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Conditional diffusion with gradient guidance for high-dimensional expensive multi-objective optimization
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DOI：10.1016/j.swevo.2026.102340.png)
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Abstract
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Multi-objective optimization with expensive function evaluations demands efficient use of limited computational budgets. Existing surrogate-assisted evolutionary algorithms rely on Gaussian processes or radial basis functions; however, these methods suffer from cubic computational complexity and degrade in high-dimensional decision spaces. Here, we propose a conditional diffusion framework that models the Pareto set as a learnable probability distribution rather than a discrete point collection. Our approach consists of three components: a transformer-based diffusion model that generates candidate solutions based on preference vectors, a gradient-guided sampling mechanism that incorporates surrogate-derived descent directions during reverse diffusion, and an entropy-weighted acquisition ensemble for batch selection. The diffusion model learns to map noise samples directly to Pareto-optimal regions. In contrast to isotropic mutation operators, the gradient guidance steers generation toward improved objective values while the repulsion mechanism preserves solution diversity. We evaluate the proposed method on multiple benchmark suites with decision dimensions up to 100 and objective counts up to 10. Results demonstrate superior performance compared to state-of-the-art methods under identical evaluation budgets.
Keywords:
Multi-objective optimization
Diffusion models
Gradient guidance
Surrogate-assisted evolutionary algorithms
High-dimensional decision spaces
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