A many-objective evolutionary algorithm using indicator-driven weight vector optimization

2025-10-03

AI Summary

Fixed-weight-vector approaches in MOEA/D suffer from poor convergence and uneven solution distribution when handling irregular Pareto fronts—e.g., degenerate, discontinuous, or inverted fronts. Method: This paper proposes an indicator-driven adaptive weight vector optimization algorithm, integrating the MOEA/D decomposition framework with a simplified hypervolume (S-HV) indicator. Under guidance from the R2 indicator, the algorithm dynamically adjusts the frequency of weight vector updates to enable real-time improvement of solution distribution. Contribution/Results: The key innovation lies in deeply embedding indicator-based evaluation into the weight vector evolution process, thereby jointly optimizing convergence and diversity. Experimental results on 12 irregular benchmark problems demonstrate that the proposed algorithm significantly outperforms six state-of-the-art multi-objective evolutionary algorithms, exhibiting superior robustness and search efficiency—particularly on complex front geometries.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Mixture of Experts (MoE)

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

For regular Pareto Fronts (PFs), such as those that are smooth, continuous, and uniformly distributed, using fixed weight vectors is sufficient for multi-objective optimization approaches using decomposition. However, when encountering irregular PFs-including degenerate, disconnected, inverted, etc. Fixed weight vectors can often cause a non-uniform distribution of the sets or even poor optimization results. To address this issue, this study proposes an adaptive many-objective evolutionary algorithm with a simplified hypervolume indicator. It synthesizes indicator assessment techniques with decomposition-based methods to facilitate self-adaptive and dynamic adjustment of the weight vectors in many-objective optimization methods. Specifically, based on the MOEA/D framework, it uses a simplified hypervolume indicator to accurately assess solution distribution. Simultaneously, applying the R2 indicator (as an approximation of hypervolume) dynamically regulates the update frequency of the weight vectors. Experimental results demonstrate that the proposed algorithm is efficient and effective when compared with six state-of-the-art algorithms.

Problem

• Addresses irregular Pareto Fronts in many-objective optimization problems
• Proposes adaptive weight vector adjustment using hypervolume indicators
• Enhances solution distribution for degenerate and disconnected Pareto Fronts

Innovation

• Adaptive weight vector optimization using hypervolume indicator
• Dynamic adjustment of weight vectors for irregular Pareto Fronts
• Combining indicator assessment with decomposition-based evolutionary algorithms