New Reliability-Driven Bounds for Architecture-Based Multi-Objective Testing Resource Allocation

Guofu ZHANG, Lei LI, Zhaopin SU, Zhisheng SHAO, Miqing LI, Bin LI, Xin YAO

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


The multi-objective testing resource allocation problem (MOTRAP) aims at seeking a good trade-off between system reliability, testing cost, and testing time, which is of significant importance to facilitate the testing planning. Yet most studies focus on the time constraint but rarely consider the practical reliability requirement. In this work, we address MOTRAP on an architecture-based model (ABM) with the personalized preference over reliability. More specifically, we first present a reliability-constrained MOTRAP model on the basis of ABM and illustrate how to use this model for real-world systems. Then, to leverage the problem's knowledge, we develop new lower and upper bounds on testing time invested in different components from both theoretical and algorithmic perspectives on the basis of the Lagrange multiplier and half-interval search. Importantly, these new derived bounds have strong implications due to the fact that they can be easily employed by optimizers as the limits of variables to prune the search space to the region of interests of the decision maker and locate feasible solutions with the expected reliability. Finally, we evaluate the proposed bounds in popular multi-objective optimizers for MOTRAP on application and empirical cases. Experimental results demonstrate that our new bounds practically improve the search performance of optimizers, and decision makers can easily combine these new bounds with off-the-shelf optimizers to find higher-quality solutions that they are interested in, which greatly soothes away stress on optimizer and solution selections of decision makers. © 1976-2012 IEEE.
Original languageEnglish
Pages (from-to)2513-2529
Number of pages17
JournalIEEE Transactions on Software Engineering
Issue number4
Early online date24 Nov 2022
Publication statusPublished - 1 Apr 2023
Externally publishedYes

Bibliographical note

This work was supported in part by Anhui Provincial Key Research and Development Program under Grant 202004d07020011 and 202104d07020001, in part by Anhui Provincial Natural Science Foundation under Grant 2208085MF166, in part by the National Natural Science Foundation of China under Grant U19B2044, in part by the MOE (Ministry of Education in China) Project of Humanities and Social Sciences under Grant 19YJC870021, in part by the Guangdong Provincial Key Laboratory under Grant 2020B121201001, and the Fundamental Research Funds for the Central Universities under Grant PA2021GDSK0073 and Grant PA2021GDSK0074.


  • architecture-based model
  • lower and upper bounds
  • Multi-objective testing resource allocation
  • preference over reliability
  • region of interest


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