Bayesian preference elicitation is a statistical framework which can aid in complex decision making processes such as engineering design by offering preference-informed recommendations to a decision maker (DM). In this framework, a DM is asked to answer a sequence of queries, called a questionnaire, where in each query they must select their preferred option among two alternatives. A common method to construct the questionnaire is through the D-optimality criterion, which seeks to select queries which lead to more precise estimates of utility model parameters. Past works have proposed and investigated adaptive methods for questionnaire construction using D-optimality as the query selection criterion. All of these adaptive methods have been based on greedy strategies to the best of our knowledge. In this work, we propose and compare various non-greedy methods for adaptive questionnaire construction in the preference elicitation setting. Our methods utilize a combination of enumeration and mixed integer programming techniques to select queries to present to the DM. Through our simulation studies, we find only a marginal improvement in D-efficiency through the use of non-greedy methods, suggesting that greedy methods are sufficient for this problem.
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