Customized Exploration of Landscape Features Driving Multi-Objective Combinatorial Optimization Performance

Ana Nikolikj; Gabriela Ochoa; Tome Eftimov

REVIEW 3 major objections 4 minor 41 references

Customized Exploration of Landscape Features Driving Multi-Objective Combinatorial Optimization Performance

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that the number of interactions $k$ dominates how hard $\rho$mnk-landscapes are for PLS, GSEMO, and NSGA-II, and that the PLOS-net, C-PLOS-net, and funnel feature sets must be combined to explain why.

desk verdict Competent, incremental footprint analysis whose central k-hardness claim is under-supported by missing surrogate accuracy and a thin 18-instance visual check. read the letter →

arxiv 2507.01638 v1 pith:IHYL52ER submitted 2025-07-02 cs.NE cs.AI

Ana Nikolikj , Gabriela Ochoa , Tome Eftimov This is my paper

classification cs.NEcs.AI

keywords landscapeanalysismulti-objectivecombinatorialoptimizationalgorithmfootprintsfeatureimportanceSHAPρmnk-landscapesC-PLOS-net

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 asks which landscape features make multi-objective combinatorial optimization problems hard for specific algorithms. Working with small $\rho$mnk-landscapes (binary strings of length 16, two or three objectives, interaction counts $k\in\{1,2,4\}$, objective correlations $\rho\in\{-0.4,0,0.4\}$), it trains a multi-target regression model to predict the resolution and hypervolume achieved by Pareto Local Search, GSEMO, and NSGA-II from 41 landscape features. It then converts the model's predictions into per-instance, per-algorithm feature-importance vectors with SHAP, clusters those vectors, and reads off which feature combinations drive performance in each performance region. The central claim is that the number of interactions is the most influential benchmark parameter: $k=1$ instances are easy and $k=4$ instances are hard, while objective count and correlation play secondary roles. The paper also claims that the PLOS-net, C-PLOS-net, and funnel feature groups are complementary and that their combination, not any single group, is what explains performance on particular landscape-algorithm pairs.

What carries the argument

The carrying mechanism is the algorithm-footprint pipeline. A multi-target regression model predicts the performance of all three algorithms from one 41-dimensional feature vector per instance; SHAP values turn the trained model into a per-instance, per-algorithm vector of local feature importances (a meta-representation); hierarchical clustering groups these meta-representations into 14 performance regions; and the aggregated feature importances per region define each algorithm's footprint. The features themselves come from three named network models of the search space: PLOS-net, its compressed form C-PLOS-net, and funnel metrics based on non-dominated sorting ranks. The pipeline is what allows landscape features to be tied to algorithm behavior locally rather than through a single global importance ranking.

What would settle it

Report the test-set R-squared and mean absolute error of the multi-target regression model, or replace the random forest with a linear or neural surrogate and rerun the SHAP footprint pipeline; if the footprints change substantially, or if the surrogate explains little variance, then the claimed dominance of $k$ and the per-cluster feature combinations are artifacts of the model rather than properties of the landscapes and algorithms.

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Extended reading notes

Core claim

The paper's central claim is that, on this benchmark suite, the number of interactions $k$ is the dominant determinant of instance hardness for all three algorithms under the resolution metric. Instances with $k=1$ sit in the high-performance region of the footprint plots and instances with $k=4$ in the low-performance region, independent of objective correlation and objective count. A second claim is that the three landscape-feature families—the 24 PLOS-net features, the 10 C-PLOS-net features, and the seven funnel features—carry complementary information: the best predictive model uses a selected subset drawn from all three, and the combined set is what becomes significant for specific landscapes. A third claim is that different algorithms reach similar performance on the same landscape for different reasons, visible as distinct clusters of SHAP feature importance, and that two newly added funnel features, pos_num and pos_strength, appear among the top-ranked features across nearly all landscapes.

Load-bearing premise

Everything rests on the trained prediction model being accurate enough that the SHAP importance scores it produces reflect how the algorithms really behave, but the paper asserts this accuracy is good without reporting the model's numerical error.

Editorial extensions

If this is right

For the resolution metric, instance hardness on $\rho$mnk-landscapes is set mainly by $k$: $k=1$ instances are easy across the portfolio, $k=4$ instances hard, and $m$ with $\rho$ play secondary roles.
A single feature family (PLOS-net, C-PLOS-net, or funnel features alone) is not enough; the best predictive model combines all three families, so future feature engineering for this benchmark family should treat them as complements.
The two new funnel features, pos_num and pos_strength, are consistently top-ranked in nearly all landscapes, making them candidate cheap indicators of hard instances.
PLS, GSEMO, and NSGA-II have genuinely different footprints: PLS excels on negatively correlated three-objective landscapes with few interactions while NSGA-II struggles there, and the ordering reverses on two-objective landscapes, so algorithm portfolios benefit from all three.

Reading between the lines

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

If the dominance of $k$ transfers beyond $n=16$, algorithm selection for $\rho$mnk-landscapes could be stratified by interaction density before expensive network features are computed, and benchmark generators could use $k$ as the primary hardness axis.
The paper notes that hypervolume-based footprints produce different top feature sets and less algorithm complementarity; a direct comparison of resolution and hypervolume footprints on the same instances could show whether the 'k dominates' claim is metric-dependent.
Because the footprints come from one surrogate model, an ablation that trains the same SHAP pipeline on each feature group in isolation, or on permuted labels, would test how much of the reported complementarity is a property of the landscapes rather than of the random forest.
The same footprint machinery could be applied to larger $\rho$mnk instances or other combinatorial structures such as multi-objective QAP instances, where the paper itself notes data collection is the main barrier.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, this is a competent, mostly incremental application of the authors' own algorithm-footprint pipeline to rmnk-landscapes, with two genuinely new funnel features and a first per-landscape/per-algorithm feature-importance analysis. Second, the paper's headline—k as the dominant hardness driver—is asserted from visual inspection of SHAP plots over 18 test instances, and the surrogate model's accuracy is never reported. The claim may well be right; the evidence as written is not enough to carry it.

What's new and good: pos_num and pos_strength are new, defined independently of algorithm performance, and the code and data are released. The train/test split is clean, SFFS and hyperparameter tuning are standard, and the clustering/footprint analysis is a reasonable way to look for problem/algorithm interactions. The paper is honest that hv results are in the repository. No circularity: features are computed from full enumeration, not from algorithm runs.

Soft spots, in proportion. The missing MAE/R2 is the biggest one. Section 4 says the final model is evaluated on the test set with MAE and R2; Section 6 says predictions 'despite minor errors' approximate ground truth; no numbers appear. Without them, SHAP-based feature importance and the k conclusion are only as trustworthy as an unvalidated surrogate. SHAP tells you what the model uses, not directly what the landscape does to the algorithms. A simple scatter of ground-truth reso vs. k for the 18 test instances would go a long way. Also, 18 instances—one per parameter combination, with no error bars—is thin for a claim about 'the most influential benchmark parameter,' even if the pattern looks clear in the PCA plots. The qualitative reading of SHAP decision plots in Figures 4–6 is also a bit freewheeling; it is plausible but not tightly argued.

None of this is fatal. The pipeline is coherent, the code is available, and the feature-importance decompositions could be useful to people working on MOO benchmark design. The fix is reporting: add test-set accuracy, add a ground-truth check on k, and show that the cluster-level feature importances are stable across the 10 instances per parameter combination rather than one test instance each.

Who it's for: researchers in multi-objective landscape analysis and automated algorithm selection on rmnk-landscapes. It deserves a serious referee; I'd send it out with a request for the missing validation, not desk reject.

Referee Report

3 major / 4 minor

Summary. The paper proposes an 'algorithm footprint' analysis pipeline for multi-objective combinatorial optimization. It trains a multi-target regression (MTR) Random Forest to predict the performance of PLS, GSEMO, and NSGA-II on ρMNK-landscapes from 41 landscape features (24 PLOS-net, 10 C-PLOS-net, and 7 funnel features, including two newly proposed ones). SHAP values provide local feature importances, which are clustered hierarchically to form performance regions and algorithm footprints. The central empirical claims are that the number of interactions k is the most influential benchmark parameter for problem hardness, and that combining feature sets (PLOS-net, C-PLOS-net, funnel) is essential for understanding algorithm-specific behavior. The hypervolume analysis is mentioned but deferred to a repository.

Significance. If the findings are valid, the paper contributes a per-instance, per-algorithm tool for comparing MOO algorithms and a concrete observation about ρMNK-landscape hardness, which would be of interest for benchmark design and algorithm selection. The data and code are publicly available, which is a reproducible strength. However, the central conclusions rest on SHAP values from a surrogate model whose predictive accuracy is never numerically reported, and on visual patterns in only 18 test instances. The manuscript is clearly written and the methodology is standard, but the evidence for the headline claims is currently incomplete. With added validation of the surrogate and direct ground-truth checks, the contribution would be substantial for the meta-learning and landscape analysis community.

major comments (3)

[Section 4 and Section 6] The manuscript states in Section 4 that the final MTR model is evaluated on the test set using Mean Absolute Error (MAE) and R-squared (R2), and in Section 6 that 'Algorithm footprints are based on MTR model predictions, which, despite minor errors, closely approximate ground-truth reso performance,' but no numeric values for MAE or R2 appear anywhere in the paper. Since every subsequent conclusion in Section 5 is derived from SHAP values of this surrogate model, the absence of any measure of predictive accuracy makes it impossible to judge whether the footprint patterns reflect true algorithm performance or artifacts of the model's errors. The authors should report the test-set and cross-validation MAE/R2 for the selected RF model and for the compared baselines, so that the central claim can be assessed.
[Section 5.1.1, Figure 2] The conclusion that 'the k benchmark parameter has the most influence on the hardness of the problem instances for the three algorithms' is based on visual inspection of PCA-projected SHAP meta-representations of only 18 test instances. This is a qualitative pattern, not a quantitative analysis: the paper provides no separation measure, no error bars, and no statistical test linking k to ground-truth reso. Moreover, SHAP values explain the model's predictions, not necessarily ground-truth performance; a systematic bias of the surrogate with respect to k would produce exactly the observed separation. To make the claim load-bearing, the authors should add a direct analysis of ground-truth reso as a function of k (e.g., an ANOVA or a per-instance plot with variability), and/or validate that the SHAP importance patterns on held-out instances match feature-performance relationships computed directly on ground-truth data.
[Section 7 and Section 4] The conclusion that 'combining two sets of features is essential' is not supported by the experimental design reported in Section 4. The Sequential Forward Feature Selection (SFFS) procedure operates on the union of all 41 features and selects a single 23-feature subset; there is no comparison between models trained on individual feature groups (PLOS-net, C-PLOS-net, funnel) and models trained on their combinations. The observed importance of features from different groups in the SHAP decision plots is an indirect indication, not a test of complementarity. The authors should either include an ablation study comparing feature-group combinations, or temper the claim to state that the analysis identifies useful features within the combined set without asserting that the combination is essential.

minor comments (4)

[Section 5.1.1] In the PLS footprint description, 'a high number of objectives (k = 3)' should read 'm = 3', and later 'k∈{2,3}' should read 'k∈{2,4}', since k takes values 1, 2, 4 in Table 1.
[Section 4] The acronym 'MTEL' for Multi-Task Elastic Net is inconsistent with the earlier 'MTEN' in the same section; please unify the notation.
[Section 6 and Abstract] The abstract and introduction state that the analysis uses both resolution and hypervolume metrics, but Section 6 says the hypervolume results are omitted due to space and are only in the repository; please clarify the scope in the abstract or include a summary of the hv results.
[General] There are several typographical errors that should be corrected: 'prepossessing' for 'preprocessing' in Section 4, 'Regulrization' in the title of reference [41], and 'the the benchmark suite' in Section 2.2.

Circularity Check

0 steps flagged · score 1.0 of 10

No circularity: the k-influence and feature-combination findings are empirical results from independent landscape features and held-out SHAP analyses, not derivations from their own inputs.

full rationale

The paper's claim chain is: compute 41 landscape features (PLOS-net, C-PLOS-net, funnel) from full landscape enumeration, train an MTR model to predict PLS/GSEMO/NSGA-II resolution and hypervolume, derive local SHAP importance, cluster meta-representations, and visually interpret benchmark-parameter patterns. None of these steps defines a feature in terms of the target performance, and no fitted constant is later renamed as a prediction. The rmnk benchmark parameters (k, m, rho) are generative inputs, not members of the 41-dimensional feature representation, so the observation that k separates SHAP meta-representations is an emergent property of the fitted model rather than a self-fulfilling input. The two new funnel features, pos_num and pos_strength, are computed from the landscape graph structure and Pareto node counts without using algorithm performance; their appearance as important SHAP features is therefore empirical evidence about the model, not a construction. The paper reuses prior performance data and C-PLOS-net/funnel feature definitions from works whose authors overlap with the present authors, but these are external data and feature definitions, not an unverified uniqueness theorem or an ansatz that already contains the conclusion. The absence of reported R2/MAE values for the MTR model and the reliance on 18 test instances for the k-hardness visual conclusion are correctness and validation concerns, not circularity: a biased surrogate would produce wrong inferences, not inferences that are true by construction. Accordingly, no circular step is exhibited, and the overall circularity score is 1, reflecting only a mild self-referential selection effect from judging newly proposed features in a model that was selected and tuned with those features present.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims depend on modeling choices rather than physical constants: the Random Forest hyperparameters and the 23-feature subset are selected from the same training data, and the 14-cluster partition is chosen by silhouette. The new pos_num and pos_strength features are defined directly from the C-PLOS-net and are not fitted parameters. The paper inherits the network and funnel feature definitions from prior work [24,25,31].

free parameters (3)

Random Forest hyperparameters = n_estimators=192, max_depth=7, min_samples_split=3, min_samples_leaf=1, max_features='all'
Selected by TPE on training folds; the footprint and feature importance results depend on this model.
SFFS selected feature subset = 23 of 41 features
Chosen by sequential forward feature selection for the Random Forest; the importance rankings are over this subset.
Hierarchical clustering configuration = 14 clusters, cosine distance, average linkage
Selected by silhouette coefficient; all footprint and cluster-level feature combinations rest on this choice.

assumptions (5)

domain assumption The SHAP values from the trained Random Forest provide valid local feature importance for landscape features.
Used throughout Section 5.1.2; if SHAP attributions are unreliable, the feature importance conclusions fail.
domain assumption The performance data from the prior study [25], with 30 runs per instance, accurately represents true algorithm performance.
Performance labels are reused verbatim from [25] in Section 4; any errors in those measurements propagate.
domain assumption Instances with n=16 are representative of general rmnk-landscapes.
Full enumeration is feasible at n=16, but conclusions may not scale to larger instances.
domain assumption The multi-target regression model's predictions closely approximate true algorithm performance.
Section 5.1.1 states that footprints are based on MTR model predictions which 'despite minor errors, closely approximate ground-truth' but no R2 or MAE values are reported.
domain assumption The C-PLOS-net and funnel feature definitions inherited from [25] and [31] capture meaningful landscape structure.
The analysis treats these features as valid descriptors; if they miss relevant structure, the importance findings are contingent.

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Cite this review

Pith. "Pith review of Customized Exploration of Landscape Features Driving Multi-Objective Combinatorial Optimization Performance." pith.science (2026). https://pith.science/paper/IHYL52ER

@misc{pith2026250701638,
  author       = {Pith},
  title        = {Pith review of: Customized Exploration of Landscape Features Driving Multi-Objective Combinatorial Optimization Performance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IHYL52ER}},
  note         = {Machine review of arXiv:2507.01638}
}

read the original abstract

We present an analysis of landscape features for predicting the performance of multi-objective combinatorial optimization algorithms. We consider features from the recently proposed compressed Pareto Local Optimal Solutions Networks (C-PLOS-net) model of combinatorial landscapes. The benchmark instances are a set of rmnk-landscapes with 2 and 3 objectives and various levels of ruggedness and objective correlation. We consider the performance of three algorithms -- Pareto Local Search (PLS), Global Simple EMO Optimizer (GSEMO), and Non-dominated Sorting Genetic Algorithm (NSGA-II) - using the resolution and hypervolume metrics. Our tailored analysis reveals feature combinations that influence algorithm performance specific to certain landscapes. This study provides deeper insights into feature importance, tailored to specific rmnk-landscapes and algorithms.

Figures

Figures reproduced from arXiv: 2507.01638 by the authors.

**Figure 1.** 2D visualization of 𝜌mnk landscapes using SHAP meta-representation from the test data, showing (a) ground-truth reso performance for three algorithms and (b) clustering results. Axes dim0 and dim1 represent the projected 2D dimensions. 1, to bring the features to the same scale as this can affect the prediction task. The scaling parameters are fitted on the training dataset, and then the test dataset is transformed … view at source ↗

**Figure 2.** 2D visualization of 𝜌mnk landscapes using SHAP meta-representation from the test data, showing the benchmark parameters. 5.1 Algorithm footprints 5.1.1 Resolution (reso) performance metric [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Algorithm footprints shown as contingency matrices: the y-axis represents 14 performance regions, and the x-axis [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Key landscape features for 𝜌mnk landscapes are shown, with each plot representing a landscape and three lines for algorithm-feature interactions influencing performance: 𝜌 ∈ {−0.4, 0}, 𝑚 ∈ {2, 3}, 𝑘 ∈ {1, 2, 4}. The x-axis shows the predicted 𝑟𝑒𝑠𝑜 performance. and is l…

**Figure 5.** Figure 5: Key landscape features for 𝜌mnk landscapes are shown, with each plot representing a landscape and three lines for algorithm-feature interactions influencing performance: 𝜌 ∈ {0, 0.4}, 𝑚 ∈ {2, 3}, 𝑘 ∈ {1, 2, 4}. The x-axis shows the predicted 𝑟𝑒𝑠𝑜 performance. observe n…

**Figure 6.** Figure 6: The key features driving reso performance are shown for each cluster (performance region). Analysis includes the top [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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Works this paper leans on

41 extracted references · 40 canonical work pages

[1]

Hernán Aguirre and Kiyoshi Tanaka. 2007. Working principles, behavior, and performance of MOEAs on MNK-landscapes. European Journal of Operational Research 181, 3 (2007), 1670–1690

work page 2007
[2]

Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, and Masanori Koyama. 2019. Optuna: A next-generation hyperparameter optimization framework. In Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining . Association for Computing Machinery, New York, NY, USA, 2623–2631

work page 2019
[3]

Gérard Biau and Erwan Scornet. 2016. A random forest guided tour. Test 25 (2016)

work page 2016
[4]

Gjorgjina Cenikj, Ana Nikolikj, Gašper Petelin, Niki van Stein, Carola Doerr, and Tome Eftimov. 2024. A Survey of Meta-features Used for Automated Selection of Algorithms for Black-box Single-objective Continuous Optimization. arXiv preprint arXiv:2406.06629 (2024)

work page Pith review arXiv 2024
[5]

Gjorgjina Cenikj, Gašper Petelin, and Tome Eftimov. 2024. A cross-benchmark examination of feature-based algorithm selector generalization in single-objective numerical optimization. Swarm and Evolutionary Computation 87 (2024), 101534

work page 2024
[6]

François Chollet. 2015. Keras. https://keras.io

work page 2015
[7]

Carlos A Coello Coello, Clarisse Dhaenens, and Laetitia Jourdan. 2010. Multi-objective combinatorial optimization: Problematic and context. In Advances in multi-objective nature inspired computing . Springer, Berlin, Heidelberg, 1–21

work page 2010
[8]

Raphaël Cosson, Bilel Derbel, Arnaud Liefooghe, Hernán Aguirre, Kiyoshi Tanaka, and Qingfu Zhang. 2021. Decomposition-based multi-objective landscape features and automated algorithm selection. In Evolutionary Computation in Combinatorial Optimization: 21st European Conference, EvoCOP 2021, Held as Part of EvoStar 2021, Virtual Event, April 7–9, 2021, Pro...

work page 2021

Show all 41 references

[9]

Aguirre, and Kiyoshi Tanaka

Fabio Daolio, Arnaud Liefooghe, Sébastien Verel, Hernán E. Aguirre, and Kiyoshi Tanaka. 2017. Problem Features versus Algorithm Performance on Rugged Multiobjective Combinatorial Fitness Landscapes. Evolutionary Computation 25, 4 (2017)

2017
[10]

Meyarivan

Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, and T. Meyarivan. 2002. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 2 (2002), 182–197

2002
[11]

Francesc J Ferri, Pavel Pudil, Mohamad Hatef, and Josef Kittler. 1994. Comparative study of techniques for large-scale feature selection. In Machine intelligence and pattern recognition . Vol. 16. Elsevier, 403–413

1994
[12]

Fieldsend and Khulood Alyahya

Jonathan E. Fieldsend and Khulood Alyahya. 2019. Visualising the Landscape of Multi-Objective Problems Using Local Optima Networks. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO 2019 . ACM, Prague, Czech Republic, 1421–1429

2019
[13]

Fieldsend, Tinkle Chugh, Richard Allmendinger, and Kaisa Miettinen

Jonathan E. Fieldsend, Tinkle Chugh, Richard Allmendinger, and Kaisa Miettinen. 2022. A visualizable test problem generator for many-objective optimization. IEEE Transactions on Evolutionary Computation 26, 1 (2022), 1–11

2022
[14]

Fonseca and Peter J

Carlos M. Fonseca and Peter J. Fleming. 1996. On the performance assessment and comparison of stochastic multiobjective optimizers. In Parallel Problem Solving from Nature, PPSN IV . Springer, Berlin, Heidelberg, 584–593

1996
[15]

Xavier Glorot and Yoshua Bengio. 2010. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics . JMLR Workshop and Conference Proceedings, 249–256

2010
[16]

Ian T Jolliffe and Jorge Cadima. 2016. Principal component analysis: a review and recent developments. Philosophical transactions of the royal society A: Mathematical, Physical and Engineering Sciences 374, 2065 (2016), 20150202

2016
[17]

Kauffman

Stuart A. Kauffman. 1993. The Origins of Order . Oxford University Press

1993
[18]

Pascal Kerschke and Christian Grimme. 2017. An Expedition to Multimodal Multi-objective Optimization Landscapes. In Evolutionary Multi-Criterion Optimization, EMO 2017 (Lecture Notes in Computer Science, Vol. 10173) . Springer, 329–343

2017
[19]

Knowles and David Corne

Joshua D. Knowles and David Corne. 2007. Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization. In Evolutionary Multi-Criterion Optimization Conference, EMO 2007 (Lecture Notes in Computer Science, Vol. 4403) . Springer, Matsushima, J...

2007
[20]

Ana Kostovska, Anja Jankovic, Diederick Vermetten, Sašo Džeroski, Tome Eftimov, and Carola Doerr. 2023. Comparing algorithm selection approaches on black-box optimization problems. In Proceedings of the Companion Conference on Genetic and Evolutionary Computation. 495–498

2023
[21]

Marco Laumanns, Lothar Thiele, and Eckart Zitzler. 2004. Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem. Natural Computing 3, 1 (2004), 37–51. 12 Customized Exploration of Landscape Features Driving Multi-Objective Combinatoria...

2004
[22]

Arnaud Liefooghe, Fabio Daolio, Sébastien Verel, Bilel Derbel, Hernan Aguirre, and Kiyoshi Tanaka. 2019. Landscape-aware performance prediction for evolutionary multiobjective optimization. IEEE Transactions on Evolutionary Computation 24, 6 (2019), 1063–1077

2019
[23]

Arnaud Liefooghe, Fabio Daolio, Sébastien Verel, Bilel Derbel, Hernán Aguirre, and Kiyoshi Tanaka. 2020. Landscape-Aware Performance Prediction for Evolutionary Multiobjective Optimization. IEEE Transactions on Evolutionary Computation 24, 6 (2020), 1063–1077

2020
[24]

Arnaud Liefooghe, Bilel Derbel, Sébastien Verel, Manuel López-Ibáñez, Hernán Aguirre, and Kiyoshi Tanaka. 2018. On Pareto Local Optimal Solutions Networks. In Parallel Problem Solving from Nature, PPSN XV . Springer International Publishing, Cham, 232–244

2018
[25]

Arnaud Liefooghe, Gabriela Ochoa, Sébastien Verel, and Bilel Derbel. 2023. Pareto local optimal solutions networks with compression, enhanced visualization and expressiveness. In Proceedings of the Genetic and Evolutionary Computation Conference . 713–721

2023
[26]

Arnaud Liefooghe, Sébastien Verel, Bilel Derbel, Hernan Aguirre, and Kiyoshi Tanaka. 2020. Dominance, indicator and decomposition based search for multi-objective QAP: landscape analysis and automated algorithm selection. In International Conference on Parallel Problem Solving...

2020
[27]

Scott M Lundberg and Su-In Lee. 2017. A Unified Approach to Interpreting Model Predictions. In Advances in Neural Information Processing Systems 30 , I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Eds.). Curran Associates, Inc., 476...

2017
[28]

Ana Nikolikj and Tome Eftimov. 2024. Comparing Solvability Patterns of Algorithms across Diverse Problem Landscapes. InProceedings of the Genetic and Evolutionary Computation Conference Companion . Association for Computing Machinery, New York, NY, USA, 143–146

2024
[29]

Ana Nikolikj, Gabriela Ochoa, and Tome Eftimov. 2025. Repository. https://doi.org/10.5281/zenodo.15116349. https://doi.org/10.5281/ zenodo.15116349

2025 doi
[30]

Gabriela Ochoa, Arnaud Liefooghe, and Sébastien Verel. 2024. Funnels in multi-objective fitness landscapes. In International Conference on Parallel Problem Solving from Nature . Springer, 343–359

2024
[31]

Gabriela Ochoa, Arnaud Liefooghe, and Sébastien Vérel. 2024. Funnels in Multi-objective Fitness Landscapes. In Parallel Problem Solving from Nature - PPSN XVIII (Lecture Notes in Computer Science, Vol. 15148). Springer, 343–359. https://doi.org/10.1007/978-3-031-70055-2_21

2024 doi
[32]

Luís Paquete, Tommaso Schiavinotto, and Thomas Stützle. 2007. On local optima in multiobjective combinatorial optimization problems. Annals of Operations Research 156, 1 (2007), 83–97

2007
[33]

Fabian Pedregosa, Gaël Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vincent Dubourg, et al. 2011. Scikit-learn: Machine learning in Python. the Journal of machine Learning research 12 (2011), 2825–2830

2011
[34]

Lennart Schäpermeier, Christian Grimme, and Pascal Kerschke. 2020. One PLOT to Show Them All: Visualization of Efficient Sets in Multi-objective Landscapes. In Parallel Problem Solving from Nature, PPSN XVI . Springer International Publishing, Cham, 154–167

2020
[35]

Moritz Seiler, Urban Škvorc, Carola Doerr, and Heike Trautmann. 2024. Synergies of deep and classical exploratory landscape features for automated algorithm selection. In International Conference on Learning and Intelligent Optimization . Springer Nature Switzerland, Cham, 361–376

2024
[36]

Eric K Tokuda, Cesar H Comin, and Luciano da F Costa. 2022. Revisiting agglomerative clustering. Physica A: Statistical mechanics and its applications 585 (2022), 126433

2022
[37]

Guy Van den Broeck, Anton Lykov, Maximilian Schleich, and Dan Suciu. 2022. On the tractability of SHAP explanations. Journal of Artificial Intelligence Research 74 (2022), 851–886

2022
[38]

Sébastien Verel, Arnaud Liefooghe, Laetitia Jourdan, and Clarisse Dhaenens. 2013. On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives. European Journal of Operational Research 227, 2 (2013), 331–342

2013
[39]

Qingfu Zhang and Hui Li. 2007. MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on evolutionary computation 11, 6 (2007), 712–731

2007
[40]

Xiantong Zhen, Mengyang Yu, Xiaofei He, and Shuo Li. 2017. Multi-target regression via robust low-rank learning. IEEE transactions on pattern analysis and machine intelligence 40 (2017), 497–504

2017
[41]

Hui Zou and Trevor Hastie. 2005. Regulrization and variable selection via the elastic net. Journal of the Royal Statistical Society Series B: Statistical Methodology 67, 2 (2005), 301–320. 13

2005

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Hernán Aguirre and Kiyoshi Tanaka. 2007. Working principles, behavior, and performance of MOEAs on MNK-landscapes. European Journal of Operational Research 181, 3 (2007), 1670–1690

work page 2007

[2] [2]

Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, and Masanori Koyama. 2019. Optuna: A next-generation hyperparameter optimization framework. In Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining . Association for Computing Machinery, New York, NY, USA, 2623–2631

work page 2019

[3] [3]

Gérard Biau and Erwan Scornet. 2016. A random forest guided tour. Test 25 (2016)

work page 2016

[4] [4]

Gjorgjina Cenikj, Ana Nikolikj, Gašper Petelin, Niki van Stein, Carola Doerr, and Tome Eftimov. 2024. A Survey of Meta-features Used for Automated Selection of Algorithms for Black-box Single-objective Continuous Optimization. arXiv preprint arXiv:2406.06629 (2024)

work page Pith review arXiv 2024

[5] [5]

Gjorgjina Cenikj, Gašper Petelin, and Tome Eftimov. 2024. A cross-benchmark examination of feature-based algorithm selector generalization in single-objective numerical optimization. Swarm and Evolutionary Computation 87 (2024), 101534

work page 2024

[6] [6]

François Chollet. 2015. Keras. https://keras.io

work page 2015

[7] [7]

Carlos A Coello Coello, Clarisse Dhaenens, and Laetitia Jourdan. 2010. Multi-objective combinatorial optimization: Problematic and context. In Advances in multi-objective nature inspired computing . Springer, Berlin, Heidelberg, 1–21

work page 2010

[8] [8]

Raphaël Cosson, Bilel Derbel, Arnaud Liefooghe, Hernán Aguirre, Kiyoshi Tanaka, and Qingfu Zhang. 2021. Decomposition-based multi-objective landscape features and automated algorithm selection. In Evolutionary Computation in Combinatorial Optimization: 21st European Conference, EvoCOP 2021, Held as Part of EvoStar 2021, Virtual Event, April 7–9, 2021, Pro...

work page 2021