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Urban areas face a conundrum, they need to reduce their greenhouse gas emissions and consumption of resources, whilst also increasing their resilience to climate change and extreme weather, and improving wellbeing. However, it is widely recognized that well intended intervention to address one of these sustainability objectives in isolation can undermine other objectives. This paper presents a framework to efficiently identify spatial development strategies that provide the best outcomes against multiple objectives. The framework has been applied to London (UK) to identify strategies that can simultaneously: (i) minimize exposure to future heat wave events; (ii) minimize the risk from flood events; (iii) minimize transport emissions; (iv) minimize urban sprawl; (v) maximize brownfield development; and, (vi) prevent development of greenspace that is recognized as important to wellbeing. Prioritizing,each objective in isolation leads to considerably different spatial planning structures, exposing conflicts between many objectives. These include tradeoffs between urban heat risk and transport emissions; and also previously undocumented conflicts between minimizing flood and heat risks. Allowing greater flexibility in development density is shown to provide benefits in terms of heat risk reduction, whilst not significantly affecting mitigation objectives. The framework is shown to significantly improve upon the London Spatial Development Strategy for the objectives analyzed. Further analysis identifies optimal spatial strategies to achieve a Low Carbon, Low Risk or Low Density city - however, these cannot be simultaneously maximized. This work shows there are difficult, and often irreconcilable, choices to be made in the spatial planning of sustainable cities. Spatial search and optimization tools strengthen the evidence-base for planning. Rapid identification of development strategies that satisfy, and minimize conflicts between, multiple objectives helps planners to develop strategies that simultaneously improve urban sustainability and reduce the risks from natural hazards.