Title: Dealing with uncertainty in automated test assembly problems
Authors: Giada Spaccapanico Proietti - University of Bologna (Italy) [presenting]
Stefania Mignani - University of Bologna (Italy)
Mariagiulia Matteucci - University of Bologna (Italy)
Abstract: Automated test assembly (ATA) models are intended to build standardized parallel test forms starting from an item bank. A general framework for ATA consists in adopting linear models which are solved by commercial solvers. Those solvers are not always able to find solutions for highly constrained and large-sized ATA instances. Moreover, all parameters are assumed to be fixed and known, a hypothesis that is not true for estimates of item response theory parameters. These restrictions motivated us to find an alternative way to define and solve ATA models. First, we suggest a chance-constrained approach, which allows maximizing the $\alpha$-quantile of the empirical distribution function of the test information function obtained by bootstrapping the calibration process. Secondly, we adapt a stochastic meta-heuristic called simulated annealing for solving the ATA models. This technique can handle large-scale models and non-linear functions of which the chance constraints are an example and avoids local optima. A Lagrangian relaxation helps to find the most feasible/optimal solution. Several simulations are performed and the solutions are compared to the results of CPLEX 12.8.0 Optimizer. The algorithms are coded in the open-source programming language Julia.