Urban morphology, examining city spatial configurations, links urban design to sustainability. Morphology metrics play a fundamental role in performance-driven computational urban design (CUD) which integrates urban form generation, performance evaluation and optimization. However, a critical gap remains between performance evaluation and complex urban form generation, caused by the disconnection between morphology metrics and urban form, particularly in metric-to-form workflows. It prevents the application of optimized metrics to generate improved urban form with enhanced urban performance. Formulating morphology metrics that not only effectively characterize complex urban forms but also enable the reconstruction of diverse forms is of significant importance. This paper highlights the importance of establishing a bi-directional mapping between morphology metrics and complex urban form to enable the integration of urban form generation with performance evaluation. We present an approach that can 1) formulate morphology metrics to both characterize urban forms and in reverse, retrieve diverse similar 3D urban forms, and 2) evaluate the effectiveness of morphology metrics in representing 3D urban form characteristics of blocks by comparison. We demonstrate the methodology with 3D urban models of New York City, covering 14,248 blocks. We use neural networks and information retrieval for morphology metric encoding, urban form clustering and morphology metric evaluation. We identified an effective set of morphology metrics for characterizing block-scale urban forms through comparison. The proposed methodology tightly couples complex urban forms with morphology metrics, hence it can enable a seamless and bidirectional relationship between urban form generation and optimization in performance-driven urban design towards sustainable urban design and planning.

We present a new algorithm A*+BFHS for solving hard problems where A* and IDA* fail due to memory limitations and/or the existence of many short cycles. A*+BFHS is based on A* and breadth-first heuristic search (BFHS). A*+BFHS combines advantages from both algorithms, namely A*'s node ordering, BFHS's memory savings, and both algorithms' duplicate detection. On easy problems, A*+BFHS behaves the same as A*. On hard problems, it is slower than A* but saves a large amount of memory. Compared to BFIDA*, A*+BFHS reduces the search time and/or memory requirement by several times on a variety of planning domains.