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A Decoupled Basis-Vector-Driven Generative Framework for Dynamic Multi-Objective Optimization

Yaoming Yang, Shuai Wang, Bingdong Li, Peng Yang, Ke Tang

Abstract

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

A Decoupled Basis-Vector-Driven Generative Framework for Dynamic Multi-Objective Optimization

Abstract

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

Paper Structure

This paper contains 35 sections, 18 equations, 9 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Proposed Method
  3. Overall Algorithm
  4. Multi-scale Frequency Decoupling Encoding
  5. Structure Learning via Basis Vectors
  6. Sparse Basis Representation
  7. Topology-Aware Contrastive Regularization
  8. Joint Generative and Predictive Modeling
  9. Latent Variable Fusion
  10. Multi-Task Decoding
  11. Overall Objective
  12. Surrogate-Assisted Generative Search
  13. Centroid-based Latent Mapping
  14. Decomposition-based Screening
  15. EXPERIMENTS
  16. ...and 20 more sections

Figures (9)

  • Figure 1: The overall framework of the proposed DB-GEN.
  • Figure 2: The IGD variation curves over environments.
  • Figure 3: Zero-shot solution generation upon specific environmental change on the DF1 problem. (a) Proposed latent centroid perturbation. (b) Perturbation on all previous solutions.
  • Figure 4: Effect of historical data scale on the mean IGD and the average rank.
  • Figure 5: Correlation between the normalized latent space distance of new environments and the average IGD improvement rate.
  • ...and 4 more figures