Constraint handling in NSGA-II for solving optimal testing resource allocation problems

Guofu ZHANG, Zhaopin SU, Miqing LI, Feng YUE, Jianguo JIANG, Xin YAO

Research output: Journal PublicationsJournal Article (refereed)peer-review

29 Citations (Scopus)


In software testing, optimal testing resource allocation problems (OTRAPs) are important when seeking a good tradeoff between reliability, cost, and time with limited resources. There have been intensive studies of OTRAPs using multiobjective evolutionary algorithms (MOEAs), but little attention has been paid to the constraint handling. This paper comprehensively investigates the effect of the constraint handling on the performance of nondominated sorting genetic algorithm II (NSGA-II) for solving OTRAPs, from both theoretical and empirical perspectives. The heuristics for individual repairs are first proposed to handle constraint violations in NSGA-II, based on which several properties are derived. Additionally, the Z-score based Euclidean distance is adopted to estimate the difference between solutions. Finally, the above methods are evaluated and the experiments show several results. 1) The developed heuristics for constraint handling are better than the Existing Strategy in terms of the capacity and coverage values. 2) The Z-score operation obtains better diversity values and reduces repeated solutions. 3) The modified NSGA-II for OTRAPs (called NSGA-II-TRA) performs significantly better than the existing MOEAs in terms of capacity and coverage values, which suggests that NSGA-II-TRA could obtain more and higher quality testing-time-allocation schemes, especially for large, complex datasets. 4) NSGA-II-TRA is robust according to the sensitivity analysis results. © 2017 IEEE.
Original languageEnglish
Article number8023833
Pages (from-to)1193-1212
Number of pages20
JournalIEEE Transactions on Reliability
Issue number4
Early online date31 Aug 2017
Publication statusPublished - Dec 2017
Externally publishedYes

Bibliographical note

This work was supported in part by the National Natural Science Foundation of China under Grant 61573125, Grant 61329302, and Grant 61371155, in part by the Engineering and Physical Sciences Research Council under Grant EP/J017515/1, in part by the Anhui Provincial Natural Science Foundation under Grant 1608085MF131, Grant 1508085MF132, and Grant 1508085QF129, and in part by the Science and Technology Innovation Committee Foundation of Shenzhen under Grant ZDSYS201703031748284.


  • Constraint handling
  • Heuristics
  • Multiobjective optimization
  • Software reliability
  • Testing-resource allocation


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