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Reformulating Regression Test Suite Optimization using Quantum Annealing -- an Empirical Study

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A QUBO reformulation of test case selection lets quantum annealing match classical methods and beat the quantum baseline BootQA.

desk verdict The three-objective TCS study is solid and reproducible, but the BootQA headline collapses because Eq. 11 is a separable linear threshold rule, not a real QUBO. read the letter →

arxiv 2411.15963 v2 pith:JHOVZSKI submitted 2024-11-24 cs.SE cs.ET

Antonio Trovato , Manuel De Stefano , Fabiano Pecorelli , Dario Di Nucci , Andrea De Lucia This is my paper · ORCID
classification cs.SEcs.ET
keywords regressiontestingtestcaseselectionquantumannealingQUBOmulti-objectiveoptimizationhybridquantum-classicalsolverempiricalsoftwareengineering
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to show that regression test case selection can be reformulated as a quadratic unconstrained binary optimization (QUBO) problem that a quantum annealer solves well enough to be practically useful. The proposed method, SelectQA, encodes the trade-off between execution cost and fault detection as a weighted Hamiltonian and hands it to a hybrid quantum-classical solver, then builds a Pareto frontier from the returned test cases. The empirical claim is that SelectQA finds more non-dominated solutions than DIV-GA and Additional Greedy on two of four open-source programs, beats the quantum baseline BootQA in effectiveness on both industrial datasets in 18 of 20 runs, and takes about 2.9 seconds regardless of suite size. If this holds, testers get a single-weight, roughly fixed-time quantum option instead of expensive genetic search or the decomposition-parameter tuning that BootQA requires.

What carries the argument

The load-bearing object is the QUBO Hamiltonian $H = \alpha \sum_i x_i\, \mathrm{cost}(\tau_i) - (1-\alpha)\sum_i e_i x_i + P\sum_k (\sum_{i\in T_k} x_i - 1)^2$, with $e_i$ replaced by the failure rate $f_i$ in the two-objective version. The binary $x_i$ says whether test $i$ is selected; the first sum charges for execution cost, the second rewards past fault detection, and the penalty term forces every statement covered by the original suite to stay covered. This one expression converts the multi-objective test case selection problem into the single-objective format a quantum annealer can minimize, and it defines what the hybrid solver is actually optimizing; the paper's Pareto-frontier construction then runs on the selected test cases. The key move is that the objective is a weighted sum with penalty terms, so no explicit constraint-solving or decomposition loop is needed.

What would settle it

Take a dataset where the per-test failure-rate-to-cost ratio is anti-correlated with statement coverage, compute the exact optimum of Eq. (11) by sorting test cases on $f_i/\mathrm{cost}(\tau_i)$, and compare it with SelectQA's returned suite and with BootQA's coverage-constrained suite: if the threshold solution differs from SelectQA's output, the solver is not optimizing its own objective, and if it matches, the reported effectiveness advantage over BootQA is an artifact of comparing a trivially separable objective with a constrained problem.

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Extended reading notes

Core claim

The paper's central claim is that the way test case selection is encoded for the annealer matters more than the annealing hardware itself. SelectQA encodes the selection problem as a QUBO Hamiltonian whose linear terms price each test case by its normalized execution cost and failure-detection value, with coverage enforced through penalty terms, and the hybrid solver minimizes it directly. Against classical methods on the four open-source programs, SelectQA produces the largest number of non-dominated reference-frontier solutions on grep and sed, loses to DIV-GA on gzip, and loses to Additional Greedy on flex. Against BootQA on the two industrial datasets, SelectQA's returned suites dominated BootQA's in 18 of 20 runs, were never dominated, and had statistically significantly lower cost and higher failure rate. The paper also reports a practically constant total runtime near 2.9 seconds across all four programs and both datasets, which it credits to the hybrid solver rather than to any problem-specific decomposition.

Load-bearing premise

The comparison with BootQA assumes that SelectQA's unconstrained two-objective QUBO (Eq. 11) is the same optimization task as BootQA's constrained minimization problem; if the two tasks are not equivalent, the paper's reported effectiveness dominance is an artifact.

Editorial extensions

If this is right

  • SelectQA offers a single-weight ($\alpha$) quantum selector whose wall-clock time stays near 2.9 seconds across the suite sizes studied, removing the need for the $(m,n)$ decomposition sweep BootQA requires.
  • On grep and sed, SelectQA contributed the largest share of non-dominated solutions to the reference frontier; on gzip, DIV-GA remained the best, so the paper does not claim one approach dominates everywhere.
  • Because SelectQA's Pareto frontier is built incrementally from annealing output, the method can be inserted into existing regression-testing pipelines that already construct frontiers from greedy or genetic search.
  • When wall-clock time is the binding constraint, SelectQA is the faster option than DIV-GA on all four programs, making quantum annealing a practical alternative for mid-size test suites.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the two-objective QUBO (Eq. 11) separates per test case, so its optimum is a simple threshold on the ratio $f_i/\mathrm{cost}(\tau_i)$; if so, a classical sort would reproduce SelectQA's suites on the BootQA datasets, meaning the reported effectiveness win is not evidence of any quantum advantage.
  • Editorial inference: the constant 2.9-second runtime is likely the hybrid solver's fixed time budget rather than a scaling law of quantum annealing; separating QPU access time from total solver time on larger suites would test this.
  • Editorial inference: adding the coverage penalty from the three-objective version to the two-objective comparison would make the contest with BootQA a like-for-like constrained optimization and would clarify whether the method's value lies in the QUBO encoding or in the unconstrained reformulation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes SelectQA, a reformulation of regression test case selection as a QUBO problem solved with D-Wave's hybrid quantum annealing service. SelectQA is evaluated in two settings: a three-objective version (execution cost, past fault coverage, statement coverage) compared against Additional Greedy and DIV-GA on four SIR programs, and a two-objective version (execution time, failure rate) compared against the quantum baseline BootQA on two industrial datasets. The authors report that SelectQA outperforms BootQA in effectiveness, is comparable to or better than the classical baselines in effectiveness, and has nearly constant execution time regardless of problem size.

Significance. If the results held, the paper would provide a useful empirical data point that hybrid quantum annealing can produce competitive test suite selections with constant wall-clock time over the tested sizes. The replication package, use of established benchmarks (SIR, PaintControl, GSDTSR), and statistical testing over ten runs are strengths. However, the central quantum-vs-quantum claim is compromised by a formulation mismatch: the two-objective SelectQA Hamiltonian is unconstrained and separable, while BootQA solves a constrained combinatorial problem. In addition, the three-objective formulation contains an incorrect coverage penalty and inconsistent algebra. These issues are load-bearing for the abstract's headline claims, although the underlying idea is potentially salvageable with a corrected formulation and re-run experiments.

major comments (3)
  1. [§3.1.2, Eq. (11); §4.3.4] The two-objective Hamiltonian in Eq. (11) has no quadratic terms and no constraints. It is equivalent to H = Σ_i x_i [α·cost(τ_i) − (1−α)·f_i], so each variable x_i can be optimized independently by setting it to 1 exactly when α·cost(τ_i) < (1−α)·f_i. The 'optimal solution in each run' reported in §4.3.4 is therefore a per-test threshold rule, not the result of a combinatorial optimization over coupled variables. BootQA, by contrast, is described in §2.2 as solving a test suite minimization problem with constraints and sampling subproblems. Since Eq. (11) drops the coverage/cardinality penalty that appears in Eq. (10), SelectQA and BootQA are not solving the same problem, and the dominance reported in Table 7 and Takeaway #3 is an artifact of the unconstrained formulation. The statement in §3.1 that both versions 'implement an algorithm that resolves the Minimum Vertex Cover problem' is contradicted by Eq. (11).
  2. [§3.1.1, Eqs. (6)–(9)] The coverage constraint is not encoded correctly. The penalty term in Eq. (6), Σ_k Σ_{i∈T_k} (x_i − 1)^2, equals |T_k| − Σ_{i∈T_k} x_i for binary variables, so it is minimized by selecting all test cases that cover statement k, not by selecting at least one as required by Eq. (5). The correct penalty for 'at least one selected' would be (Σ_{i∈T_k} x_i − 1)^2 or an equivalent formulation. In addition, the algebra in Eqs. (8)–(9) is inconsistent: the expansion in Eq. (8) does not follow from Eq. (7), and Eq. (9) drops a constant and changes the linear coefficient. Since Eq. (10) is presented as the BQM actually submitted to the solver, the implemented Hamiltonian and the experiments need to be rechecked against the intended constraint.
  3. [§5 (Internal Validity); §4.3.4] The α parameter is tuned on the same datasets used for the evaluation ('validated following repeated trials'), and in the two-objective formulation α directly selects the threshold that defines 'optimality'. Because Eq. (11) is linear and separable, tuning α on the test data makes the claim that SelectQA 'always finds the optimal trade-off solution' circular. The authors should provide a validation protocol, a sensitivity analysis over α, or a held-out dataset before claiming that SelectQA dominates BootQA in effectiveness.
minor comments (6)
  1. [Abstract] There is a typo: 'traditionaltest suite optimization' should read 'traditional test suite optimization'.
  2. [Table 3] The row labeled 'Additional Method' is not defined in the experiment configuration in §4.2.2; either define it or remove it.
  3. [Figure 3] The figure lacks axis labels and a legend, making it difficult to see which points correspond to which algorithm and which runs; the caption should specify the plotted quantities.
  4. [§5, Conclusion Validity] The Vargha-Delaney effect size is cited as reference [41], but the correct bibliographic entry appears to be [42]; the citation should be corrected.
  5. [§4.3.5] The phrase 'large 0 effect sizes' appears to be a typo; it should likely read 'large effect sizes' or 'effect sizes of 0.0'.
  6. [§3.1.2] The phrase 'without repeating the previous procedure' is vague; the authors should state explicitly whether the coverage penalty from Eq. (10) is intentionally omitted and why.

Circularity Check

2 steps flagged · score 6.0 of 10

The BootQA-effectiveness claim is not a quantum result: Eq. 11 is a separable linear threshold objective, and alpha is tuned on the same datasets, so SelectQA's 'optimal trade-off' dominance is forced by construction.

  1. self definitional [Sections 3.1, 3.1.2, Eq. (11); Section 4.3.4, Takeaway #3]
    "The two versions implement an algorithm that resolves the Minimum Vertex Cover problem. ... Without repeating the previous procedure, we formulate the two objectives and combine them into a linear equation. We obtain: H = α Σ xi·cost(τi) − (1−α) Σ (fi·xi) ... SelectQA could find the optimal solution to the problem in each run and for both datasets."

    Eq. (11) is a sum of independent per-test linear terms: there are no quadratic x_i x_j terms and no coverage or cardinality constraint. With α fixed, each binary variable is optimized separately by the threshold x_i=1 iff (1−α)f_i > α cost(τ_i). The 'optimal solution' claimed in §4.3.4 is thus the closed-form minimizer of the same objective, not a combinatorial quantum search result. The paper itself says both versions implement a Minimum Vertex Cover problem, but Eq. (11) contains none of the constraint structure needed for MVC.

  2. fitted input called prediction [Section 4.3.1, Section 4.3.4, and Section 5 (Internal Validity)]
    "The α parameter has been validated following repeated trials. ... SelectQA could find the optimal solution to the problem in each run and for both datasets."

    The α weight is tuned on the same PaintControl and GSDTSR datasets used for the reported comparison, and the claimed 'optimal trade-off' is measured with the same weighted objective that α controls. Reporting that SelectQA always finds the optimal solution on these datasets is a restatement of the tuning criterion, not an independent empirical prediction; the comparison against BootQA on those tuned results is consequently forced rather than a test of quantum-annealing effectiveness.

full rationale

The classical-arm comparison is largely self-contained: SelectQA's three-objective Hamiltonian (Eq. 10) includes per-statement coverage penalties with quadratic terms, and the comparison to DIV-GA/additional greedy is judged against an external reference Pareto frontier on SIR programs, so no reduction to a fitted parameter or load-bearing self-citation is present. The circularity is concentrated in the BootQA arm. Eq. 11 is a purely linear, separable weighted sum with no coverage or cardinality constraints, so the 'optimal solution' reported in Section 4.3.4 is a closed-form per-test threshold; presenting this as an annealing-based advantage over BootQA's constrained Minimum Vertex Cover formulation makes the dominance an artifact of comparing an unconstrained linear objective to a constrained combinatorial one. Additionally, α is tuned by repeated trials on the same datasets that are then used to claim the optimal trade-off, so the headline effectiveness result is partially fitted rather than independently predicted. The efficiency comparison (Takeaway #4) is not circular, though it largely measures hybrid-solver overhead. Score 6 reflects that the central BootQA-effectiveness claim reduces to the chosen objective and tuning, while the three-objective comparison retains independent content.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central empirical claims rest on two tunable coefficients (α and P) and several modeling axioms. The most consequential is the ad hoc assumption that an unconstrained, separable QUBO is comparable to BootQA's constrained problem; this assumption is what makes SelectQA appear to dominate BootQA. No new physical or conceptual entities are introduced.

free parameters (2)
  • alpha (α) = not reported
    Weight balancing execution cost and failure coverage in the QUBO objective; tuned by repeated trials on the evaluation datasets (Section 5, Internal Validity).
  • penalty P = set by upper bound strategy
    Penalty coefficient for the statement coverage constraint, chosen using the upper bound strategy (Section 3.1.1).
assumptions (4)
  • standard math Binary variables satisfy x_i^2 = x_i in QUBO simplifications
    Used in the simplification of the penalty term in Section 3.1.1, Eqs. 8-10.
  • domain assumption Test case selection can be modeled as weighted set cover with statement coverage constraints
    The QUBO formulation in Eq. 7 assumes the goal is minimum-cost set of tests covering all statements covered by the original suite.
  • domain assumption Historical fault detection (e_i or f_i) is a valid proxy for future fault detection effectiveness
    Used in the objectives in Eqs. 2-3 and Eq. 11; this is standard in regression testing research.
  • ad hoc to paper SelectQA's unconstrained two-objective QUBO (Eq. 11) is a fair model for comparing with BootQA's constrained problem
    The comparison in Section 4.3 uses this formulation, but BootQA solves a constrained minimization; this assumption drives the reported dominance.

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Cite this review

Pith. "Pith review of Reformulating Regression Test Suite Optimization using Quantum Annealing -- an Empirical Study." pith.science (2026). https://pith.science/paper/JHOVZSKI

@misc{pith2026241115963,
  author       = {Pith},
  title        = {Pith review of: Reformulating Regression Test Suite Optimization using Quantum Annealing -- an Empirical Study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JHOVZSKI}},
  note         = {Machine review of arXiv:2411.15963}
}
read the original abstract

Maintaining software quality is crucial in the dynamic landscape of software development. Regression testing ensures that software works as expected after changes are implemented. However, re-executing all test cases for every modification is often impractical and costly, particularly for large systems. Although very effective, traditional test suite optimization techniques are often impractical in resource-constrained scenarios, as they are computationally expensive. Hence, quantum computing solutions have been developed to improve their efficiency but have shown drawbacks in terms of effectiveness. We propose reformulating the regression test case selection problem to use quantum computation techniques better. Our objectives are (i) to provide more efficient solutions than traditional methods and (ii) to improve the effectiveness of previously proposed quantum-based solutions. We propose SelectQA, a quantum annealing approach that can outperform the quantum-based approach BootQA in terms of effectiveness while obtaining results comparable to those of the classic Additional Greedy and DIV-GA approaches. Regarding efficiency, SelectQA outperforms DIV-GA and has similar results with the Additional Greedy algorithm but is exceeded by BootQA.

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Reference graph

Works this paper leans on

45 extracted references · 43 canonical work pages

  1. [1]

    Software testing, verification and reli- ability 22(2), 67–120 (2012)

    Yoo, S., Harman, M.: Regression testing minimization, selection and prioritization: a survey. Software testing, verification and reli- ability 22(2), 67–120 (2012)

    work page 2012

  2. [2]

    IEEE Transactions on Software Engineering 24(6), 401–419 (1998)

    Rothermel, G., Harrold, M.J.: Empirical studies of a safe regression test selection technique. IEEE Transactions on Software Engineering 24(6), 401–419 (1998)

    work page 1998

  3. [3]

    Software Quality Journal 20, 605–643 (2012)

    Perrouin, G., Oster, S., Sen, S., Klein, J., Baudry, B., Le Traon, Y.: Pairwise testing for software product lines: comparison of two approaches. Software Quality Journal 20, 605–643 (2012)

    work page 2012

  4. [4]

    In: Proceedings of the 2007 International Symposium on Software Testing and Analysis, pp

    Yoo, S., Harman, M.: Pareto efficient multi- objective test case selection. In: Proceedings of the 2007 International Symposium on Software Testing and Analysis, pp. 140–150 (2007)

    work page 2007

  5. [5]

    Journal of Systems and Software 83(4), 689–701 (2010)

    Yoo, S., Harman, M.: Using hybrid algo- rithm for pareto efficient multi-objective test suite minimisation. Journal of Systems and Software 83(4), 689–701 (2010)

    work page 2010

  6. [6]

    In: Search Based Software Engineering: Third International Symposium, SSBSE 2011, Szeged, Hungary, 15 September 10-12, 2011

    Yoo, S., Harman, M., Ur, S.: Highly scal- able multi objective test suite minimisa- tion using graphics cards. In: Search Based Software Engineering: Third International Symposium, SSBSE 2011, Szeged, Hungary, 15 September 10-12, 2011. Proceedings 3, pp. 219–236 (2011). Springer

    work page 2011

  7. [7]

    In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, pp

    Wang, S., Ali, S., Gotlieb, A.: Minimizing test suites in software product lines using weight- based genetic algorithms. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, pp. 1493–1500 (2013)

    work page 2013

  8. [8]

    IEEE Transactions on Software Engineering 41(4), 358–383 (2014)

    Panichella, A., Oliveto, R., Di Penta, M., De Lucia, A.: Improving multi-objective test case selection by injecting diversity in genetic algorithms. IEEE Transactions on Software Engineering 41(4), 358–383 (2014)

    work page 2014

Show all 45 references
  1. [9]

    Information and Software Technology 114, 137–154 (2019)

    Arrieta, A., Wang, S., Markiegi, U., Arru- abarrena, A., Etxeberria, L., Sagardui, G.: Pareto efficient multi-objective black-box test case selection for simulation-based testing. Information and Software Technology 114, 137–154 (2019)

    2019

  2. [10]

    ACM Transactions on Software Engineering and Methodology (TOSEM) 29(3), 1–50 (2020)

    Xue, Y., Li, Y.-F.: Multi-objective inte- ger programming approaches for solving the multi-criteria test-suite minimization prob- lem: Towards sound and complete solu- tions of a particular search-based software- engineering problem. ACM Transactions on Software Engineering an...

    2020

  3. [11]

    IEEE Transactions on software engi- neering 33(4), 225–237 (2007)

    Li, Z., Harman, M., Hierons, R.M.: Search algorithms for regression test case prioriti- zation. IEEE Transactions on software engi- neering 33(4), 225–237 (2007)

    2007

  4. [12]

    Information Sciences 267, 119–139 (2014)

    Assun¸ c˜ ao, W.K.G., Colanzi, T.E., Vergilio, S.R., Pozo, A.: A multi-objective optimiza- tion approach for the integration and test order problem. Information Sciences 267, 119–139 (2014)

    2014

  5. [13]

    In: Proceedings of the 2015 International Symposium on Software Test- ing and Analysis, pp

    Epitropakis, M.G., Yoo, S., Harman, M., Burke, E.K.: Empirical evaluation of pareto efficient multi-objective regression test case prioritisation. In: Proceedings of the 2015 International Symposium on Software Test- ing and Analysis, pp. 234–245 (2015)

    2015

  6. [14]

    IEEE Transactions on Software Engineering 46(6), 674–696 (2018)

    Di Nucci, D., Panichella, A., Zaidman, A., De Lucia, A.: A test case prioritization genetic algorithm guided by the hypervolume indicator. IEEE Transactions on Software Engineering 46(6), 674–696 (2018)

    2018

  7. [15]

    Information and Software Technology 52(1), 14–30 (2010)

    Engstr¨ om, E., Runeson, P., Skoglund, M.: A systematic review on regression test selec- tion techniques. Information and Software Technology 52(1), 14–30 (2010)

    2010

  8. [16]

    The Computer Journal 48(1), 49–52 (2005)

    Hoare, T., Milner, R.: Grand challenges for computing research. The Computer Journal 48(1), 49–52 (2005)

    2005

  9. [17]

    what are we going to do with them

    Knight, W.: Serious quantum computers are finally here. what are we going to do with them. MIT Technology Review. Retrieved on October 30, 2018 (2018)

    2018

  10. [18]

    arXiv:2308.05505 [cs.SE] (2023)

    Wang, X., Muqeet, A., Yue, T., Ali, S., Arcaini, P.: Test case minimization with quantum annealers. arXiv:2308.05505 [cs.SE] (2023)

    2023 arXiv

  11. [19]

    IEEE Transactions on Software Engineering (2024)

    Wang, X., Ali, S., Yue, T., Arcaini, P.: Quan- tum approximate optimization algorithm for test case optimization. IEEE Transactions on Software Engineering (2024)

    2024

  12. [20]

    [Online] https://www.dwavesys.com (Accessed on: 14-11-2024)

    D-Wave: D-wave environment. [Online] https://www.dwavesys.com (Accessed on: 14-11-2024)

    2024

  13. [21]

    arXiv preprint arXiv:1411.4028 (2014)

    Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algo- rithm. arXiv preprint arXiv:1411.4028 (2014)

    2014 arXiv

  14. [22]

    B. K. Chakrabart, A.D.: Colloquium: Quan- tum annealing e analog quantum computa- tion. Reviews of Modern Physics, vol. 80, no. 3, p. 1061 (2008)

    2008

  15. [23]

    Physical Review E 58(5), 5355 (1998)

    Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse ising model. Physical Review E 58(5), 5355 (1998)

    1998

  16. [24]

    In: Journal of Physics: Conference Series, vol

    Suzuki, S.: A comparison of classical and quantum annealing dynamics. In: Journal of Physics: Conference Series, vol. 143, p. 012002 (2009). IOP Publishing

    2009

  17. [25]

    IEEE Transactions on software engineering 22(8), 529–551 (1996)

    Rothermel, G., Harrold, M.J.: Analyzing 16 regression test selection techniques. IEEE Transactions on software engineering 22(8), 529–551 (1996)

    1996

  18. [26]

    Fischer, K.F.: A test case selection method for the validation of software maintenance modifications (1977)

    1977

  19. [27]

    In: Proceedings-IEEE Computer Soci- ety’s International Computer Software & Applications Conference, pp

    Yau, S.S., Kishimoto, Z.: Method for revali- dating modified programs in the maintenance phase. In: Proceedings-IEEE Computer Soci- ety’s International Computer Software & Applications Conference, pp. 272–277 (1987). IEEE

    1987

  20. [28]

    In: 1993 Conference on Software Maintenance, pp

    Rothermel, G., Harrold, M.J.: A safe, efficient algorithm for regression test selection. In: 1993 Conference on Software Maintenance, pp. 358–367 (1993). IEEE

    1993

  21. [29]

    In: Proceedings of the 20th ACM SIGPLAN- SIGACT Symposium on Principles of Pro- gramming Languages, pp

    Bates, S., Horwitz, S.: Incremental program testing using program dependence graphs. In: Proceedings of the 20th ACM SIGPLAN- SIGACT Symposium on Principles of Pro- gramming Languages, pp. 384–396 (1993)

    1993

  22. [30]

    In: Proceed- ings of the Twenty-eighth Annual ACM Sym- posium on Theory of Computing, pp

    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceed- ings of the Twenty-eighth Annual ACM Sym- posium on Theory of Computing, pp. 212– 219 (1996)

    1996

  23. [31]

    Zeitschrift f¨ ur Physik, no

    Born, M., Fock, V.: Beweis des adiabaten- satzes. Zeitschrift f¨ ur Physik, no. 6 (1928)

    1928

  24. [32]

    Journal of Mathematical Physics, vol

    Morita, S., Nishimori, H.: Mathematical foundation of quantum annealing. Journal of Mathematical Physics, vol. 49, no. 12 (2008)

    2008

  25. [33]

    D-Wave, Tech

    Catherine, M., Pau, F.: The d-wave advan- tage system: An overview. D-Wave, Tech. Rep., 2022. [Online] https://www.dwavesys. com/media/s3qbjp3s/14-1049a-a the d-wave advantage system an overview.pdf (Accessed on: 14-11-2024)

    2022

  26. [34]

    [Online] https: //www.dwavesys.com/media/m2xbmlhs/ 14-1048a-a d-wave hybrid solver service plus advantage technology update.pdf (Accessed on: 14-11-2024)

    McGeoch, C., Farr´ e, P., Bernoudy, W.: D-wave hybrid solver service + advan- tage: Technology update. [Online] https: //www.dwavesys.com/media/m2xbmlhs/ 14-1048a-a d-wave hybrid solver service plus advantage technology update.pdf (Accessed on: 14-11-2024)

    2024

  27. [35]

    Software Quality Journal, 1–30 (2023)

    Serrano, M.A., S´ anchez, L.E., Santos-Olmo, A., Garc´ ıa-Rosado, D., Blanco, C., Barletta, V.S., Caivano, D., Fern´ andez-Medina, E.: Minimizing incident response time in real- world scenarios using quantum computing. Software Quality Journal, 1–30 (2023)

    2023

  28. [36]

    Gary Kochenberger: Quantum bridge analytics i: A tutorial on for- mulating and using qubo models

    Fred Glover, R.H.e.Y.D. Gary Kochenberger: Quantum bridge analytics i: A tutorial on for- mulating and using qubo models. Ann Oper Res 314, 141–183 (2022)

    2022

  29. [37]

    John Wiley, New York (1986)

    Steuer, R.E.: Multi-criteria optimization: Theory, computation, and application. John Wiley, New York (1986)

    1986

  30. [38]

    Ayodele, M.: Penalty weights in qubo formu- lations: Permutation problems (2022)

    2022

  31. [39]

    [Online] https://sir.csc.ncsu.edu/ portal/index.php (Accessed on: 14-11-2024)

    SIR: Software-artifact infrastructure repos- itory. [Online] https://sir.csc.ncsu.edu/ portal/index.php (Accessed on: 14-11-2024)

    2024

  32. [40]

    [Online] https: //github.com/AntonioTrovato/SelectQA (Accessed on: 14-11-2024)

    Trovato, A.: Appendix. [Online] https: //github.com/AntonioTrovato/SelectQA (Accessed on: 14-11-2024)

    2024

  33. [41]

    Conover, W.J.: Practical nonparametric statistics. 3rd ed. New York, NY, USA: Wiley (1998)

    1998

  34. [42]

    Vargha, A., Delaney, H.D.: A critique and improvement of the cl common language effect size statistics of mcgraw and wong. J. Educ. and Behav. Stat. 25(2), 101–132 (2000)

    2000

  35. [43]

    [Online] http://new.abb.com/ products/robotics (Accessed on: 14-11-2024)

    Robotics, A.: Industrial robot supplier and manufacturer. [Online] http://new.abb.com/ products/robotics (Accessed on: 14-11-2024)

    2024

  36. [44]

    [Online] https://code.google.com/archive/p/ google-shared-dataset-of-test-suite-results/ wikis/DataFields.wiki (Accessed on: 14-11-2024)

    Google: Google code archive. [Online] https://code.google.com/archive/p/ google-shared-dataset-of-test-suite-results/ wikis/DataFields.wiki (Accessed on: 14-11-2024)

    2024

  37. [45]

    [Online] https://github

    Muqeet, A.: Bootqa. [Online] https://github. com/AsmarMuqeet/BootQA (Accessed on: 14-11-2024) 17

    2024

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