q-bio.GNMar 31, 2026
SaveGenetic algorithms for multi-omic feature selection: a comparative study in cancer survival analysis
Organizations: Institute of Biomedicine, School of Medicine, University of Eastern Finland, Yliopistonranta 8, 70210, Finland
Abstract
Multi-omic datasets offer opportunities for improved biomarker discovery in cancer research, but their high dimensionality and limited sample sizes make identifying compact and effective biomarker panels challenging. Feature selection in large-scale omics can be efficiently addressed by combining machine learning with genetic algorithms, which naturally support multi-objective optimization of predictive accuracy and biomarker set size. However, genetic algorithms remain relatively underexplored for multi-omic feature selection, where most approaches concatenate all layers into a single feature space. To address this limitation, we introduce Sweeping*, a multi-view, multi-objective algorithm alternating between single- and multi-view optimization. It employs a nested single-view multi-objective optimizer, and for this study we use the genetic algorithm NSGA3-CHS. It first identifies informative biomarkers within each layer, then jointly evaluates cross-layer interactions; these multi-omic solutions guide the next single-view search. Through repeated sweeps, the algorithm progressively identifies compact biomarker panels capturing cross-modal complementary signals. We benchmark five Sweeping* strategies, including hierarchical and concatenation-based variants, using survival prediction on three TCGA cohorts. Each strategy jointly optimizes predictive accuracy and set size, measured via the concordance index and root-leanness. Overall performance and estimation error are assessed through cross hypervolume and Pareto delta under 5-fold cross-validation. Our results show that Sweeping* can improve the accuracy-complexity trade-off when sufficient survival signal is present and that integrating omic layers can enhance survival prediction beyond clinical-only models, although benefits remain cohort-dependent.
Figures & tables
Figure 1: CHV and across TCGA cohorts. (a) CHV for each multi-omic feature selection strategy evaluated in this study across TCGA-KIRC, TCGA-LGG, and TCGA-SARC. CHV is a MO measure of overall performance that can be applied to cross-validation situations. The objectives here are the predictive performance and the biomarker set size (number of selected features). Higher values indicate better overall utility of solution sets. (b) measures the discrepancy between training and testing performance of the solutions across the whole approximated Pareto front, when objectives are based on ML performance metrics. quantifies overestimation, with lower values indicating smaller train–test gaps and more robust performance. Error bars represent variability across cross-validation folds.
Figure 2: Accuracy-complexity trade-offs across TCGA cohorts. C-index as a function of the number of selected features for each multi-omic feature selection strategy in TCGA-KIRC, TCGA-LGG, and TCGA-SARC. Each curve represents the best average performance achieved across cross-validation folds at a given feature count, illustrating the empirical trade-off between predictive accuracy and biomarker set size. Strategies include clinical-only models, direct concatenation of omic layers, and sweeping-based MV optimization variants. The figure highlights how different optimization designs navigate the accuracy–sparsity spectrum under distinct survival data regimes.
Figure 3: Expected versus measured C-index comparison of clinical-only and multi-omic feature selection strategies in TCGA-KIRC and TCGA-LGG. Top panels show C-index as a function of the number of selected features. “Expected” points represent internal cross-validation performance, while “measured” points denote testing performance on the left-out sets. The results from all the 5 folds are plotted together. Left column corresponds to clinical-only optimization, and right column to the multi-omic sweeping strategy integrating clinical with expression-based features. Bottom panels display the distribution of selected feature counts required to achieve increasing concordance levels, illustrating model complexity and composition. They show the counts and the expected C-index resulting from optimizing on the whole dataset. The comparison highlights cohort-dependent differences in incremental molecular value and generalization stability.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Supplementary Figure S1: Schematic representation of the Sweeping* algorithm. The algorithm begins with a set of initial solutions, which may be provided by the user or empty (in which case the algorithm starts from scratch). These solutions form the starting populations for each view. The user specifies objectives, i.e., evaluation metrics (functions mapping a solution to a numerical value, possibly data‑dependent), and views, where each view corresponds to a feature subset representing a data modality for the same sample set. These define the problem the algorithm will optimize. A sweep is the main unit of iteration. Each sweep consists of: a SV step, “for each view → optimize view” (for every view, an SV optimizer with warm start is applied), and a MV step, “master” optimizer (after updating all views individually, master MV optimizer jointly optimizes across all views). The SV → MV cycle is repeated for a user‑defined number of sweeps. After all sweeps are completed, a tuner MV optimizer further refines the final MV population. The tuner may also be the identity function, making this phase optional. This final MV optimization step produces the resulting solutions.
Supplementary Figure S2: UML class diagram that visually summarizes the main software components used to implement the Sweeping* algorithm and their dependencies. The classes fall into several conceptual groups, each playing a specific role in the framework. The core optimizer classes that are the fundamental building blocks for optimization: MOOptimizer (the base class for all SV MO optimizers, it extends MOOptimizerWS to support MV optimization with warm start), Sweeping* (a composite optimizer implementing MVMOOptimizer ), NSGAWS (a warm‑start version of the NSGA algorithm, can be used both as SV and MV optimizer inside the Sweeping* framework). Warm‑start infrastructure (warm‑starting allows optimizers to begin from existing populations, enabling pipelines): MOOptimizerWS (extends MOOptimizer to add an optimizeWS method that accepts an initial population), MOOptimizerWSFactory and NSGA*Factory (these factory classes create warm‑start optimizers on demand, using the current populations). Genetic algorithm components, these classes determine how populations evolve during optimization: GAStrategy (an abstract class encapsulating GA‑specific behaviors), two concrete implementations are shown ( GASBitList , bitlist‑based feature encoding, GASSelector , MV individuals composed of SV individuals, one per view), GASFactory , GASFactoryBitList , GASFactorySelector (factories for creating GAStrategy instances tailored to the current population handling strategy). MVMOOptimizer implementations with specific MV composition strategies, these define how separate views are combined to form MV individuals: Concatenated (concatenates SV feature sets into a single large feature set, possibly with probabilistic feature retention in the lean configuration), Resampled (uses a GA where each MV individual is formed by one SV individual per view, handles MV structure through resampling rather than concatenation). Together, these classes form a modular and extensible architecture for MV MO optimization.
| name | nick | master | sweeping generations | tuning generations |
|---|---|---|---|---|
| concatenated | [] | 300 | ||
| resampled sweeping | Sw | Resampled | [50, 50, 50] | 0 |
| concatenated sweeping | CSw | Concatenated(lean=false) | [150] | 0 |
| lean concatenated sweeping | LCSw | Concatenated(lean=true) | [150] | 0 |
| resampled sweeping with tuning | SwT | Resampled | [50, 50] | 100 |
Supplementary Table S1: Considered configurations of the Sweeping* algorithm.
Supplementary Figure S3: Event accumulation and censoring patterns across TCGA survival cohorts. Stacked area plots show cumulative numbers of deceased, censored, and surviving individuals over follow-up time for TCGA-KIRC, TCGA-LGG, and TCGA-SARC. The three cohorts display distinct survival data regimes, with differences in timing and density of observed events as well as censoring proportions.
Supplementary Figure S4: Expected versus measured C-index comparison of clinical-only and multi-omic feature selection strategies in TCGA-SARC. Top panels show C-index as a function of the number of selected features. “Expected” points represent internal cross-validation performance, while “measured” points denote testing performance on the left-out sets. The results from all the 5 folds are plotted together. Left column corresponds to clinical-only optimization, and right column to the multi-omic sweeping strategy integrating clinical with expression-based features. Bottom panels display the distribution of selected feature counts required to achieve increasing concordance levels, illustrating model complexity and composition. They show the counts and the expected C-index resulting from optimizing on the whole dataset.
Supplementary Figure S5: Top features identified for the TCGA‑KIRC cohort across all Sweeping* configurations and view combinations. The figure lists, for each multi‑view (clinic; clinic + miRNA; clinic + miRNA + mRNA) and Sweeping* configuration (concatenated; Sw; SwT; CSw; LCSw), the 6 features most frequently selected in the approximated Pareto front after optimizing on the whole dataset. The more frequent the feature the darker the background.
Supplementary Figure S6: Top features identified for the TCGA‑LGG cohort across all Sweeping* configurations and view combinations. The figure lists, for each multi‑view (clinic; clinic + miRNA; clinic + miRNA + mRNA) and Sweeping* configuration (concatenated; Sw; SwT; CSw; LCSw), the 6 features most frequently selected in the approximated Pareto front after optimizing on the whole dataset. The more frequent the feature the darker the background.
Supplementary Figure S7: Top features identified for the TCGA‑SARC cohort across all Sweeping* configurations and view combinations. The figure lists, for each multi‑view (clinic; clinic + miRNA; clinic + miRNA + mRNA) and Sweeping* configuration (concatenated; Sw; SwT; CSw; LCSw), the 6 features most frequently selected in the approximated Pareto front after optimizing on the whole dataset. The more frequent the feature the darker the background.
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