TY - JOUR

T1 - The stochastic test collection problem

T2 - Models, exact and heuristic solution approaches

AU - Douek-Pinkovich, Yifat

AU - Ben-Gal, Irad

AU - Raviv, Tal

N1 - Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/6/16

Y1 - 2022/6/16

N2 - The classic test collection problem (TCP) selects a minimal set of binary tests needed to classify the state of a system correctly. The TCP has applications in various domains, such as the design of monitoring systems in engineering, communication, and healthcare. In this paper, we define the stochastic test collection problem (STCP) that generalizes the TCP. While the TCP assumes that the tests' results can be deterministically mapped into classes, in the STCP, the results are mapped to probability distributions over the classes. Moreover, each test and each type of classification error is associated with some cost. A solution of the STCP is a subset of tests and a mapping of their results to classes. The objective is to minimize the weighted sum of the tests' costs and the expected cost of the classification errors. We present an integer linear programming formulation of the problem and solve it using a commercial solver. To solve larger instances, we apply three metaheuristics for the STCP, namely, Tabu Search (TS), Cross-Entropy (CE), and Binary Gravitational Search Algorithm (BGSA). These methods are tested on publicly available datasets and shown to deliver nearly optimal solutions in a fraction of the time required for the exact solution.

AB - The classic test collection problem (TCP) selects a minimal set of binary tests needed to classify the state of a system correctly. The TCP has applications in various domains, such as the design of monitoring systems in engineering, communication, and healthcare. In this paper, we define the stochastic test collection problem (STCP) that generalizes the TCP. While the TCP assumes that the tests' results can be deterministically mapped into classes, in the STCP, the results are mapped to probability distributions over the classes. Moreover, each test and each type of classification error is associated with some cost. A solution of the STCP is a subset of tests and a mapping of their results to classes. The objective is to minimize the weighted sum of the tests' costs and the expected cost of the classification errors. We present an integer linear programming formulation of the problem and solve it using a commercial solver. To solve larger instances, we apply three metaheuristics for the STCP, namely, Tabu Search (TS), Cross-Entropy (CE), and Binary Gravitational Search Algorithm (BGSA). These methods are tested on publicly available datasets and shown to deliver nearly optimal solutions in a fraction of the time required for the exact solution.

KW - Combinatorial optimization

KW - Integer linear programming

KW - Metaheuristics

KW - The test collection problem

UR - http://www.scopus.com/inward/record.url?scp=85123690652&partnerID=8YFLogxK

U2 - 10.1016/j.ejor.2021.12.043

DO - 10.1016/j.ejor.2021.12.043

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AN - SCOPUS:85123690652

SN - 0377-2217

VL - 299

SP - 945

EP - 959

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 3

ER -