Automated Parallel Test Forms Assembly using Zero-suppressed Binary Decision Diagrams

Recently, through the progress achieved in the study of computer science, automated test assemblies of parallel test forms, for which each form has equivalent measurement accuracy but with a different set of items, have emerged as a new standard tool. An important goal for automated test assembly is to assemble as many parallel test forms as possible. Although many automated test assembly methods exist, maximum clique using the integer programming method is known to be able to assemble the greatest number of assembled test forms with the highest measurement accuracy. Nevertheless, because of the high time complexity of integer programming, the method requires a month or more to assemble 300,000 tests. This study proposes a new automated test assembly using Zero-suppressed Binary Decision Diagrams (ZDD): a graphical representation for a set of item combinations. This representation is derived by reducing a binary decision tree. According to the proposed method, each node in the binary decision tree corresponds to an item of an item pool, which is a test item database. Each node has two edges, each signifying that the corresponding item is included in a test form or not. Furthermore, all equivalent nodes are shared, providing that they have equal measurement accuracy and equal test length. Numerical experiments demonstrate that the proposed method can assemble 1,500,000 test forms within 24 hr, although earlier methods have been capable of assembling only 300,000 test forms within 10 days.