LLM-driven evolutionary search can discover algorithm designs that achieve Pareto-efficient trade-offs difficult to reach through manual design, with SMAC hyperparameter optimization integrated into the evolutionary loop.
Abstract
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.
A framework that combines large language models (LLMs) for problem understanding with a structured Biased Random-Key Genetic Algorithm (BRKGA) configurator for algorithm realization is presented, allowing users to describe optimization problems in natural language and receive executable GPU-accelerated GA implementations.
Harishjitu Seesandrn, M. Sodhi, Resit Sendag· Proceedings of the Genetic a...· 0 citations
Large Language Models (LLMs) are opening new directions for automated heuristic design (AHD), allowing evolutionary methods to create and enhance heuristics for constrained optimization problems (COPs). However, most existing approaches face the challenge of the exploration-exploitation balance, where the evolution needs to escape convergence to homogeneous populations and discover as large a heuristic landscape as possible. To address this challenge, we introduce Quality-Diversity Evolution (QDEvo), a multi-objective framework that integrates Quality-Diversity optimization with LLM-based AHD. At its core, QDEvo employs a semantic survival selection mechanism that clusters algorithms by functional similarity, then applies local Pareto competition. Evaluation on well-known COPs benchmarks and real-world problems shows that our method consistently outperforms the state-of-the-art baseline in both Hypervolume and Inverted Generational Distance metrics. These results facilitate further exploration of the algorithmic design space, while ensuring competitive solution quality and efficiency.
Nam Do Khanh, Nhat Nguyen Tran Minh, Dat Pham Vu Tuan et al.· Proceedings of the Genetic a...· 1 citation
Model merging combines trained models directly in weight space, offering a compute-efficient alternative to additional fine-tuning. Selecting merge parameters is nevertheless difficult because downstream evaluations are expensive, gradients are unavailable, and source capabilities can conflict. We formulate merge-parameter selection as a black-box multi-objective optimization problem and introduce MOBO-Merge, a merge-operator agnostic framework that uses multi-objective Bayesian optimization to approximate the Pareto front under a limited evaluation budget. We evaluate Qwen3-4B and Llama-3.1-8B in two-model instruction-math and three-model instruction-math-code settings using Linear, SLERP, TIES, and block-wise merge operators. On held-out benchmark partitions, MOBO-Merge obtains higher mean hypervolume than random search in 11 of 12 reported comparisons. The gain is small for one-dimensional Linear interpolation but substantially larger for several TIES, block-wise, and three-objective searches. No merge operator is uniformly best: TIES leads in three of four family-setting combinations, whereas Block-Linear 4x is strongest for the Llama three-model merge. These results show that multi-objective Bayesian optimization is valuable as a search layer for expressive merge parameterizations.
Utkarsh Agarwal, V. Bonagiri, Raul Astudillo et al.· 0 citations
Multi-objective optimization provides the mathematical foundation for reasoning about trade-offs in complex decision problems, from engineering design to resource allocation. Software testing exemplifies such problems: practitioners must simultaneously optimize for fault detection capability, code coverage, execution cost, and test suite diversity—objectives that are fundamentally incommensurable. Since the early 2000s, multi-objective evolutionary algorithms (MOEAs) such as NSGA-II, MOEA/D, and their many-objective extensions (MOSA; DynaMOSA) have served as the dominant mathematical framework for navigating these trade-offs through Pareto-front approximation with hand-crafted fitness functions. However, the recent emergence of reinforcement learning (RL) and large language models (LLMs) is shifting the optimization paradigm from numerical Pareto-front approximation toward neural, semantically aware decision making over learned representations. This paper presents a systematic mapping study of multi-objective optimization algorithms, tracing their evolution from classical Pareto-based methods toward AI-driven and hybrid approaches, with software testing as the primary application domain. We survey 120+ papers published from 2000 to 2025 and propose a novel five-level taxonomy (L1–L5) that classifies optimization approaches along the intelligence spectrum: classical MOEAs, ML-guided MOEAs, RL-driven optimization, LLM-driven optimization, and hybrid neuro-evolutionary systems. For each level, we analyze the mathematical problem formulations (Pareto optimality conditions, Markov decision processes, and neural loss landscapes), objective function design, algorithmic convergence properties, and computational complexity. We further conduct a cross-cutting mathematical analysis comparing these paradigms along dimensions of convergence, diversity, scalability, and interpretability. Our survey identifies critical open mathematical challenges: the lack of formal convergence guarantees for LLM-driven optimization, the under-exploration of many-objective (m≥4) formulations in AI-driven testing, the sample complexity of reinforcement learning for combinatorial test optimization, and the absence of standardized benchmarks with known Pareto-optimal frontiers. We conclude by outlining a research roadmap for the next generation of multi-objective optimization systems that combine the complementary mathematical strengths of neural function approximation and evolutionary diversity preservation.
Physics-informed neural networks (PINNs) are unusually sensitive to interacting choices of architecture, activation, loss weighting, collocation, optimization, and constraint enforcement. Large language models (LLMs) can propose these choices, but independent recommendations do not accumulate experience from previously trained PINNs. We propose a closed-loop evolutionary algorithm that guides an LLM to generate complete, executable PINN configurations across generations, using measured training outcomes to determine subsequent search decisions. The algorithm maintains an evaluated population and lineage, applies parent-conditioned mutation and crossover, preserves elite and diverse solutions, rejects effective duplicates, and converts parent-relative successes and failures into the next-generation context supplied to the LLM. Every proposed configuration is executed directly under an exact optimizer-step budget. On a one-dimensional multiscale wave equation, two independent ten-generation runs trained 60 PINNs for 600,000 optimizer steps. In both runs, the best configuration appeared in the final generation, with best mean-squared error reduced by 2.97\% and 95.38\% relative to the initial population. The stronger run validated residual connections and increased depth on separate branches, combined them in a later generation, and then refined width and collocation density. It also revealed that low solution error can coexist with a high PDE residual. These results demonstrate the feasibility of evolutionary-algorithm-guided LLMs for PINN design on a controlled PDE while motivating broader, physics-aware evaluation.
Bayesian optimization (BO) is a sample-efficient, surrogate-based approach to black-box optimization (BBO), but its evaluation remains dominated by synthetic functions and hyperparameter optimization (HPO) tasks that are typically low-dimensional and single-objective. Engineering design poses a substantially different regime: problems are physics-based, often high-dimensional, constrained by requirements such as cost and manufacturability, and may involve multiple objectives or mixed variables. To close this benchmarking gap, we introduce BOCoDe, an open-source, PyTorch-native benchmark comprising 307 BBO problems, including 159 engineering design tasks and widely used synthetic and HPO benchmarks. Each problem includes cited provenance and machine-readable metadata that supports programmatic discovery, including by LLM-based agents, and all tasks are exposed through a unified API compatible with open-source BO libraries. We evaluate 31 BO and evolutionary algorithms across five problem classes spanning single- and multi-objective optimization, constrained and unconstrained settings, and mixed-variable search spaces. Analyses of problem structure show that engineering tasks uniquely span constrained and multi-objective settings that synthetic and HPO suites rarely cover, while embeddings from a tabular foundation model separate them most clearly from HPO tasks. Algorithm rankings also vary substantially across domains; in several problem classes, rankings obtained on standard benchmarks do not transfer to engineering tasks. BOCoDe establishes a reproducible and extensible foundation for developing and evaluating BO methods that better reflect the demands of engineering design. Code&data can be found at https://github.com/rosenyu304/BOCoDe
Rosen Yu, Christophe Hatterer, A. Narayanan et al.· 0 citations