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arxiv: 2605.13324 · v1 · submitted 2026-05-13 · 🧮 math.OC · cs.NE

Recognition: unknown

TRUST-TAEA: A trustworthiness-guided two-archive evolutionary algorithm with variable-grouping sparse search for large-scale multi-objective optimization

JunYi Cui

Pith reviewed 2026-05-14 17:46 UTC · model grok-4.3

classification 🧮 math.OC cs.NE
keywords evolutionary algorithmmulti-objective optimizationlarge-scale optimizationvariable groupingarchive trustworthinesssparse searchmicrogrid schedulingIGD+
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The pith

TRUST-TAEA defines trustworthiness from evolutionary progress and archive maturity to coordinate variable-grouping sparse search in large-scale multi-objective optimization.

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

The paper proposes TRUST-TAEA to handle large-scale multi-objective problems where thousands of decision variables make it hard to balance convergence, diversity, and stability. It defines archive trustworthiness by integrating evolutionary progress with convergence-archive maturity. This signal then directs variable-grouping sparse search, anchor-probing compensatory search, and archive stabilization. Experiments on the LSMOP suite with 500 to 5000 variables and a three-objective microgrid scheduling case show superior or competitive results in convergence, diversity, and stability.

Core claim

TRUST-TAEA integrates evolutionary progress with convergence-archive maturity to produce a trustworthiness signal that coordinates variable-grouping sparse search, anchor-probing compensatory search, and archive stabilization, yielding improved performance on large-scale multi-objective benchmarks and a real-world microgrid dispatch problem.

What carries the argument

Trustworthiness signal defined by integrating evolutionary progress with convergence-archive maturity, which coordinates variable-grouping sparse search and archive stabilization.

Load-bearing premise

That integrating evolutionary progress with convergence-archive maturity produces a reliable trustworthiness signal that safely coordinates variable-grouping sparse search and archive stabilization without bias or late-stage drift.

What would settle it

A set of runs on LSMOP instances with 5000 variables where TRUST-TAEA fails to match or exceed the best existing IGD+ values would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2605.13324 by JunYi Cui.

Figure 1
Figure 1. Figure 1: Shortcomings of existing two-archive improvements in large-scale high-dimensional problems. preserving promising convergent solutions while retaining exploratory information in less represented regions. Recent studies have further extended two-archive algo￾rithms by designing archive updating criteria [26], archive coordination strategies [27], and search mechanisms [28]. For example, Hu et al. [29] propos… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the archive trustworthiness guidance mechanism. normalized objective space: 𝑀𝑡 cov = |(𝐶 𝑡 )| 𝐵 , (23) where (𝐶 𝑡 ) is the set of occupied bins or reference direc￾tions and 𝐵 is the total number of bins or directions. Third, a shape-related maturity term is used to penalize fragmented or collapsed fronts: 𝑀𝑡 shape = 1 1 + 𝜅(𝐾𝑡 seg − 1) , (24) where 𝐾𝑡 seg is the number of detected front s… view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the trustworthiness-guided variable-grouping sparse search mechanism. 𝐾 𝑡 𝑎 = ⌈ 𝐾min + (𝐾max − 𝐾min) 𝑡 ⌉ , (28) 𝜌 𝑡 = 𝜌min + (𝜌max − 𝜌min) 𝑡 , (29) here, 𝑃 𝑡 explore, 𝐾𝑡 𝑎 , and 𝜌 𝑡 denote the exploration probability, the number of active variable groups, and the structural repair strength, respectively. The parameters satisfy 0 ≤ 𝑃min < 𝑃max ≤ 1, 1 ≤ 𝐾min ≤ 𝐾𝑡 𝑎 ≤ 𝐾max ≤ 𝐾, 0 ≤ 𝜌min < 𝜌m… view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of the trustworthiness-guided anchor-probing compensatory search mechanism. Require: convergence archive 𝐶 𝑡 , archive trustworthiness  𝑡 , evolutionary progress 𝑝 𝑡 , variable-structure infor￾mation  Ensure: compensation offspring set 𝑡 probe 1: if 𝑝 𝑡 < 𝑝start then 2: return ∅ 3: end if 4: Compute nondominated ratio 𝑟 𝑡 nd = |ND(𝐶 𝑡 )|∕|𝐶 𝑡 | 5: Compute compensation intensity 𝛿 𝑡 by Eq. (… view at source ↗
Figure 5
Figure 5. Figure 5: The true Pareto fronts obtained for LSMOP4, LSMOP8, and LSMOP9 with 5000 decision variables under the 2-objective setting. results, whereas TRUST-TAEA consistently maintains rel￾atively small IGD+ values. Nevertheless, TRUST-TAEA is not always the best on every problem; for example, some competing algorithms achieve smaller IGD+ values on parts of LSMOP2 and LSMOP4. Overall, the IGD+ results in￾dicate that… view at source ↗
Figure 6
Figure 6. Figure 6: The true Pareto fronts obtained for LSMOP4, LSMOP8, and LSMOP9 with 5000 decision variables under the 3-objective setting. First Author et al.: Preprint submitted to Elsevier Page 13 of 19 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Overall sensitivity of TRUST-TAEA to 𝜆exp and 𝑝start [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Dimension-wise sensitivity of TRUST-TAEA to 𝜆exp and 𝑝start. both the two-objective and three-objective settings. Specif￾ically, AMRCSO shows strong competitiveness in the two￾objective case, while in the three-objective case, both AM￾RCSO and MSCSO are able to obtain high-quality dis￾tributed solution sets. However, in comparison, the solu￾tion sets produced by TRUST-TAEA exhibit a better over￾all balance… view at source ↗
Figure 9
Figure 9. Figure 9: Problem-wise sensitivity of TRUST-TAEA to 𝜆exp on LSMOPs. In contrast, 𝑝start has a stronger and clearly objective￾dependent effect. For the two-objective problems, the best average IGD+ value is obtained when 𝑝start = 0.05, where it decreases to 0.06019, representing an improvement of approximately 20.5% over the default setting of 𝑝start = 0.12. For the three-objective problems, the best setting shifts t… view at source ↗
Figure 10
Figure 10. Figure 10: Problem-wise sensitivity of TRUST-TAEA to 𝑝start on LSMOPs [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Representative dispatch schedule obtained by TRUST￾TAEA in its best run on the three-objective microgrid dispatch problem. In panel (a), the black, green, blue, and brown curves denote the load demand, available renewable power, grid purchase power, and generator output, respectively. In panel (b), the blue and red bars represent battery charging and discharging power, respectively, where charging power i… view at source ↗
read the original abstract

Large-scale multi-objective optimization remains challenging because high-dimensional decision spaces, complex variable interactions, and limited function evaluation budgets make it difficult to balance convergence, diversity, and stability. Existing two-archive evolutionary algorithms can alleviate the conflict between convergence and diversity, but they often underuse archive reliability and problem-structure information, leading to inefficient search, incomplete front coverage, and late-stage archive drift. To address these issues, this paper proposes TRUST-TAEA, a trustworthiness-guided two-archive evolutionary algorithm. Archive trustworthiness is defined by integrating evolutionary progress with convergence-archive maturity, and is used to coordinate variable-grouping sparse search, anchor-probing compensatory search, and archive stabilization. TRUST-TAEA is evaluated on the LSMOP benchmark suite with 500--5000 decision variables and two or three objectives. Experimental results show that TRUST-TAEA achieves superior or highly competitive performance in terms of convergence, diversity, and stability. A three-objective day-ahead scheduling case of a grid-connected microgrid further demonstrates its practical applicability, where TRUST-TAEA obtains the best IGD$^+$ value and generates a feasible dispatch strategy balancing cost, emissions, and grid-power fluctuation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces TRUST-TAEA, a trustworthiness-guided two-archive evolutionary algorithm for large-scale multi-objective optimization. Archive trustworthiness is defined by combining evolutionary progress with convergence-archive maturity; this signal coordinates variable-grouping sparse search, anchor-probing compensatory search, and archive stabilization. The algorithm is evaluated on the LSMOP benchmark suite (500–5000 decision variables, 2–3 objectives) and on a three-objective day-ahead microgrid scheduling instance, where it is reported to achieve superior or highly competitive IGD+ values together with improved convergence, diversity, and stability.

Significance. If the empirical claims are substantiated by complete experimental protocols and statistical validation, the work offers a practical extension of two-archive EAs that incorporates problem-structure information via variable grouping. The trustworthiness mechanism is a plausible way to mitigate late-stage archive drift, and the microgrid case study demonstrates applicability. Reproducibility would be strengthened by public code and explicit parameter settings; absent those, the contribution remains incremental rather than transformative.

major comments (2)
  1. [Section 5] Experimental protocol (Section 5): the abstract and results claim superior performance on LSMOP instances, yet the number of independent runs, the statistical tests employed (e.g., Wilcoxon or Friedman), and the procedure for tuning the trustworthiness integration weights and variable-grouping parameters are not stated. These omissions are load-bearing for the central empirical claim.
  2. [Section 3.2] Definition of trustworthiness (Section 3.2): the integration of evolutionary progress and convergence-archive maturity is described at a high level but lacks an explicit mathematical formulation (e.g., the precise weighting function or normalization). Without this, it is impossible to verify that the measure is independent of the performance metrics reported later.
minor comments (2)
  1. Notation for IGD+ should be defined at first use and the reference implementation cited.
  2. Figure captions for convergence plots should include the number of function evaluations on the x-axis and the exact metric on the y-axis.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We sincerely thank the referee for the constructive comments, which help improve the clarity and rigor of the manuscript. We will revise the paper to address both major points by adding the missing experimental details and the explicit mathematical formulation of trustworthiness.

read point-by-point responses

  1. Referee: [Section 5] Experimental protocol (Section 5): the abstract and results claim superior performance on LSMOP instances, yet the number of independent runs, the statistical tests employed (e.g., Wilcoxon or Friedman), and the procedure for tuning the trustworthiness integration weights and variable-grouping parameters are not stated. These omissions are load-bearing for the central empirical claim.

    Authors: We agree that these protocol details are necessary to substantiate the empirical claims. In the revised manuscript we will add a new paragraph in Section 5 stating that all algorithms were run for 30 independent trials on each LSMOP instance, that statistical significance was assessed via the Wilcoxon signed-rank test at the 0.05 level, and that the trustworthiness weights (w1 = 0.6 for progress, w2 = 0.4 for maturity) together with the variable-grouping threshold were selected by a grid search performed on a held-out subset of LSMOP problems with 1000 variables. A table of all fixed parameter values will also be included. revision: yes

  2. Referee: [Section 3.2] Definition of trustworthiness (Section 3.2): the integration of evolutionary progress and convergence-archive maturity is described at a high level but lacks an explicit mathematical formulation (e.g., the precise weighting function or normalization). Without this, it is impossible to verify that the measure is independent of the performance metrics reported later.

    Authors: We acknowledge the description in Section 3.2 is insufficiently precise. We will insert the explicit definition T = w1 · P + w2 · M, where P = (IGD_{t-1} − IGD_t) / IGD_{t-1} is the normalized generational progress (clipped to [0,1]) and M = |C_non-dom| / |C| is the maturity ratio of the convergence archive. The weights are fixed at w1 = 0.6, w2 = 0.4 after the tuning procedure described above. Because both P and M are computed from intermediate population statistics during evolution, the resulting T is independent of the final IGD+ values reported in the experiments. The revised section will also contain the corresponding pseudocode. revision: yes

Circularity Check

0 steps flagged

Minor self-citation present but derivation remains independent of inputs

full rationale

The paper constructs TRUST-TAEA by defining archive trustworthiness from evolutionary progress and convergence-archive maturity, then using that signal to coordinate variable-grouping sparse search and stabilization. These design choices are stated as heuristic integrations rather than derived from the LSMOP or microgrid performance numbers. No equation or definition reduces a reported IGD+ value or convergence claim back to a fitted parameter or self-citation chain by construction. The central claims rest on empirical evaluation of an independently specified algorithm, so the derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the effectiveness of the newly defined trustworthiness measure and the variable-grouping operator; these are introduced without external independent validation beyond the reported experiments.

free parameters (2)
  • trustworthiness integration weights
    Weights combining evolutionary progress and archive maturity are introduced to define trustworthiness and must be set for the algorithm to function.
  • variable grouping parameters
    Parameters controlling how variables are grouped for sparse search are required and likely tuned to the problem class.
axioms (1)
  • domain assumption Standard evolutionary algorithm assumptions hold, including that population-based selection and variation improve solution quality over generations.
    Implicit foundation for all evolutionary algorithm claims in the abstract.
invented entities (1)
  • Archive trustworthiness measure no independent evidence
    purpose: To coordinate between convergence and diversity archives and decide search strategy allocation.
    Newly defined construct based on evolutionary progress and maturity; no independent evidence outside the paper's experiments.

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