University of Hong Kong, where he is also the Co-director of Computational Social Science Laboratory, Faculty of Social Science and Associate Director of Institute of Space and Earth Information Science. His research interests include spatial-temporal statistics, unified satellite image fusion and multi-objective spatial optimization, and their applications in environmental monitoring, urban growth assessment and sustainable land use and transportation planning. He contributed to the conceptualization, writing, and revision of this paper.