  Discrete Choice Experiments (DCEs) investigate the attributes that influence
individuals' choices when selecting among various options. To enhance the
quality of the estimated choice models, researchers opt for Bayesian optimal
designs that utilize existing information about the attributes' preferences.
Given the nonlinear nature of choice models, the construction of an appropriate
design requires efficient algorithms. Among these, the Coordinate-Exchange (CE)
algorithm is most commonly employed for constructing designs based on the
multinomial logit model. Since this is a hill-climbing algorithm, obtaining
better designs necessitates multiple random starting designs. This approach
increases the algorithm's run-time, but may not lead to a significant
improvement in results. We propose the use of a Simulated Annealing (SA)
algorithm to construct Bayesian D-optimal designs. This algorithm accepts both
superior and inferior solutions, avoiding premature convergence and allowing a
more thorough exploration of potential designs. Consequently, it ultimately
obtains higher-quality choice designs within the same time-frame. Our work
represents the first application of an SA algorithm in constructing Bayesian
optimal designs for DCEs. Through computational experiments and a real-life
case study, we demonstrate that the SA designs consistently outperform the CE
designs in terms of Bayesian D-efficiency, especially when the prior preference
information is highly uncertain.
