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REVIEW 3 major objections 5 minor 108 references

Benchmarking global optimization techniques for unmanned aerial vehicle path planning

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper argues that UAV path-planning instances, generated from random terrains with cylindrical threats, form a distinct and reusable real-world benchmark family, and that on these problems the top evolutionary algorithms from recent…

desk verdict The UAV benchmark suite is a real addition to the field, and the comparison is mostly sound, but the best-found baseline with a hard infeasibility penalty means the rankings partly measure feasibility, not objective-function quality. read the letter →

arxiv 2501.14503 v1 pith:DUH2ZAQF submitted 2025-01-24 cs.NE cs.ROmath.OC

Mhd Ali Shehadeh , Jakub Kudela This is my paper · ORCID
classification cs.NEcs.ROmath.OC
keywords unmannedaerialvehiclepathplanningglobaloptimizationbenchmarkingexploratorylandscapeanalysisvariabledimensionevolutionarycomputationDIRECTalgorithm
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 argues that UAV path planning, formulated as a continuous black-box optimization problem with 56 hand-picked instances, is a useful addition to global optimization benchmark suites. The instances, generated from random terrains with cylindrical threats, have landscape features that differ clearly from established BBOB, CEC, and ABS problems. In computational comparisons across four dimensions and three budgets, the best performers are consistently top-ranked evolutionary methods from recent numerical-optimization competitions—EA4eig, APGSK, and ELSHADE—rather than deterministic DIRECT-type methods. The paper also shows that the problem's dimension can vary, and that most best-found solutions occur at the lowest dimension. If true, this gives the optimization community a reusable real-world benchmark family with a largely unexplored variable-dimension characteristic.

What carries the argument

The central object is a problem-instance generator producing 56 UAV path-planning instances: 28 randomly generated terrains, each with 15 or 30 cylindrical threats, combined with a weighted four-criterion cost function (path length, obstacle avoidance, altitude limits, and smoothness) whose decision variables are the waypoint coordinates. The argument is carried by comparing these instances to established benchmark suites through Exploratory Landscape Analysis (ELA) features, and by evaluating twelve solvers with relative error to the best-found solution, number of wins, and Friedman ranks across dimensions 15, 30, 45, 60 and budgets $10^3$, $10^4$, $10^5$ function evaluations.

What would settle it

For a given terrain, construct an instance whose optimal path is known (e.g., place all threats so the straight line from start to goal is feasible and optimal) and check whether the relative-error rankings of EA4eig, APGSK, and ELSHADE against the true optimum reproduce the rankings the paper reports against best-found solutions.

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Extended reading notes

Core claim

The central claim is that the generated UAV path-planning problems form a distinct, reusable benchmark family whose landscape characteristics are unlike those of the BBOB, CEC, and ABS suites, and that on these problems the best-performing methods are almost universally the top evolutionary algorithms from recent numerical-optimization competitions. At large computational budgets, EA4eig and APGSK consistently have the lowest Friedman ranks, with statistically significant advantages over most other methods, while ELSHADE, LSHADE, and SPSO also perform well in specific settings; deterministic DIRECT-type methods (BIRMIN, I-DTC-GL) and simple local search (NM) lag behind, especially as dimension and budget grow. The conclusion is stated on the paper's own terms: the UAV instances 'may form an interesting addition to the established benchmark suits.'

Load-bearing premise

The global optima of the 56 instances are unknown, so all relative-error metrics and rankings are computed against the best solution found by any method on each instance; if those best-found solutions are far from the true optima, or if all methods fail similarly on hard instances, the reported rankings may not reflect true performance.

Editorial extensions

If this is right

  • The 56 UAV instances are a reusable benchmark family: code and data are publicly released, so other researchers can run the same problems without re-implementing the generator.
  • On these instances, method rankings depend on both dimension and computational budget, so benchmarks that test only a single budget or dimension will miss the patterns.
  • The variable-dimension view of the problem favors starting at low dimension ($D_V=5$) and refining: in most cases best-found solutions come from the lowest-dimension setting, and higher dimensions rarely compensate for added difficulty.
  • For large budgets, the performance gap between many methods narrows, but APGSK and EA4eig remain consistently ahead.
  • High-density threat instances are harder and show larger improvements when the budget grows, because methods need more evaluations to escape infeasible or locally optimal corridors.

Reading between the lines

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

  • Because the global optima are unknown, the rankings are relative to the best-found solution; a direct extension would be to construct instances with known optimal paths (e.g., by placing threats so the straight line is optimal) to check whether the reported ordering holds under an absolute reference.
  • The variable-dimension finding suggests a practical recipe for UAV path planning: start with few waypoints to find a feasible corridor, then refine with more waypoints; this could be tested as a standalone 'variable-dimension' method and compared against fixed-dimension baselines.
  • The landscape-uniqueness result implies that these instances may expose failure modes hidden by artificial benchmarks; a concrete way to check this is to see whether methods tuned on established suites degrade less or more on UAV instances relative to their landscape-similar artificial functions.
  • Porting the MATLAB generator to other languages and to established profiling platforms would let the community measure per-run behavior (e.g., anytime curves) rather than only final errors.
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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 / 5 minor

Summary. The paper proposes a benchmark suite of 56 UAV path-planning instances generated from 28 hand-picked terrains with two threat densities, and compares 12 global optimization methods (DIRECT-type, classical EC, and recent CEC competition winners) under four dimensionalities (DV=5,10,15,20) and three computational budgets (B=1e3,1e4,1e5). The authors use Exploratory Landscape Analysis (ELA) to argue that the instances are distinct from BBOB, CEC, and ABS benchmark functions, and they report mean relative errors, numbers of best-found solutions, Friedman ranks, and Wilcoxon tests with Holm correction. They find that EA4eig, APGSK, and ELSHADE are the best-performing methods overall, and they discuss the variable-dimension nature of the problem, concluding that solving in lower dimensions is generally more beneficial.

Significance. If the results hold, the proposed UAV instances could serve as a reusable real-world benchmark family, addressing the need for non-artificial test problems in global optimization. The paper provides a public Zenodo repository with code, data, and instance generation routines, which is a valuable asset for reproducibility. The finding that recent CEC-winning evolutionary algorithms outperform DIRECT-type deterministic methods on these discontinuous, constrained landscapes is of interest to both the evolutionary computation and path-planning communities. The variable-dimension investigation is a useful step toward a largely under-studied benchmark scenario. However, the validity of the quantitative conclusions depends on the choice of reference baseline and on the experimental design; these issues are addressed in the major comments.

major comments (3)
  1. [Section 4, first paragraph; Eq. (2)] The performance metric is defined as the relative error of a method's best-found solution to the best-found solution across all methods in that setting. Because the objective contains the hard infeasibility penalty Jpen=1e4, instances on which no method finds a feasible path (e.g., terrain 32 in Fig. 6d) have an infeasible reference solution with objective value above the cliff. On such instances, the relative errors measure degrees of infeasibility rather than closeness to the unknown optimum, and a method that finds a feasible path would have a negative relative error under the formula given in the text. Since all quantitative conclusions (mean relative error, number of wins, Friedman ranks, Wilcoxon tests) are computed against this baseline, the abstract's claim that the best-ranking methods are 'almost universally' the top CEC evolutionary techniques is not established for hard instances. The authors should report feasibility rates separately, compute relative errors against the best feasible solution found by any method across all settings, and verify whether the qualitative rankings survive this re-analysis.
  2. [Section 3.2] All methods are run once per instance and setting, starting from an identical random seed. For stochastic global optimizers, a single run provides no information about run-to-run variability, and the Wilcoxon signed-rank tests in Tables 2, 4, and 6 are based on a single paired sample per method, so the reported significance results may not be robust to the choice of seed. The authors should either run multiple independent repetitions (e.g., 10 or more) and report median/mean values with appropriate variance-aware statistical tests, or they should justify the single-run design by, for example, demonstrating low variance on a subset of instances. This is load-bearing because the central ranking claims depend on statistical significance assertions.
  3. [Section 2.1; Section 2.3] The 56 instances are selected from a pool of 5000 by 'hand-picking twenty-eight terrains that displayed interesting and real-life looking characteristics' without quantitative selection criteria. This makes the instance selection subjective and not independently reproducible, and it may bias the ELA-based novelty analysis toward instances that appear unique by construction. The authors should either specify a quantitative selection procedure (e.g., based on terrain roughness statistics, obstacle coverage, or ELA feature values) or provide the full set of selection criteria so that readers can assess whether the claimed separation from BBOB/CEC/ABS suites is an artifact of hand-picking.
minor comments (5)
  1. [Throughout] There are several typos: 'AUV path planning' in Section 1 should be 'UAV path planning'; 'threads' appears in place of 'threats' in the discussion of Fig. 7 and in the text near Table 8; 'nad' in Section 2.2.2 should be 'and'; and the statistical test caption says 'Wilcoxon text' instead of 'Wilcoxon test'.
  2. [Section 4, first paragraph] The term 'relative error' is a misnomer when the reference is a best-found solution rather than a known optimum; consider using 'relative deviation from the best-found solution' or 'performance ratio' to avoid implying ground-truth error.
  3. [Tables 2, 4, and 6] The text says 'The only two methods for which no statistically significant difference from the best method (EA4eig) was found were APGSK (for DV=5) and LSHADE (for DV={5,15})' for B=1e3, but Table 2 shows LSHADE DV=15 with p*=0.0503, which is exactly the significance level; this borderline result should be reported with caution.
  4. [Section 4, variable dimension analysis] In Table 7, the best-found solutions for each DV are taken from methods that may have used different budgets and may have been truncated by the three-hour limit for B=1e5; this should be stated more prominently so that the comparison across DV values is interpreted with the appropriate caveats.
  5. [Section 2.3] The ELA computations use uniform sampling with 250*dim samples in dim=30, which is a relatively small sample for a 30-dimensional discontinuous objective; the authors should discuss whether the ELA features are stable with respect to sample size, especially given the Jpen=1e4 discontinuity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the UAV benchmark ranking is an empirical result with independent algorithm provenance; self-citations are contextual, not load-bearing.

full rationale

The paper's central claim is an empirical observation: on 56 newly generated UAV instances, certain CEC-winning evolutionary methods rank best. This ranking is not derived from a fitted parameter or from the authors' own prior conclusions. The objective function (Eq. 9) is fixed, the terrain instances are generated from an external tool, and the 12 compared algorithms are independently published methods with CEC provenance. The relative-error metric is computed against the best-found solution across methods because the global optima are unknown (Section 4, first paragraph); this is a comparison baseline, not a fitted prediction, so it does not constitute circularity. The infeasibility cliff (Jpen = 1e4, Eq. 2) and the terrain-32 case where no method finds a feasible path are correctness and robustness concerns about the benchmark, not circular steps. Self-citations appear in the paper: [64] is used to select methods, [34] is cited to motivate real-world benchmark suits, and [56] is the code repository. None of these is the evidence for the headline claim; the ELA-based novelty claim is computed with flacco features and compared against established suites, not assumed from a citation. Thus no step reduces to its own input, and no load-bearing self-citation chain forces the reported result.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The UAV benchmark inherits its cost model and penalties from prior work; the only free constants are the adopted objective weights and penalty parameters. The new content is the instance generator and the 56 selected instances, not a new physical model. The main structural assumptions are about the representativeness of the cost model, the sufficiency of single-run evaluations, and the best-found reference for unknown optima.

free parameters (1)
  • Objective function weights b1-b4, smoothness penalties beta1-beta2, Jpen=1e4, danger-zone margin S, UAV diameter D = Adopted from [9,59]; values not re-fit
    These constants define the cost landscape of all 56 instances; the benchmark properties and method rankings are conditional on them.
assumptions (5)
  • domain assumption The UAV path-planning cost model of [9,59] (path length, cylindrical threats, altitude bounds, smoothness penalties) adequately represents real UAV path planning.
    Adopted in Section 2.2; the benchmark's validity rests on this model being representative.
  • domain assumption A single run per method-instance-budget-dimension combination, using an identical random seed, gives a representative performance estimate.
    Section 3.2 states all methods started from an identical random seed; no repeated runs or variance estimates are provided.
  • domain assumption ELA features computed from 250*dim uniform samples in dim=30 capture the relevant landscape differences between the UAV instances and established suites.
    Section 2.3 uses flacco features and PCA/TSNE/UMAP; the novelty claim is based on these sampled features.
  • domain assumption The best-found solution across methods is a suitable reference for the unknown global optimum when computing relative errors.
    Section 4 explicitly uses this reference; rankings depend on it.
  • standard math The Wilcoxon signed-rank test with Holm-Bonferroni correction provides valid inference for the paired comparisons.
    Used in Section 4 to decide statistically significant differences between methods; assumes paired data from the 56 instances are exchangeable under the null.

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Pith. "Pith review of Benchmarking global optimization techniques for unmanned aerial vehicle path planning." pith.science (2026). https://pith.science/paper/DUH2ZAQF

@misc{pith2026250114503,
  author       = {Pith},
  title        = {Pith review of: Benchmarking global optimization techniques for unmanned aerial vehicle path planning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DUH2ZAQF}},
  note         = {Machine review of arXiv:2501.14503}
}
read the original abstract

The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We devise a problem instance generator and pick 56 representative instances, which we compare to established benchmarking suits through Exploratory Landscape Analysis to show their uniqueness. For the computational comparison, we select twelve well-performing global optimization techniques from both subfields of stochastic algorithms (evolutionary computation methods) and deterministic algorithms (Dividing RECTangles, or DIRECT-type methods). The experiments were conducted in settings with varying dimensionality and computational budgets. The results were analyzed through several criteria (number of best-found solutions, mean relative error, Friedman ranks) and utilized established statistical tests. The best-ranking methods for the UAV problems were almost universally the top-performing evolutionary techniques from recent competitions on numerical optimization at the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation. Lastly, we discussed the variable dimension characteristics of the studied UAV problems that remain still largely under-investigated.

Figures

Figures reproduced from arXiv: 2501.14503 by the authors.

Figure 1
Figure 1. General scheme of the adopted approach. Shehadeh and Kudela: Preprint submitted to Elsevier Page 3 of 23 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. A Side view of four generated terrains with 900 pixels. The black rectangle/circle resembles the start/goal points respectively. The red cylinders represent the threats that the UAV must avoid. 2.2. Objective Function Formulation The objective function can be defined as a mathematical formula accommodating specific requirements that need to be optimized. In our case, we adapt the objective function proposed in [59] … view at source ↗
Figure 3
Figure 3. Different scenarios considered in the penalty function 𝑇𝑘 for UAV passing a line segment from point 𝑃𝑖𝑗 to 𝑃𝑖,𝑗+1. The red circle represents the area of collision with penalty 𝐽pen, while the yellow circle indicates the surrounding dangerous zone. . 2.2.2. Obstacle Avoidance Cost Beyond path-length optimality, the planned path must prioritize the safety of UAV operations. This involves deftly maneuvering around pote… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: UAV’s turning angle and climbing angle. The dark green points denote the waypoints 𝑃𝑖𝑗, with their projection on the terrain colored light green, and the projection on the horizontal plane represented by black points 𝑃 ′ 𝑖𝑗. 𝑃 ′′ 𝑖,𝑗+1 is the projection of 𝑃𝑖,𝑗+1 onto …
Figure 5
Figure 5. Figure 5: Visualization of the ELA features using different dimension reduction techniques. 3. Selected Optimization Methods and Experimental Setup As 𝐹 is a nonlinear and nonconvex function, solving it using classic methods is not feasible. Instead, various global optimization …
Figure 6
Figure 6. Figure 6: Resulting trajectories and objective function values of the different methods in 𝐵 = 1𝑒4, 𝐷𝑉 = 10 setting. Lastly, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Convergence plots of the different methods in 1E4, DV10 setting [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Boxplots of the relative errors of the selected methods in different dimensions with 𝐵 = 1𝑒3. To perform a more in-depth statistical comparison of the selected algorithms, we followed the guidelines published in [65]. The results of this comparison are in [PITH_FULL_I…
Figure 9
Figure 9. Figure 9: Boxplots of the relative errors of the selected methods in different dimensions with 𝐵 = 1𝑒4. Shehadeh and Kudela: Preprint submitted to Elsevier Page 14 of 23 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Boxplots of the relative errors of the selected methods in different dimensions with 𝐵 = 1𝑒5. main exceptions are APGSK and EA4eig, which perform much better than the rest, and EBOwCMAR, which has the highest relative errors. This is also somewhat true for the other 𝐷…
Figure 11
Figure 11. Figure 11: The trajectories and objective function values of the best methods in different dimensions, 𝐵 = 1𝑒4. methods needed more than three hours of computation and therefore were truncated far before reaching the 𝐵 = 1𝑒5 call limit (meaning that the function calls are actual…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.