Objective Selection in Many-Objective Optimization via Conditioning-Based Analysis of Objective Redundancy
- 1IPC—Institute for Polymers and Composites, University of Minho, 4800-058 Guimarães, Portugal
Abstract
Evolutionary many-objective algorithms lose selection pressure and become harder to steer as the number of objectives grows, so objective selection is often applied before the search. Most selection methods measure dependence directly on the objective values and therefore cannot distinguish dependence induced by shared decision variables from redundancy between the objectives themselves. This paper proposes a conditioning-based selection criterion in which each objective is regressed on the decision variables, and redundancy is measured on the residuals; in the linear case, the measure is the partial correlation given the design space. A greedy score combining relevance, unexplained variability, and residual redundancy, with standardized components, builds the subset, and an admissibility gate reports when the conditioning model is too weak or the residual variance too small for the criterion to apply. On DTLZ and WFG benchmarks, the complete procedure admits five of twelve configurations and declares the other seven non-applicable; in four of the five admitted configurations, the conditioned subset differs from those of PCA, mRMR-like selection, and clustering. An active NSGA-III validation with paired Wilcoxon tests shows no uniform performance advantage. The admitted subsets are invariant to the cross-validation seed, and the re-seeded nonlinear selector recovers its own modal subset in 93.1% of runs. A controlled example with known redundant and conflicting objectives shows that absolute residual correlation can discard a pure residual conflict, which a sign-aware variant avoids. In an injection-molding case with 35 indicators, an ablation shows that the unexplained-variability term is decisive: removing it changes two of the three selected objectives. The contribution is therefore a selection criterion conditional on an adequacy diagnostic, not a general-purpose objective-selection method, and the analysis states when it should be used instead of marginal-dependence baselines.
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BibTeX
@article{marques2026objective,
title = {{Objective Selection in Many-Objective Optimization via Conditioning-Based Analysis of Objective Redundancy}},
author = {Tomás Marques and António J. Pontes and António Gaspar-Cunha},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14214051},
url = {https://www.mdpi.com/2227-7390/14/21/4051},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Objective Selection in Many-Objective Optimization via Conditioning-Based Analysis of Objective Redundancy
AU - Tomás Marques
AU - António J. Pontes
AU - António Gaspar-Cunha
PY - 2026
DA - 2026/11/05
JO - Mathematics
DO - 10.3390/math14214051
UR - https://www.mdpi.com/2227-7390/14/21/4051
AB - Evolutionary many-objective algorithms lose selection pressure and become harder to steer as the number of objectives grows, so objective selection is often applied before the search. Most selection methods measure dependence directly on the objective values and therefore cannot distinguish dependence induced by shared decision variables from redundancy between the objectives themselves. This paper proposes a conditioning-based selection criterion in which each objective is regressed on the decision variables, and redundancy is measured on the residuals; in the linear case, the measure is the partial correlation given the design space. A greedy score combining relevance, unexplained variability, and residual redundancy, with standardized components, builds the subset, and an admissibility gate reports when the conditioning model is too weak or the residual variance too small for the criterion to apply. On DTLZ and WFG benchmarks, the complete procedure admits five of twelve configurations and declares the other seven non-applicable; in four of the five admitted configurations, the conditioned subset differs from those of PCA, mRMR-like selection, and clustering. An active NSGA-III validation with paired Wilcoxon tests shows no uniform performance advantage. The admitted subsets are invariant to the cross-validation seed, and the re-seeded nonlinear selector recovers its own modal subset in 93.1% of runs. A controlled example with known redundant and conflicting objectives shows that absolute residual correlation can discard a pure residual conflict, which a sign-aware variant avoids. In an injection-molding case with 35 indicators, an ablation shows that the unexplained-variability term is decisive: removing it changes two of the three selected objectives. The contribution is therefore a selection criterion conditional on an adequacy diagnostic, not a general-purpose objective-selection method, and the analysis states when it should be used instead of marginal-dependence baselines.
SN - 2227-7390
ER -