Batch sequential designs in Bayesian preference elicitation with application to tradespace exploration for vehicle concept design

Engineering design is a complex decision making process that depends on multiple design objectives and often requires frequent information exchange between designers and decision makers (DM), such as product managers or users. A common method to facilitate this information exchange and explore the tradespace of different design objectives is through <i>preference elicitation</i>, where DMs are asked to answer a sequence of queries to inquire preference comparisons between multiple design alternatives. In this work, we generalize the <i>ellipsoid method</i> proposed by Sauré and Vielma (2019) to the <i>batch sequential</i> setting, where multiple queries are selected at a time to be provided to the DM when some operational constraints make a fully sequential questionnaire impractical. In our setting, we use <i>D-error</i> as our selection criterion, the minimization of which leads to more precise estimates of the DM’s utility model parameters. We propose approximations of this criterion using linear surrogate models where the predictors are functions of certain summary statistics of the batch design whose effect can be estimated <i>via</i> offline experiments. Based on these approximations, we propose mixed integer programming formulations for constructing batch designs which can be solved in commercial optimization solvers. Our simulation studies show that the proposed methods provide highly D-efficient batch designs when compared to randomly generated designs. In addition, we show that our methods are comparable to a fully adaptive method when the batch size is small. Lastly, we present an example of using our methodology to aid in tradespace exploration for vehicle concept design.