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Are You Concerned about Limited Function Evaluations: Data-Augmented Pareto Set Learning for Expensive Multi-Objective Optimization
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Proposes DA-PSL, a multi-objective Bayesian optimization method that uses GAN-based data augmentation plus a dominance prediction model to enlarge and filter training data for regularity-model Pareto set learning under limited evaluations.
Problem
Expensive multi-objective optimization with very limited function evaluations, where the scarce data hurts surrogate models and Pareto set learning, especially in higher-dimensional decision spaces.
Approach
Augments already-evaluated solutions with GAN-generated samples (labeled real vs. fake by SDE fitness), screens the generated samples with a voting-based dominance prediction model, and fits a local-PCA regularity model as the Pareto set learner, combined with GP-based EHVI batch selection.
Key results
- DA-PSL achieves superior hypervolume convergence on most synthetic benchmarks and real-world problems compared with nine baselines, and outperforms PSL-MOBO on all problem types.
- Surrogate prediction MSE for DA-PSL is lower than PSL-MOBO and DGEMO on DTLZ2 with d=6 and d=20 (Figure 1).
- Experiments use 100 initial LHS samples and 20 batches of size 5, with 10 independent runs per method.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DA-PSL instead of the compared MOBO algorithms | Expensive multi-objective optimization · Synthetic benchmarks and real-world applications | hypervolume (HV) | Helped |
| Use DA-PSL instead of PSL-MOBO | Expensive multi-objective optimization · Synthetic benchmarks and real-world applications | Pareto front approximation quality | Helped |
| Use DA-PSL instead of PSL-MOBO | DTLZ2 · DTLZ2 (M = 3, d = 6 and d = 20) | surrogate prediction MSE | Helped |
| Remove data augmentation (ablation) | DA-PSL · Synthetic benchmarks and real-world applications | Pareto front convergence and diversity | Hurt |
Surprising findings
- Non-dominated solutions without the data augmentation strategy fail to achieve satisfactory convergence and diversity on many problems, similar to PSL-MOBO.
Limitations
- Risk of GAN model collapse, mitigated by adding genetic-operator samples
- Approximation quality depends on surrogate accuracy in early stages, as shown by high MSE for baselines
Experimental setup
Datasets: ZDT1 ZDT2 ZDT3 DTLZ2 DTLZ3 DTLZ4 DTLZ5 DTLZ6 DTLZ7 RE1-RE7 real-world engineering design problems
Benchmarks: ZDT1 ZDT2 ZDT3 DTLZ2 DTLZ3 DTLZ4 DTLZ5 DTLZ6 DTLZ7 RE1 RE2 RE3
Metrics: hypervolume mean squared error of surrogate predictions
Baselines: NSGA-II MOEA/D-EGO TSEMO USeMO-EI DGEMO PSL-MOBO qNParEGO qEHVI qNEHVI
Builds on: PSL-MOBO GMOEA regularity model SDE (shift-based density estimation) qNEHVI
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