During the early design process, simulations allow numeric assessment and 3D models allow visual inspection for qualitative criteria. However, exploring different design alternatives based on both is challenging. To support the design exploration of quantitative performance and geometry typology of various design alternatives during the early design stages of indoor arenas, this paper proposed a novel design method of SOM-MLPNN by combing self-organizing map (SOM) and multi-layer perceptron neural network (MLPNN), based on the inspiration of local linear mapping based on self-organizing map (SOM-LLM). In SOM-LLM or SOM-MLPNN, the SOM can support designers to explore the whole design space according to geometry typologies and provides reference/labelled inputs for LLM/MLPNN to approximate multiple quantitative performance data for various design alternatives. Both SOM-LLM and SOM-MLPNN are applied and compared in a design of indoor arena. Besides the development of the method, original contributions include 1) proposing two operations (using a large size of SOM network and using a small amount of input data to train the SOM network) to save the computational time and increase the accuracy in data approximation and 2) proposing a series of data visualizations to interpret the results and support design explorations in different ways.

The benefits of applying multi-objective optimization (MOO) in building design have been increasingly recognized in recent decades. The existing or traditional computational design optimization (CDO) approaches mostly focus on optimization problem solving (OPS), as they often conduct optimizations directly by assuming the optimization problems in question are good enough. In contrast, the computational design exploration (CDE) approaches defined in this research mainly focus on optimization problem formulation (OPF), which are considered more essential and aim to achieve or ensure appropriate optimization problems before conducting optimizations. However, the application of the CDE is very limited especially in conceptual architectural design. The necessity of re-formulating original optimization problems and its potential impacts on optimization results are often overlooked or not emphasized enough. This paper proposes a new CDE approach that highlights the knowledge-supported re-formulation of a changeable initial optimization problem. It improves upon the traditional CDO approach by introducing a changeable initial OPF and inserting a CDE module. The changeable initial OPF allows expanding the dimensionality of an objective space and design space being investigated, and the CDE module can re-formulate the changeable optimization problem using the information and knowledge extracted from statistical analyses. To facilitate designers in achieving the proposed approach, an improved computational platform is used which combines parametric modeling software (including simulation plug-ins) and design optimization software. Assisted by the platform, the proposed approach is applied to the conceptual design of an indoor sports building that considers multi-disciplinary performance criteria (including architecture-, climate- and structure-related criteria) and a wide range of geometric variations. Through the case study, this paper demonstrates the use of the proposed approach, verifies its benefits over the traditional method, and unveils the factors that may affect the behaviour of the proposed approach. Besides, it also shows the suitability of the computational platform used.