Evolutionary Computation

This research investigates the application of genetic algorithms to the conceptual design of spatial configurations. The approach integrates form generation and performance evaluation to design spatial configurations whose morphology emerges rather than being predetermined.

A Genetic Algorithm (GA) works by evolving sets of candidate solutions called populations. A “body plan” is first defined to characterize the relationships among the constituent components, i.e., the configuration topology. Each individual in a population is generated through a series of geometrical operations. The body-plan representation, i.e., the configuration geometry, depends on the numerical values of the design variables encoded in a compact set of information called the genome. For example, one way to define the body plan is through a series of closed planar curves at different elevations, which are used as profiles to generate a closed volumetric envelope. The coordinates of the control points defining each closed planar curve are the design variables encoded in the genotype as a string of binary numbers. The mapping from genotype to phenotype, defined by the set of rules used to build each candidate solution, is predetermined and non-evolvable. This means that, while different geometrical configurations are investigated by searching the solution space, the configuration topology remains unchanged. A new generation is produced by recombining the genomes of previously generated solutions through crossover and mutation. These solutions are selected based on their fitness. Candidate solutions with high fitness scores have a high probability of being selected to pass their genomes to the next generation.

Evolution requires an “environment” that puts pressure on the candidate solutions. The environment can be thought of as a set of design objectives used to evaluate each candidate solution and assign it a fitness score. A multi-objective optimization process has been formulated for the conceptual design of tall buildings. It involves maximizing daylight during winter, minimizing exposure to prevailing winds, maximizing the height of the volumetric centroid, and maximizing the volume-to-footprint ratio. Daylight and wind analyses use a low-resolution approach based on vector projections. This approach is appropriate for early-stage design and important for achieving convergence within a reasonable time because the solution space is very large. Following the cumulative sky-dome approach, a series of vectors representing energy radiated from the sky-dome patches is defined. The angle between these vectors and the vectors normal to the facade panels indicates the degree of exposure to solar radiation and can be used to evaluate daylight performance. A similar approach is adopted to compute the pressure caused by wind on the building facade. Depending on the angle between the prevailing wind directions and the facade-panel normals, a pressure coefficient is assigned to each panel (Eurocode 1 - Actions on Structures - Wind Actions). The lower the overall pressure caused by wind actions, the more aerodynamically efficient the building geometry. Other measures are implemented to consider feasibility. For example, the volume-to-facade-area ratio is maximized, and the facade-to-floor-area ratio is minimized, to limit the facade area, which is usually one of the most expensive parts of a building. A minimum radius of curvature is imposed on the facade surface to avoid discontinuities that could be problematic for the supporting structural system. Simplified equilibrium conditions are implemented by checking that the projection of the volumetric centroid falls within the contour of the first profile defining the building envelope at ground level.

The different objective values are normalized, weighted, and combined to form a single fitness score. The optimal combination of weights is estimated through a fractional factorial design (Taguchi design) to maximize the mean population fitness in each generation. This technique requires a set of simulations before the evolutionary process begins and therefore incurs a computational cost. However, it enables the quantification of parameters that contribute most significantly to increasing population fitness, as well as those that might negatively affect the direction of evolution. The termination criterion employed in this work is based on fitness stationarity, i.e., the process terminates when the mean population fitness shows no significant improvement after a specified number of generations. This process produces a set of feasible solutions that, over successive generations, become expressions of the design objectives. Depending on aesthetic criteria and other factors, one or more solutions may be selected for detailed design.