Multi-stage optimization framework for synergetic grey-green infrastructure in response to long-term climate variability based on shared socio-economic pathways

Global climate change and rapid urbanization have increasingly intensified extreme rainfall events and surface runoff, posing significant challenges to urban hydrological security. Synergetic Grey-Green Infrastructure (SGGI) has been widely applied to enhance stormwater management in urban areas. However, current research primarily focused on optimizing and evaluating either grey infrastructure (GREI) or green infrastructure (GI) under single rainfall event, neglecting the non-stationary impacts of long-term climate change on infrastructure performance. Therefore, this study introduced a multi-stage optimization framework for SGGI layouts based on shared socio-economic pathways, utilizing graph theory and genetic algorithms to identify optimal solutions through life cycle cost (LCC) and hydraulic reliability in response to varying climate change scenarios. A case study of Shenzhen, China, was conducted to validate this method. The results indicated that: (1) SSP2-4.5 and SSP5-8.5 scenarios revealed significant phase-specific variations in Shenzhen's annual precipitation series; (2) The optimized SGGI layouts yielded substantial LCC savings compared to GREI, with centralized and decentralized strategies achieving reductions of 6.6% and 4.7%, respectively. (3) The SGGI adapted to extreme rainfall conditions by shifting preference from permeable pavements to bioretention cells; (4) The Change-GREI&GI (CGG) strategy consistently outperformed the Change-only-GI (COG) strategy in LCC control and hydraulic reliability, particularly a 1.68% cost advantage under extreme scenarios. These findings highlight the critical role of multi-stage optimization in improving the cost-effectiveness and resilience of integrated grey-green infrastructure systems, providing valuable insights for designing adaptive SGGI strategies that effectively respond to long-term climate variability in urban environments.