Enhanced constraint handling for reliability-constrained multiobjective testing resource allocation

Zhaopin Su, Guofu Zhang, Feng Yue, Dezhi Zhan, Miqing Li, Bin Li, Xin Yao

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The multiobjective testing resource allocation problem (MOTRAP) is how to efficiently allocate the finite testing time to various modules, with the aim of optimizing system reliability, testing cost, and testing time simultaneously. To deal with this problem, a common approach is to use multiobjective evolutionary algorithms (MOEAs) to seek a set of tradeoff solutions between the three objectives. However, such a tradeoff set may contain a substantial proportion of solutions with very low reliability level, which consume lots of computational resources but may be valueless to the software project manager. In this article, a MOTRAP model with a prespecified reliability is first proposed. Then, new lower bounds on the testing time invested in different modules are theoretically deduced from the necessary condition for the achievement of the given reliability, based on which an exact algorithm for determining the new lower bounds is presented. Moreover, several enhanced constraint-handling techniques (ECHTs) derived from the new bounds are successively developed to be combined with MOEAs to correct and reduce the constraint violation. Finally, the proposed ECHTs are evaluated in comparison with various state-of-the-art constraint-solving approaches. The comparative results demonstrate that the proposed ECHTs can work well with MOEAs, make the search focus on the feasible region of the prespecified reliability, and provide the software project manager with better and more diverse, satisfactory choices in test planning.
Original languageEnglish
Article number9340399
Pages (from-to)537-551
Number of pages15
JournalIEEE Transactions on Evolutionary Computation
Issue number3
Early online date29 Jan 2021
Publication statusPublished - Jun 2021

Bibliographical note

Funding Information:
Manuscript received June 7, 2020; revised September 26, 2020 and December 3, 2020; accepted January 25, 2021. Date of publication January 29, 2021; date of current version May 28, 2021. This work was supported in part by the Anhui Provincial Key Research and Development Program under Grant 202004d07020011; in part by the National Natural Science Foundation of China under Grant U19B2044; in part by the Ministry of Education in China Project of Humanities and Social Sciences under Grant 19YJC870021 and Grant 18YJC870025; and in part by the Fundamental Research Funds for the Central Universities under Grant PA2020GDKC0015, Grant PA2019GDQT0008, and Grant PA2019GDPK0072. (Corresponding author: Guofu Zhang.) Zhaopin Su, Guofu Zhang, Feng Yue, and Dezhi Zhan are with the School of Computer Science and Information Engineering, Hefei University of Technology, Hefei 230601, China, also with the Intelligent Interconnected Systems Laboratory of Anhui Province, Hefei University of Technology, Hefei 230009, China, also with the Key Laboratory of Knowledge Engineering with Big Data, Hefei University of Technology, Ministry of Education, Hefei 230601, China, and also with the Anhui Province Key Laboratory of Industry Safety and Emergency Technology, Hefei University of Technology, Heifei 230601, China (e-mail: szp@hfut.edu.cn; zgf@hfut.edu.cn; yuefeng@hfut.edu.cn; dzzhan@mail.hfut.edu.cn).

Publisher Copyright:
© 1997-2012 IEEE.


  • Constraint handling
  • evolutionary algorithms (EAs)
  • multiobjective testing resource allocation
  • reliability constraint

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics


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