Optimally directed shape generation by shape annealing

A Grammar-Based Optimization Approach for Designing Urban Fabrics and Locating Amenities for 15-Minute Cities

Providing pedestrian accessibility to urban services is a big challenge and a key factor in creating more walkable urban areas. Moreover, it is a critical aspect of climate-resilient urban planning as it is broadly assumed that neighborhoods with greater walkability discourage automobile use and reduce CO2 emissions. The idea of 15-minute cities, defined as urban environments where most places that residents need to access are within a 15-minute walk, is gaining increasing attention worldwide. Because aspects of urban performance are increasingly quantifiable, generative, and data-driven design approaches can explore broader sets of potential solutions, while optimization can help identify designs with desired properties. This work demonstrates and tests a new approach that combines shape grammars, a formal method for shape generation that facilitates the elaboration of complex patterns and meaningful solutions, with multi-objective optimization. The goal was to optimize the design of urban fabric layouts and the location of amenities to provide 15-minute neighborhood configurations that minimize infrastructure cost (as estimated by cumulative street length) and the number of amenities, while maximizing pedestrian accessibility to urban services (as assessed by overall integration and the average distance from all plots to nearest amenities).

The MINLP Approach to Topology, Shape and Discrete Sizing Optimization of Trusses

The paper presents the Mixed-Integer Non-linear Programming (MINLP) approach to the synthesis of trusses. The solution of continuous/discrete non-convex and non-linear optimization problems is discussed with respect to the simultaneous topology, shape and discrete sizing optimization of trusses. A truss MINLP superstructure of different topology and design alternatives has been generated, and a special MINLP model formulation for trusses has been developed. In the optimization model, a mass objective function of the structure has been defined and subjected to design, load and dimensioning constraints. The MINLP problems are solved using the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm. Multi-level MINLP strategies are introduced to accelerate the convergence of the algorithm. The Modified Two-Phase and the Sequential Two-Phase MINLP strategies are proposed in order to solve highly combinatorial topology, shape and discrete sizing optimization problems. The importance of local buckling constraints on topology optimization is also discussed. Some simple numerical examples are shown at the end of the paper to demonstrate the suitability and efficiency of the proposed method.

Computing with Emergence

The concept of emergence has its roots in 19th-century philosophy. Today it is central to many computational systems which retain the hallmarks of emergence laid out much earlier. The role of emergence in creative design and its unique embodiment in shape grammars have been emphasized by March, Stiny, and others. Shape grammars generate emergent shapes—shapes not predefined in a grammar. Emergent shapes are not only the output of a shape grammar computation; they can be the input for further computation. The history of emergence and its characterization in shape grammars are discussed here. Different sorts of shape emergence in grammars are then distinguished: anticipated, possible, and unanticipated. Unanticipated emergent shapes are shapes not premeditated by the author or user of a grammar. Generally, unanticipated shapes require on-the-spot definitions of rules to compute with them. However, for some interesting design problems, it is possible to know in advance what to do with unanticipated shapes, and to predefine rules accordingly. Special rules for computing with unanticipated shapes are proposed here. These rules allow for processes that have previously been handled extragrammatically—outside of grammars—to be handled within grammars. Examples of applications of these rules within a single grammar and across parallel grammars are given.