Designing effective multi-objective Bayesian optimization (MOBO) algorithms requires balancing many interdependent design choices whose optimal configuration is problem-dependent and typically demands deep expertise. We extend the LLaMEA framework to MOBO, using large language models as mutation and crossover operators within evolutionary strategies to generate complete algorithm implementations, with SMAC hyperparameter optimization integrated into the evolutionary loop. Across nine evolutionary runs we generated approximately 900 algorithms and benchmarked them on twelve synthetic problems (ZDT, DTLZ, WFG) and three real-world engineering problems (RE), using a BoFire qParEGO implementation as a state-of-the-art Bayesian-optimization baseline. On the synthetic suite the strongest generated algorithm attains the highest mean normalized hypervolume (0.971, vs. 0.869 for qParEGO) while requiring roughly 60x less wall-clock time; a Friedman test with post-hoc analysis places the two in a single top-performing group, and per-problem tests find the generated algorithm significantly better than qParEGO on 7 of the 12 problems and never worse, matching state-of-the-art accuracy at an order-of-magnitude lower cost. On the three unseen real-world engineering problems a generated algorithm attains the best mean normalized hypervolume (0.985, vs. 0.971 for qParEGO)--significantly better than qParEGO on two of the three problems--at roughly 3.4x lower wall-clock cost, confirming that the gains transfer beyond the synthetic regime. LLM-driven evolutionary search can thus discover algorithm designs that achieve Pareto-efficient trade-offs difficult to reach through manual design.
Optimization benchmarks play a fundamental role in assessing algorithm performance; however, existing artificial benchmarks often fail to capture the diversity and irregularity of real-world problem structures, while benchmarks derived from real-world problems are costly and difficult to construct. To address these challenges, we propose an evolutionary automatic benchmark generation framework that leverages a large language model (LLM) as a generative operator, termed the LLM-driven evolutionary benchmark generator (LLM-EBG). In this framework, the LLM serves as an evolutionary operator that generates and evolves benchmark problems within a flexible, expressive representation space. As a case study, we generate unconstrained single-objective continuous minimization problems represented as mathematical expressions designed to induce significant performance differences between a genetic algorithm (GA) and differential evolution (DE). Experimental results show that LLM-EBG successfully produces benchmark problems in which the designated target algorithm consistently outperforms the comparative algorithm in more than 80% of trials. Furthermore, exploratory landscape analysis reveals that benchmarks favoring GA are highly sensitive to variable scaling, demonstrating that the proposed framework can generate problems with distinct geometric characteristics that reflect the intrinsic search behaviors of different optimization algorithms.
Despite recent progress in constructing generalizable parallel algorithm portfolios (PAPs), no general-purpose approach is yet available for multi-objective binary optimization problems (MOBOPs). To fill this gap, this paper proposes domain-agnostic co-evolution of parameterized search for multi-objective binary optimization~(DACMO), which features two technical innovations. First, we propose a neural instance representation architecture that decouples domain-invariant and instance-specific features, enabling class-consistent instance generation across varying dimensions without problem-specific instance generators. Second, we introduce LLM-based automatic search operator generation into PAP construction, extending the search space from parameter tuning of predefined templates to operator-level algorithm design. We evaluate DACMO on four representative MOBOP classes to demonstrate its effectiveness as a general-purpose PAP construction method: the multi-objective match max problem~(MMMP), the multi-objective knapsack problem~(MKP), the multi-objective contamination control problem (MCCP), and the multi-objective complementary influence maximization problem~(MCIMP). Experimental results show that DACMO can be directly applied to all four problem classes without modification, outperforms PAPs built from classic MOEA templates, and achieves performance comparable to a privileged state-of-the-art baseline that relies on manually designed problem-specific instance generators, while outperforming it on two of the four evaluated problem classes.
Bayesian Optimization (BO) is widely used for optimizing expensive black-box functions, yet many real-world optimization problems contain substantially richer information than function evaluations alone. Examples include training curves in hyperparameter optimization, expert notes and images in scientific experimentation, and prior knowledge about where optima may lie. We show that large language models (LLMs) can effectively leverage such rich auxiliary information to guide optimization. Motivated by these findings, we develop three methods for incorporating auxiliary information into BO using LLMs. Across hyperparameter optimization benchmarks and a real-world nuclear fusion optimization task, our methods consistently outperform both standard BO and existing LLM-based optimization approaches. Our results demonstrate the effectiveness of LLMs for leveraging rich auxiliary information in BO.