The need to explore and/or optimize expensive simulators with many qualitative factors arises in broad scientific and engineering problems. Our motivating application lies in path planning - the exploration of feasible paths for navigation, which plays an important role in robotics, surgical planning and assembly planning. Here, the feasibility of a path is evaluated via expensive virtual experiments, and its parameter space is typically discrete and high-dimensional. A carefully selected experimental design is thus essential for timely decision-making. We propose here a novel framework, called QuIP, for experimental design of Qualitative factors via Integer Programming under a Gaussian process surrogate model with an exchangeable covariance function. For initial design, we show that its asymptotic D-optimal design can be formulated as a variant of the well-known assignment problem in operations research, which can be efficiently solved to global optimality using state-of-the-art integer programming solvers. For sequential design (specifically, for active learning or black-box optimization), we show that its design criterion can similarly be formulated as an assignment problem, thus enabling efficient and reliable optimization with existing solvers. We then demonstrate the effectiveness of QuIP over existing methods in a suite of path planning experiments and an application to rover trajectory optimization.

The surge in data availability has inundated decision-makers with an overwhelming array of choices. While existing approaches focus on optimizing decisions based on quantifiable metrics, practical decision-making often requires balancing measurable quantitative criteria with unmeasurable qualitative factors embedded in the broader context. In such cases, algorithms can generate high-quality recommendations, but the final decision rests with the human, who must weigh both dimensions. We define the process of selecting the optimal set of algorithmic recommendations in this context as human-centered decision making. To address this challenge, we introduce a novel framework called generative curation, which optimizes the true desirability of decision options by integrating both quantitative and qualitative aspects. Our framework uses a Gaussian process to model unknown qualitative factors and derives a diversity metric that balances quantitative optimality with qualitative diversity. This trade-off enables the generation of a manageable subset of diverse, near-optimal actions that are robust to unknown qualitative preferences. To operationalize this framework, we propose two implementation approaches: a generative neural network architecture that produces a distribution $\pi$ to efficiently sample a diverse set of near-optimal actions, and a sequential optimization method to iteratively generates solutions that can be easily incorporated into complex optimization formulations. We validate our approach with extensive datasets, demonstrating its effectiveness in enhancing decision-making processes across a range of complex environments, with significant implications for policy and management.

Arvind Gopalakrishnan is a part of the AIM Writers Programme.… Data mining is taking turns in the industry like anything, but have you ever heard of Opinion Mining? Leveraging customer opinion as quantifiable data is a concept of future to a layman but with Natural Language Processing, the world can finally process and completely absorb customer feedback. Often data is associated with quantity-based statistics with numbers and metrics floating around, however, with natural language processing (NLP), qualitative factors like customer feedback can be processed and used as quantifiable data. For example, if a specific mobile phone models witness a higher number of sales in a given year, the manufacturers tend to incorporate features of that mobile phone to increase the sales of other models where they somehow miss to make upgrades properly basis the customer feedback.

Although Bayesian Optimization (BO) has been employed for accelerating materials design in computational materials engineering, existing works are restricted to problems with quantitative variables. However, real designs of materials systems involve both qualitative and quantitative design variables representing material compositions, microstructure morphology, and processing conditions. For mixed-variable problems, existing Bayesian Optimization (BO) approaches represent qualitative factors by dummy variables first and then fit a standard Gaussian process (GP) model with numerical variables as the surrogate model. This approach is restrictive theoretically and fails to capture complex correlations between qualitative levels. We present in this paper the integration of a novel latent-variable (LV) approach for mixed-variable GP modeling with the BO framework for materials design. LVGP is a fundamentally different approach that maps qualitative design variables to underlying numerical LV in GP, which has strong physical justification. It provides flexible parameterization and representation of qualitative factors and shows superior modeling accuracy compared to the existing methods. We demonstrate our approach through testing with numerical examples and materials design examples. It is found that in all test examples the mapped LVs provide intuitive visualization and substantial insight into the nature and effects of the qualitative factors. Though materials designs are used as examples, the method presented is generic and can be utilized for other mixed variable design optimization problems that involve expensive physics-based simulations.

Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and relate them via a multiresponse cross-covariance matrix. We introduce a substantially different approach that maps each qualitative factor to an underlying numerical latent variable (LV), with the mapped value for each level estimated similarly to the covariance lengthscale parameters. This provides a parsimonious GP parameterization that treats qualitative factors the same as numerical variables and views them as effecting the response via similar physical mechanisms. This has strong physical justification, as the effects of a qualitative factor in any physics-based simulation model must always be due to some underlying numerical variables. Even when the underlying variables are many, sufficient dimension reduction arguments imply that their effects can be represented by a low-dimensional LV. This conjecture is supported by the superior predictive performance observed across a variety of examples. Moreover, the mapped LVs provide substantial insight into the nature and effects of the qualitative factors.