A Constraint Programming Approach to Extract the Maximum Number of Non-Overlapping Test Forms

Belov, Dmitry I.; Armstrong, Ronald D.

doi:10.1007/s10589-005-3058-z

Cited by 15 publications

(13 citation statements)

References 18 publications

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“…Our complexity results follow the line of previous works (like Belov & Armstrong, 2006;Nguyen & Fong, 2013;Ishii et al, 2014) in which other formula-800 tions of the test assembly design problem were identified as classical strongly NP-hard combinatorial optimization problems. Our approach differs when we consider the resolution considerations, as Belov & Armstrong (2006) ;Nguyen & Fong (2013); Ishii et al (2014) apply classical algorithms of the identified optimization problem to the resolution of the test design problem, while our Bin Packing-based formulation significantly differs from the classical problem, thus forcing us to develop specially tailored procedures for its resolution.…”

Section: Discussionsupporting

confidence: 83%

“…Our approach differs when we consider the resolution considerations, as Belov & Armstrong (2006) ;Nguyen & Fong (2013); Ishii et al (2014) apply classical algorithms of the identified optimization problem to the resolution of the test design problem, while our Bin Packing-based formulation significantly differs from the classical problem, thus forcing us to develop specially tailored procedures for its resolution.…”

Section: Discussionmentioning

confidence: 99%

“…Ishii et al (2014) considers the maximization of the number of tests using a maximum clique formulation. Their work builds upon the study by Belov & Armstrong (2006), in which the problem is assimilated to a set packing problem and solved using a constraint programming approach. The proposal of Ishii 180 et al (2014) constructs a graph in which a maximal subset of tests that share none or few items (the clique) is sought.…”

Section: Literature Reviewmentioning

confidence: 99%

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Variable neighborhood search heuristics for a test assembly design problem

Pereira

Vilà

2015

Expert Systems with Applications

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Test assembly design problems appear in the areas of psychology and education, among others. The goal of these problems is to construct one or multiple tests to evaluate some criteria. This paper studies a recent formulation of the problem known as the one-dimensional minimax bin-packing problem with bin size constraints (MINIMAX BSC). In the MINIMAX BSC, items are initially divided into groups and multiple tests need to be constructed using a single item from each group, while minimizing the difference among the tests. We first show that the problem is NP-Hard, which remained an open question. Second, we propose three different local search neighborhoods derived from the exact resolution of special cases of the problem, and combine them into a Variable Neighborhood Search (VNS) metaheuristic. Finally, we test the proposed algorithm using real-life-based instances. The results show that the algorithm is able to obtain optimal or near-optimal solutions for instances with item pools with up to 60.000 items. Consequently, the algorithm is a viable option to design large-scale tests, as well as to provide tests for online small-sized situations such as those found in e-learning platforms.

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Section: Discussionsupporting

confidence: 83%

Section: Discussionmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

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Variable neighborhood search heuristics for a test assembly design problem

Pereira

Vilà

2015

Expert Systems with Applications

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“…Subsequently, alternative methods have been developed that greatly outperform sequential assembly by utilizing properties of the feasible set. Belov and Armstrong (2006) suggested a set packing approach. They assembled multiple nonoverlapping tests in two stages:…”

Section: Extracting Multiple Nonoverlapping (Or Partially Overlappingmentioning

confidence: 99%

Uniform Test Assembly: Concepts, Problems, Solvers, and Applications for Adaptive Testing

Белов¹

2017

JCAT

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This paper presents the latest developments since the publication of the seminal book by van der Linden (2005) on general types of test assembly (TA) problems, major automated test assembly (ATA) methods, and various practical situations in which a TA problem arises. With the power of modern combinatorial optimization (CO) methods, multiple practical tasks in test development and design that were previously intractable can now be solved. The TA problem is, therefore, no longer a central issue for test development but rather a subproblem embedded in different practical tasks, where two major approaches are currently exploited: mixed-integer programming (MIP) and uniform test assembly (UTA). In the world of ATA, the MIP approach is dominant. However, UTA has multiple advantages over MIP. This paper concentrates on UTA and enumerates its multiple applications for adaptive testing. Keywords: automated test assembly, item pool analysis, item pool extension, item pool design, combinatorial optimization, mixed-integer programming, monte-carlo methods, uniform test assemblyTesting organizations periodically produce test forms for assessments in various formats: paper-and-pencil (P&P), computer-based testing (CBT), multistage testing (MST), and computerized adaptive testing (CAT). Each test form includes items selected from an item bank to optimize a given objective function and/or to satisfy given test specifications in terms of both statistical and

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“…Since each item from the pool can be used in multiple combinations satisfying test specifications, tests from the feasible set can overlap each other. Certain subsets of the feasible set play an important role in practice, in particular, subsets where tests do not overlap each other (van der Linden, 2005a;Belov & Armstrong, 2005a;Belov & Armstrong, 2006). If the test specifications describe m > 1 non-overlapping tests (van der Linden, Ariel, & Veldkamp, 2006), we interpret them as one lengthy test and the solution to the corresponding system of inequalities is a 0-1 vector of size n = mn.…”

Section: Introductionmentioning

confidence: 99%