Optimal designs for mixture choice experiments by simulated annealing

Mixture choice experiments investigate people’s preferences for products composed of different ingredients. To ensure the quality of the experimental design, many researchers use Bayesian optimal design methods. Efficient search algorithms are essential for obtaining such designs. Yet, research in the field of mixture choice experiments is not extensive. Our paper pioneers the use of a simulated annealing (SA) algorithm to construct Bayesian optimal designs for mixture choice experiments. Our SA algorithm not only accepts better solutions, but also has a certain probability of accepting inferior solutions. This approach effectively prevents rapid convergence, enabling broader exploration of the solution space. Although our SA algorithm may start more slowly than the widely used mixture coordinate-exchange method, it generally produces higher-quality mixture choice designs after a reasonable runtime. We demonstrate the superior performance of our SA algorithm through extensive computational experiments and a real-life example.