One purpose of cognitive diagnostic model (CDM) is designed to make inferences about unobserved latent classes based on observed item responses. A heuristic for test construction based on the CDM information index (CDI) proposed by Henson and Douglas (2005) has a far-reaching impact, but there are still many shortcomings. He and other researchers had also proposed new methods to improve or overcome the inherent shortcomings of the CDI test assembly method. In this study, one test assembly method of maximizing the minimum inter-class distance is proposed by using mixed-integer linear programming, which aims to overcome the shortcomings that the CDI method is limited to summarize the discriminating power of each item into a single CDI index while neglecting the discriminating power for each pair of latent classes. The simulation results show that compared with the CDI test assembly and random test assembly, the new test assembly method performs well and has the highest accuracy rate in terms of pattern and attributes correct classification rates. Although the accuracy rate of the new method is not very high under item constraints, it is still higher than the CDI test assembly with the same constraints.

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The implementation of cognitive diagnostic computerized adaptive testing often depends on a high-quality item bank. How to online estimate the item parameters and calibrate the Q-matrix required by items becomes an important problem in the construction of the high-quality item bank for personalized adaptive learning. The related previous research mainly focused on the calibration method with the random design in which the new items were randomly assigned to examinees. Although the way of randomly assigning new items can ensure the randomness of data sampling, some examinees cannot provide enough information about item parameter estimation or Q-matrix calibration for the new items. In order to increase design efficiency, we investigated three adaptive designs under different practical situations: (a) because the non-parametric classification method needs calibrated item attribute vectors, but not item parameters, the first study focused on an optimal design for the calibration of the Q-matrix of the new items based on Shannon entropy; (b) if the Q-matrix of the new items was specified by subject experts, an optimal design was designed for the estimation of item parameters based on Fisher information; and (c) if the Q-matrix and item parameters are unknown for the new items, we developed a hybrid optimal design for simultaneously estimating them. The simulation results showed that, the adaptive designs are better than the random design with a limited number of examinees in terms of the correct recovery rate of attribute vectors and the precision of item parameters.