Multi-objective automatic optimization design of low-carbon courtyard landscape based on NSGA-II algorithm: a case study of the Guangdong-Hong Kong-Macao greater bay area

Under the “dual carbon” strategy, achieving synergistic optimization of carbon sequestration, aesthetics, and economic costs in limited courtyard spaces has become a critical challenge in landscape architecture. This study selected three courtyards of different scales (280 m², 420 m², 650 m²) in the Guangdong-Hong Kong-Macao Greater Bay Area and constructed a low-carbon optimization framework based on the NSGA-II multi-objective evolutionary algorithm. The framework optimizes three objectives: maximization of annual net carbon sequestration, maximization of landscape aesthetic score, and minimization of life-cycle cost. A hybrid chromosome encoding strategy was designed to characterize discrete-continuous decision variables for plant species selection and spatial layout. Pareto front convergence and diversity were maintained through non-dominated sorting and crowding distance. The algorithm converged stably within 300 generations, with the coefficient of variation of the hypervolume indicator across 30 independent experiments being only 1.99%, validating the reliability of the optimization framework. The Pareto solution set revealed positive trade-off relationships between carbon sequestration and cost (r = 0.847) and between aesthetics and cost (r = 0.623), while a weak positive correlation was found between carbon sequestration and aesthetics (r = 0.385), indicating their potential for synergistic optimization. Compared with the original experience-based design, the comprehensively balanced optimization scheme achieved a 50.3% increase in carbon sequestration, a 16.5% increase in aesthetic score, with only a 13.8% increase in cost. Additionally, the carbon sequestration intensity per unit area of small courtyards was higher than that of large courtyards, preliminarily suggesting the potential of decentralized greening strategies in high-density urban areas. This study provides a quantifiable decision-support method for low-carbon courtyard design, contributing theoretical and practical value for the green transformation of human settlements. It should be noted, however, that this scale-related observation is subject to the confounding influence of cross-case variation in existing green space ratios (48.2%, 53.6%, 45.8%), and therefore should be interpreted as a tentative finding requiring further validation. Under the “dual carbon” strategy, achieving synergistic optimization of carbon sequestration, aesthetics, and economic costs in limited courtyard spaces has become a critical challenge in landscape architecture. This study selected three courtyards o... [2101 chars]