Balancing convergence and diversity: Gaussian mixture models in adaptive weight vector strategies for multi-objective algorithms

Abstract

In the study of decomposition-based multi-objective evolutionary algorithms, the adaptive weight vector approach effectively balances algorithm convergence and diversity. A common method for weight vector adaptation uses a population sparsity strategy, which calculates sparsity via Euclidean distance. However, this method causes individuals with low sparsity to cluster at the center of the objective space, while those with high sparsity spread to the edges, disrupting the convergence-diversity balance. To address this issue, this paper proposes using a Gaussian mixture model. This model treats data as a mix of multiple Gaussian distributions, partitioning the data space more flexibly. First, the paper analyzes various algorithms that adjust weight vectors using the sparsity strategy, highlighting their shortcomings. Then, it demonstrates how Gaussian mixture models can better divide the space and accurately identify individuals with different sparsity levels, correcting traditional sparsity calculation flaws. Since the population in the objective space changes during evolution, selecting appropriate component parameters is crucial. This paper uses the elbow rule to adaptively select these parameters. The experimental section includes three sets of experiments comparing the proposed algorithm with several popular algorithms, including a study on real mechanical bearing optimization. Results show that the proposed algorithm is highly competitive.