In this paper, we introduce a novel approach for large language model merging via black-box multi-objective optimization algorithms. The goal of model merging is to combine multiple models, each excelling in different tasks, into a single model that outperforms any of the individual source models. However, model merging faces two significant challenges: First, existing methods rely heavily on human intuition and customized strategies. Second, parameter conflicts often arise during merging, and while methods like DARE [1] can alleviate this issue, they tend to stochastically drop parameters, risking the loss of important delta parameters. To address these challenges, we propose the MM-MO method, which automates the search for optimal merging configurations using multi-objective optimization algorithms, eliminating the need for human intuition. During the configuration searching process, we use estimated performance across multiple diverse tasks as optimization objectives in order to alleviate the parameter conflicting between different source models without losing crucial delta parameters. We conducted comparative experiments with other mainstream model merging methods, demonstrating that our method consistently outperforms them. Moreover, our experiments reveal that even task types not explicitly targeted as optimization objectives show performance improvements, indicating that our method enhances the overall potential of the model rather than merely overfitting to specific task types. This approach provides a significant advancement in model merging techniques, offering a robust and plug-and-play solution for integrating diverse models into a unified, high-performing model.

Multi-objective combinatorial optimization (MOCO) problems are prevalent in various real-world applications. Most existing neural MOCO methods rely on problem decomposition to transform an MOCO problem into a series of singe-objective combinatorial optimization (SOCO) problems. However, these methods often approximate partial regions of the Pareto front and spend excessive time on diversity enhancement because of ambiguous decomposition and time-consuming precise hypervolume calculation. To address these limitations, we design a Geometry-Aware Pareto set Learning algorithm named GAPL, which provides a novel geometric perspective for neural MOCO via a Pareto attention model based on hypervolume expectation maximization. In addition, we propose a hypervolume residual update strategy to enable the Pareto attention model to capture both local and non-local information of the Pareto set/front. We also design a novel inference approach to further improve quality of the solution set and speed up hypervolume calculation. Experimental results on three classic MOCO problems demonstrate that our GAPL outperforms several state-of-the-art baselines via superior decomposition and efficient diversity enhancement.

Multi-objective Bayesian optimization (MOBO) has shown promising performance on various expensive multi-objective optimization problems (EMOPs). However, effectively modeling complex distributions of the Pareto optimal solutions is difficult with limited function evaluations. Existing Pareto set learning algorithms may exhibit considerable instability in such expensive scenarios, leading to significant deviations between the obtained solution set and the Pareto set (PS). In this paper, we propose a novel Composite Diffusion Model based Pareto Set Learning algorithm, namely CDM-PSL, for expensive MOBO. CDM-PSL includes both unconditional and conditional diffusion model for generating high-quality samples. Besides, we introduce an information entropy based weighting method to balance different objectives of EMOPs. This method is integrated with the guiding strategy, ensuring that all the objectives are appropriately balanced and given due consideration during the optimization process; Extensive experimental results on both synthetic benchmarks and real-world problems demonstrates that our proposed algorithm attains superior performance compared with various state-of-the-art MOBO algorithms.