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REVIEW 5 major objections 6 minor 38 references

A Quantum Annealing Approach for Solving Optimal Feature Selection and Next Release Problems

T0 review · 5 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that quantum annealing, after recasting next-release and feature-selection problems as QUBO models, produces more non-dominated solutions than NSGA-II in most tested cases and does so in substantially less time.

desk verdict A genuine first application of quantum annealing to NRP and FSP with real D-Wave runs, but the headline comparison against NSGA-II is undermined by a self-constructed Pareto front and missing QUBO details. read the letter →

arxiv 2506.14129 v2 pith:UDVH2XLJ submitted 2025-06-17 cs.SE quant-ph

Shuchang Wang , Xiaopeng Qiu , Yingxing Xue , Yanfu Li , Wei Yang This is my paper · ORCID
classification cs.SEquant-ph
keywords NextReleaseProblemFeatureSelectionMulti-ObjectiveBinaryOptimizationQuantumAnnealingQUBOSearch-BasedSoftwareEngineeringParetofrontMEIdecomposition
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

Search-based software engineering's next release problem (NRP) and feature selection problem (FSP) ask for a set of requirement or feature choices that balance cost against stakeholder value, and exact solvers become impractically slow as instances grow. This paper tries to establish quantum annealing (QA) as a practical subroutine for these multi-objective problems by converting them into quadratic unconstrained binary optimization (QUBO) models. For small instances, MOQA aggregates the objectives with random weights and samples the annealer many times; for large instances, CQHA splits the QUBO into sub-problems by maximum energy impact and combines QA with a classical steepest-descent local search. On common benchmarks the QA-based methods find more non-dominated solutions than NSGA-II in most cases while cutting runtime by roughly 31% on small cases and 94% on large cases. The exact epsilon-constraint method still finds more Pareto solutions, but becomes over 100 times slower as size grows.

What carries the argument

The central machinery is the QUBO reformulation plus a decomposition-and-composition loop. For MOQA, the multi-objective problem is converted to many single-objective QUBOs by random weights; the trick is that suboptimal samples from a given weighted QUBO are retained, since they can be non-dominated for the original problem, so sampling volume and weight diversity control Pareto coverage. For CQHA, the maximum energy impact (MEI) decomposer iteratively picks the variable with the largest coefficient, follows connected quadratic terms to grow a sub-QUBO up to a size that fits the annealer's qubit connectivity, and ranks sub-QUBOs by energy so low-impact ones can be dropped; a composer then overwrites the current solution's variables with annealed sub-solutions, and steepest descent polishes the result. The paper also reports that the annealer solves random QUBOs up to 150 variables, while 200-variable QUBOs fail to embed, which is what forces the decomposition strategy.

What would settle it

Re-run MOQA and CQHA on the paper's NRP and FSP instances with the QUBO penalty coefficients multiplied by 0.1 and by 10, keeping everything else fixed: if the set of feasible non-dominated solutions changes substantially with penalty scale, the reported speed advantage rests on an unverified modeling choice. A complementary check is to grant NSGA-II the same wall-clock time as the QA methods rather than a fixed generation count; the paper's efficiency claim would be falsified if NSGA-II then recovers at least as many non-dominated solutions.

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Extended reading notes

Core claim

The paper's central claim is that quantum annealing can act as a practical, fast subroutine for two multi-objective search-based software engineering problems once they are encoded as quadratic unconstrained binary optimization (QUBO) models. MOQA handles small instances by drawing random weights, converting each weighted scalarization into a QUBO, sampling the annealer hundreds of times per weight, and keeping every sampled solution that is non-dominated in the original multi-objective sense. CQHA handles large instances by decomposing the QUBO with a maximum energy impact heuristic into sub-problems small enough to embed on current hardware, annealing each sub-problem, composing the sub-solutions, and applying steepest descent as a classical local search. On the benchmarks studied, the QA-based methods yield more non-dominated solutions than NSGA-II in most cases, with average runtime reductions of 30.8% on small cases and 94.1% on large cases, while the epsilon-constraint method still finds more Pareto solutions but becomes more than 100 times slower as instances grow.

Load-bearing premise

The load-bearing premise is that the penalty coefficients hidden inside the QUBO conversion are large enough that low-energy annealer samples are feasible, high-quality solutions of the original constrained problem, yet the manuscript does not display that conversion or the penalty magnitudes.

Editorial extensions

If this is right

  • For large-scale NRP and FSP instances where epsilon-constraint cannot finish in a reasonable time (E-Shop exceeds 72 hours in the small-scale set), MOQA and CQHA provide feasible approximate solutions in seconds to minutes.
  • CQHA finds thousands of non-dominated solutions on large FSP benchmarks like uClinux, whereas NSGA-II with 500,000 evaluations finds only dozens, so the QA-based pipeline can be used when a heuristic baseline collapses.
  • Discarding up to 70% of the low-energy sub-QUBOs can make CQHA faster and sometimes increase its non-dominated count, although it worsens the spacing of the solution set, so rate is a practical tuning knob on current hardware.
  • The annealer's embedding limit near 150-200 variables means the decomposition strategy, not the annealing time, is the current bottleneck for scaling QA-based SBSE solvers.

Reading between the lines

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

  • If the penalty-coefficient assumption holds, the same random-weight aggregation plus annealed sampling recipe could be lifted to other binary multi-objective software engineering problems, such as test-case prioritization or product-line configuration, without redesigning the solver.
  • Because CQHA's runtime falls as problem size grows from 100 to 1000 variables, most of its cost appears to be fixed decomposition and embedding overhead; that makes the speedup partly attributable to the decomposition scheme, so a classical simulated-annealing solver on the same sub-QUBOs would be a clean test of how much the quantum sampler itself contributes.
  • The MEI decomposition is lossy, so replacing it with a partition that respects the constraint graph rather than raw energy coefficients is a natural next experiment that might improve the evenness (Spacing) of CQHA's solution sets while preserving speed.
  • An equal-time comparison against NSGA-II, rather than the paper's fixed-generation settings, would separate the algorithmic advantage of QA-based search from the effect of evaluation budget.
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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

5 major / 6 minor

Summary. The paper proposes two quantum-annealing-based algorithms for the multi-objective Next Release Problem (NRP) and Feature Selection Problem (FSP): MOQA, which converts a weighted aggregation of the objectives into QUBO form and samples it on a quantum annealer, and CQHA, which decomposes large QUBOs via maximum energy impact (MEI), solves sub-QUBOs with QA, and applies steepest descent as a local search. The authors compare these methods with NSGA-II and an ILP epsilon-constraint method on standard NRP and FSP datasets, reporting execution times and quality indicators (IGD, HV, SP, and non-dominated counts). The central claim is that the QA-based methods produce more non-dominated solutions than NSGA-II while being substantially faster, and that they are the first QA-based approaches for these SBSE problems.

Significance. If established, this work would be a meaningful contribution to search-based software engineering: it offers a concrete pipeline for applying quantum annealing to two well-known multi-objective problems, uses a real D-Wave machine, and reports large wall-clock reductions over NSGA-II. The paper also has reproducible elements: open data and code repositories are named, and the runtime measurements are external rather than fitted to a model. These strengths are, however, offset by the absence of the promised QUBO derivation, an evaluation methodology in which the reference Pareto front is partly constructed by the methods being compared, and internal inconsistencies in the reported tables. The central claims are therefore promising but not yet convincingly supported.

major comments (5)
  1. [Contribution 1; Methods, Algorithms 1 and 2] The first contribution states that the authors provide the QUBO conversion of FSP and NRP constraints and its derivation, but the full text never displays the QUBO formulation, the penalty terms, or the magnitude of the penalty coefficients. Algorithms 1 and 2 invoke ModeltoQUBO(F', W, G) without specifying the resulting Hamiltonian, so a reader cannot verify that low-energy samples of the annealer correspond to feasible solutions of the original constrained problems. Every experimental table in the paper depends on this unverified modeling step, so the central algorithmic premise is currently unsupported.
  2. [Quality Indicators; Answer to RQ2 (Tables 3 and 4)] The approximate Pareto front is built from the union of the methods being compared, and in RQ2 that front is overwhelmingly composed of CQHA's own output: on classic-2, CQHA contributes 134.2 solutions while NSGA-II contributes 7.6. Consequently, CQHA's IGD=0.0 on classic-2 and its high NS counts are computed against a front that CQHA itself largely defines, making these metrics self-referential rather than independent evidence of solution quality. The paper should use a reference front that does not depend on the methods under evaluation, for example an exact epsilon-constraint front on small instances or a high-budget run of a third algorithm, or it should report pairwise dominance counts that do not rely on a union front.
  3. [Table 5 versus Tables 3 and 4] The 100% rate rows in Table 5 are internally inconsistent with the corresponding CQHA rows in Tables 3 and 4. For classic-2, Table 3 reports time 57.96 s, S=134.2, NS=134.2, IGD=0.0, and HV=0.50 for CQHA, while Table 5 reports the same time and S but NS=9.7, IGD=142.37, and HV=0.54. Similar discrepancies appear for classic-3, toybox, and uClinux. It appears that Table 5 computes metrics against a different reference front than Tables 3 and 4, but the paper does not explain this. The reader therefore cannot tell which numbers represent the headline CQHA performance, and the contradictions raise doubts about the reliability of the reported indicators.
  4. [Abstract and Table 4] The abstract claims without qualification that, compared with NSGA-II, the proposed methods 'deliver more non-dominated solutions.' This is contradicted by Table 4 on the toybox FSP dataset, where NSGA-II finds S=429.8 while CQHA finds S=375.0. The claim holds only for the NS metric, which is computed against a union front dominated by CQHA's output, and it does not hold for the raw number of non-dominated solutions. The claim needs to be qualified accordingly, or the analysis needs to aggregate results across datasets in a way that matches the actual raw counts.
  5. [Evaluation Setup; Results (Tables 1-5)] All reported quality and runtime metrics are averages without standard deviations or confidence intervals, even though RQ1 states that runs are repeated 30 times. Several comparisons are close enough that sampling variability could change the conclusion: for example, BerkeleyDB in Table 2 reports MOQA S=54.2 versus NSGA-II S=55.4, and RP in Table 1 reports MOQA time 0.64 s versus NSGA-II 0.68 s. The paper should report the distribution over repeated runs and use an appropriate statistical test to support the claimed superiority in solution count and runtime.
minor comments (6)
  1. [Throughout] There are numerous typographical and notation inconsistencies, such as 'T able' in table captions, 'Pproblems' in the Table 7 header, 'epsilon-constrain' versus 'epsilon-constraint', and 'inter-complexity' where 'time complexity' seems intended.
  2. [Algorithm 3] In Algorithm 3, line 15, 'num <- Size(SQ) * rate' is ambiguous because rate is a percentage and the result should be an integer; the paper should clarify how rounding is performed and how SelectMaxEnergySQ selects among sub-QUBOs when num is not integer.
  3. [Answer to RQ4 (Table 6)] The result that elapsed time decreases as problem size increases, for example uClinux dropping from 33.37 s at size 100 to 4.73 s at size 1000, is counterintuitive and needs a more detailed explanation than 'the decomposer proves time-consuming for small-scale problems.' As written, the observation appears to contradict the expectation that larger instances require more work.
  4. [Introduction; Abstract] The claim that this is the first application of QA to NRP and FSP should be checked against the recent literature on QUBO formulations for search-based software engineering; the reference list does not include any QA-for-SBSE work, leaving the novelty claim unverified.
  5. [Evaluation Setup; Code availability] The manuscript should state explicitly which experiments were run on real D-Wave hardware and which used classical simulation, since the code availability section refers both to a D-Wave-API-based solver and to a separate classical simulation repository.
  6. [Quality Indicators] The terms 'correct non-dominated solutions' in the definitions of S and NS are not defined; the paper should clarify whether feasibility with respect to the original constraints is verified and how dominated or infeasible solutions are excluded.

Circularity Check

1 steps flagged · score 6.0 of 10

RQ2's IGD/HV/∥NS∥ comparison is scored against an 'approximate Pareto front' that is the union of CQHA and NSGA-II outputs, so CQHA helps define the benchmark used to praise it; Table 4 shows NSGA-II actually outnumbers CQHA in raw non-dominated solutions on toybox.

  1. self definitional [Results, 'Quality Indicators' and 'Answer to RQ2' (Tables 3–4)]
    "We first calculate the approximate Pareto front by the union of all methods, and then use it to guide the calculation of ∥NS∥, HV, IGD, and SP. ... We use the solution composition of CQHA and NSGA-II to approximate the Pareto front to calculate metrics such as IGD and HV, which is logical in verifying the solution performance of the two methods."

    The reference front used to score each method is defined as the union of the outputs of the very methods being compared. For any CQHA solution that survives to the approximate front, its distance in IGD is zero by construction because that point lies in CQHA's own output; the more solutions CQHA contributes, the more zero-distance reference points it creates. The same self-membership enriches the front used for HV and ∥NS∥, so the RQ2 conclusion that 'CQHA outperforms NSGA-II' on IGD/HV and yields 'more non-dominated solutions' is not independent evidence but an artifact of defining the benchmark from the contestants' own solution sets.

full rationale

The derivation chain for the headline comparison is partially self-referential. In RQ1 the authors benchmark against the exact ε-constraint Pareto front, which is independent and appropriate. In RQ2, however, no exact front is available, and the paper explicitly constructs the reference front as the union of the two methods being compared. This makes IGD and HV partly tautological: a method's own solutions are always present in the reference set used to score it, so a method that contributes more solutions automatically creates more zero-distance reference points for its own IGD and enriches the front used for HV and ∥NS∥. The large-count advantage of CQHA in classic-2 (134.2 vs 7.6) is therefore not independent evidence of front quality. The same self-built front is also why the abstract's unconditional 'more non-dominated solutions' claim ignores Table 4, where NSGA-II's raw ∥S∥ is 429.8 vs CQHA's 375.0 on toybox. Runtime comparisons are wall-clock measurements and are not circular; the MEI citation to D-Wave and the authors' earlier NRP/FSP papers are ordinary references, not a load-bearing self-citation chain. The QUBO conversion is claimed but its derivation is not shown, which is a missing-support/verifiability issue, not circularity. On balance, the large-scale quality comparison reduces in part to the definition of the metric, so the paper is partially circular rather than fully independent.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central efficiency claim rests on an unshown QUBO conversion, a lossy decomposition, scalarization assumptions, and assumptions about hardware behavior. Each of these is an assumption the paper pulls in without independent derivation. The free parameters are chosen by hand or by hardware constraints, and the rate parameter is selected post hoc after inspecting RQ3 results.

free parameters (4)
  • rate (fraction of sub-QUBOs processed by QA in CQHA) = 100%
    Set to 100% after RQ3 showed no clear pattern across 30%, 50%, 70%, and 90%; this post hoc choice affects all CQHA results in RQ2.
  • maximum sub-QUBO size s in Decomposer = not specified in paper; adjusted downward until hardware embedding succeeds
    Controls decomposition granularity and therefore how much of the original QUBO reaches the annealer; chosen by hardware constraints rather than derived.
  • annealing time per sample = 20 microseconds
    Chosen for all QA runs; solution quality and runtime both depend on it.
  • number of random weight vectors n and samples r = n=10, r=500
    Chosen for MOQA and CQHA; controls how many linear scalarizations are solved and how densely the Pareto front is sampled.
assumptions (5)
  • ad hoc to paper NRP and FSP constraints can be represented exactly by QUBO penalty terms with coefficients large enough that infeasible solutions never have lower energy than the true constrained optimum.
    Contribution 1 promises the conversion and penalty derivation, but no explicit QUBO or penalty coefficients appear in the manuscript; the experiments silently assume such coefficients exist.
  • domain assumption A random weighted sum of the objectives, with uniformly random weights, produces samples whose non-dominated subset approximates the Pareto front.
    MOQA and CQHA scalarize multi-objective problems this way in Algorithm 1 and Algorithm 2; weighted-sum scalarization can miss non-convex Pareto regions.
  • domain assumption The MEI decomposition of a large QUBO into sub-QUBOs preserves enough of the original problem structure that composed solutions are good.
    The paper labels the decomposition lossy in the Generality of Quantum Annealing discussion, and RQ3 shows rate variation produces no consistent pattern, yet all large-scale results depend on this decomposition.
  • domain assumption D-Wave Advantage sampling at 20 microseconds returns low-energy solutions often enough for the algorithm to find high-quality non-dominated sets.
    No checks against exact optima are reported for large cases, and RQ5 shows the hardware fails to embed a 200-variable QUBO, so behavior on larger subproblems is not verified.
  • domain assumption Wall-clock time comparisons across Python with D-Wave API, Java jMetal, and CPLEX are fair measures of algorithm efficiency.
    The paper directly compares runtimes obtained with different languages, different machine access patterns, and cloud QPU overhead, as shown in Tables 1 through 4.

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Cite this review

Pith. "Pith review of A Quantum Annealing Approach for Solving Optimal Feature Selection and Next Release Problems." pith.science (2026). https://pith.science/paper/UDVH2XLJ

@misc{pith2026250614129,
  author       = {Pith},
  title        = {Pith review of: A Quantum Annealing Approach for Solving Optimal Feature Selection and Next Release Problems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UDVH2XLJ}},
  note         = {Machine review of arXiv:2506.14129}
}
abstract

Search-based software engineering (SBSE) addresses critical optimization challenges in software engineering, including the next release problem (NRP) and feature selection problem (FSP). While traditional heuristic approaches and integer linear programming (ILP) methods have demonstrated efficacy for small to medium-scale problems, their scalability to large-scale instances remains unknown. Here, we introduce quantum annealing (QA) as a subroutine to tackling multi-objective SBSE problems, leveraging the computational potential of quantum systems. We propose two QA-based algorithms tailored to different problem scales. For small-scale problems, we reformulate multi-objective optimization (MOO) as single-objective optimization (SOO) using penalty-based mappings for quantum processing. For large-scale problems, we employ a decomposition strategy guided by maximum energy impact (MEI), integrating QA with a steepest descent method to enhance local search efficiency. Applied to NRP and FSP, our approaches are benchmarked against the heuristic NSGA-II and the ILP-based $\epsilon$-constraint method. Experimental results reveal that while our methods produce fewer non-dominated solutions than $\epsilon$-constraint, they achieve significant reductions in execution time. Moreover, compared to NSGA-II, our methods deliver more non-dominated solutions with superior computational efficiency. These findings underscore the potential of QA in advancing scalable and efficient solutions for SBSE challenges.

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.