Abstract Indicator-based (multi-objective) diversity optimization aims at finding a set of near (Pareto)optimal solutions that maximizes a diversity indicator, where diversity is typically interpreted as the number of essentially different solutions. Whereas, in the first diversity-oriented evolutionary multi-objective optimization algorithm, the NOAH algorithm by Ulrich and Thiele, the Solow Polasky Diversity (SP Diversity, also known as Magnitude [1]) served as a metric, other diversity indicators could be considered. We examine the parameter-free Max-Min Diversity and the Riesz $$s$$ s -Energy, which features uniformly distributed solution sets. Focusing on multi-objective diversity optimization, we discuss different diversity indicators from the perspective of indicator-based evolutionary algorithms with multiple objectives. We examine theoretical, computational, and practical properties of these indicators, such as monotonicity in species, twinning, monotonicity in distance, strict monotonicity in distance, uniformity of maximizing point sets, computational effort for a set of size $$n$$ n , single-point contributions, subset selection, and submodularity. We present new theorems—including a proof of the NP-hardness of the Riesz $$s$$ s -Energy Subset Selection Problem—and consolidate existing results from the literature. In the experiments, we apply these indicators in the NOAH algorithm to analyze search dynamics via an example. We study how optimizing one indicator impacts others and propose NOAH-specific modifications for the Max-Min indicator.

Design ideation requires both creative and divergent thinking as well as collaboration and exchange to bring forth new insights and design possibilities. In this paper, we investigate such a collaboration with the use of emerging generative AI tools, and we explore how they may help in achieving agreement and semantic convergence between designers. We conducted workshops using Text-to-Image AI with design students and found that in addition to known advantages of brainstorming, the text prompts required by the AI system engaged students in verbal articulations that aided their design process. In collaborative contexts, the generated images shifted the centre of attention for team members to reach convergence through sharing their interpretations. We conclude that text-to-image AI can be beneficial for students’ design processes as a catalyst for brainstorming rather than a tool for generating design imagery and presentations.

Abstract A building spatial design (BSD) determines external and internal walls and ceilings of a building. The design space has a hierarchical structure, in which decisions on the existence or non-existence of spatial components determine the existence of variables related to these spaces, such as sizing and angles. In the optimization of BSDs it is envisioned to optimize various performance indicators from multiple disciplines in concert, such as structural, functional, thermal, and daylight performance. Existing representations of design spaces suffer from severe limitations, such as only representing orthogonal designs or representing the structures in parametric superstructure, allowing only for limited design variations. This paper proposes prism nets - a new way of representing the search space of BSDs based on triangulations defining space filling collections of triangular prisms that can be combined via coloring parameters to spaces. Prism nets can accommodate for non-orthogonal designs and are flexible in terms of topological variations. We follow the guidelines for representation and operator design proposed in the framework of metric-based evolutionary algorithms. The main contribution of the paper is a detailed discussion of the search space representation and corresponding mutation operators. Moreover, a proof of concept example demonstrates the integration into multi-objective evolutionary algorithms and provides first results on a simple, but reproducible, benchmark problem.

A new three-dimensional spatial zoning procedure that has been tailored to structural design is presented in this work. Zoning is the grouping of spaces or sub-parts of spaces such that the resulting spatial layout is logical from a disciplinary perspective. Two automated structural design methods, so-called grammars, have been defined to generate structural designs for zoned building spatial designs. The first grammar, here termed stable design grammar, places structural slabs at the boundaries of a zone, and columns at places where a zone intersects with a space. The second grammar, here termed unstable grammar, generates a structural frame that is unstable by definition. Via a new stabilization method, which is also presented in this work, the unstable structural frame is stabilized by considering the boundaries of a zone for the placement of stabilizing measures. In a case study, the zoning procedure is applied in conjunction with each of the design grammars to three distinct building spatial designs. The case study shows—for both design grammars—that structural designs use less material and are stiffer when they are generated based on a zoned building spatial design. Moreover, the zoning procedure has been tailored such that it yields a subset of all possible zoned designs for which, in general, the generated structural designs perform well.

In this paper solution approaches for solving the building spatial design optimisation problem for structural and energy performance are advanced on multiple fronts. A new initialisation operator is introduced to generate an unbiased initial population for a tailored version of SMS-EMOA with problem specific operators. Improvements to the mutation operator are proposed to eliminate bias and allow mutations consisting of multiple steps. Moreover, landscape analysis is applied in order to explore the landscape of both objectives and investigate the behaviour of the mutation operator. Parameter tuning is applied with the irace package and the Mixed Integer Evolution Strategy to find improved parameter settings and explore tuning with a relatively small number of expensive evaluations. Finally, the performances of the standard and tailored SMS-EMOA algorithms with tuned parameters are compared.