Hybrid Maximum Clique Algorithm Using Parallel Integer Programming for Uniform Test Assembly

Fuchimoto, Kazuma; Ishii, Takatoshi; Ueno, Maomi

doi:10.1109/tlt.2022.3163360

Cited by 5 publications

(8 citation statements)

References 37 publications

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“…Hybrid Maximum Clique Algorithm Using Parallel Integer Programming method (HMCAPIP) [5] is known to assemble the greatest number of tests with the highest measurement accuracy.…”

Section: B Hybrid Maximum Clique Algorithm Using Parallel Integer Pro...mentioning

confidence: 99%

“…To overcome this difficulty, Fuchimoto et al [5] proposed a two-step parallel algorithm. The first step of their method assembles parallel test forms with an overlapping constraint as a maximum clique problem [3], [16] that has low time complexity but high space complexity.…”

Section: B Hybrid Maximum Clique Algorithm Using Parallel Integer Pro...mentioning

confidence: 99%

“…With the rapid development of computer science technologies, automated test assemblies [1]- [5] of parallel test forms, for which each form has equivalent measurement accuracy but with a different set of items, have been put to practical use. For instance, parallel test forms are necessary when a testing organization administers tests at different times.…”

mentioning

confidence: 99%

“…Automated test assemblies have resolved difficulties such as high computational costs [1], [2], maximization of the number of tests [3], [5], minimization of item exposure bias [4], and so on. Most recently, automated test assembly has been applied for computerized adaptive testing (such as [6], [7]), which selects and presents the optimal item for individual examiners.…”

mentioning

confidence: 99%

“…To reduce the high space complexity of the maximum clique method, Fuchimoto et al [5] proposed the Hybrid Maximum Clique Algorithm with Parallel Integer Programming (HMCAPIP), which is known to assemble the greatest number of assembled test forms with the highest measurement accuracy. As the first step, test forms are assembled with the overlapping constraint as a maximum clique problem with low time complexity, but with high space complexity.…”

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confidence: 99%

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

Fuchimoto,

Minato,

Ueno

2023

IEEE Access

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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 during a week or more.INDEX TERMS automated test assembly, item response theory, parallel test, zero-suppressed binary decision diagrams I. INTRODUCTION

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“…Hybrid Maximum Clique Algorithm Using Parallel Integer Programming method (HMCAPIP) [5] is known to assemble the greatest number of tests with the highest measurement accuracy.…”

Section: B Hybrid Maximum Clique Algorithm Using Parallel Integer Pro...mentioning

confidence: 99%

Section: B Hybrid Maximum Clique Algorithm Using Parallel Integer Pro...mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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

Fuchimoto,

Minato,

Ueno

2023

IEEE Access

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Item Difficulty Constrained Uniform Adaptive Testing

Kishida,

Fuchimoto,

Miyazawa

et al. 2023

Communications in Computer and Information Science

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The Development of an Automatic Test Assembly System for a Formative Assessment in Mastery Learning Instruction: Case of the SQL Mastery Course

Chen,

Liu,

Liu

et al. 2023

IEEE Access

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The teaching method of mastery learning requires lectures to conduct the regular formative assessments so as to monitor each student's learning progress. However, regularly preparing quality test forms for these assessments has caused a tremendous workload on lecturers and has prevented them from executing the master learning instruction effectively. To resolve the problem, this study has built an automatic test assembly system with the automatic and manual test assembly functions for preparing fixed-length testing forms. Our system is implemented in a SQL mastery course that helps students prepare for the ORACLE SQL Certification (OCE SQL) examination. OCE SQL is a program offered by the Oracle Corporation to validate and recognize the skills of professionals in the SQL programming. By applying the Hambleton and De Gruijter's method [1], our system can automatically assemble items to a test form with a quality indication of the maximum probability of misclassifying mastery. Furthermore, our system can evaluate the prementioned probability for a manually assembled test form. The present study has also investigated the numeric methods for converting the domain cutoff score to the latent ability scale for items with heterogeneous parameters when applying the Hambleton and De Gruijter's method [1]. The empirical computing results showed that the secant method is superior to the bisection method for the conversion. This study contributes an automatic test assembly system to the engineering education practice so as to lighten the lecturers' burden of preparing quality assessments and to further facilitate the execution of the regular formative assessments in the mastery learning instruction.

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Hybrid Maximum Clique Algorithm Using Parallel Integer Programming for Uniform Test Assembly

Cited by 5 publications

References 37 publications

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

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

Item Difficulty Constrained Uniform Adaptive Testing

The Development of an Automatic Test Assembly System for a Formative Assessment in Mastery Learning Instruction: Case of the SQL Mastery Course

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