Multi-Objective Hierarchical Optimization with Large Language Models

• URL: http://arxiv.org/abs/2601.13892v1
• Date: Tue, 20 Jan 2026 12:10:13 GMT
• Title: Multi-Objective Hierarchical Optimization with Large Language Models
• Authors: Andrej Schwanke, Lyubomir Ivanov, David Salinas, Frank Hutter, Arber Zela,
• Abstract summary: Large Language Models (LLMs) are not the off-the-shelf choice to drive multi-objective optimization yet.<n>In this paper, we close this gap by leveraging LLMs as surrogate models and candidate samplers inside a structured hierarchical search strategy.
• Score: 41.41567058185742
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite their widespread adoption in various domains, especially due to their powerful reasoning capabilities, Large Language Models (LLMs) are not the off-the-shelf choice to drive multi-objective optimization yet. Conventional strategies rank high in benchmarks due to their intrinsic capabilities to handle numerical inputs and careful modelling choices that balance exploration and Pareto-front exploitation, as well as handle multiple (conflicting) objectives. In this paper, we close this gap by leveraging LLMs as surrogate models and candidate samplers inside a structured hierarchical search strategy. By adaptively partitioning the input space into disjoint hyperrectangular regions and ranking them with a composite score function, we restrict the generative process of the LLM to specific, high-potential sub-spaces, hence making the problem easier to solve as the LLM doesn't have to reason about the global structure of the problem, but only locally instead. We show that under standard regularity assumptions, our algorithm generates candidate solutions that converge to the true Pareto set in Hausdorff distance. Empirically, it consistently outperforms the global LLM-based multi-objective optimizer and is on par with standard evolutionary and Bayesian optimization algorithm on synthetic and real-world benchmarks.

Related papers

• Multi-Paradigm Collaborative Adversarial Attack Against Multi-Modal Large Language Models [67.45032003041399]
  We propose a novel Multi-Paradigm Collaborative Attack (MPCAttack) framework to boost the transferability of adversarial examples against MLLMs.<n>MPCO adaptively balances the importance of different paradigm representations and guides the global optimisation.<n>Our solution consistently outperforms state-of-the-art methods in both targeted and untargeted attacks on open-source and closed-source MLLMs.
  arXiv  Detail & Related papers  (2026-03-05T06:01:26Z)
• Reasoning in a Combinatorial and Constrained World: Benchmarking LLMs on Natural-Language Combinatorial Optimization [28.52469449694436]
  Large language models (LLMs) have shown strong performance in math and logic reasoning.<n>But their ability to handle systematic optimization (CO) remains underexplored.<n>We introduce NLCO, a benchmark that evaluates LLMs on end-to-end CO reasoning.
  arXiv  Detail & Related papers  (2026-02-02T14:55:48Z)
• LLM4CMO: Large Language Model-aided Algorithm Design for Constrained Multiobjective Optimization [54.35609820607923]
  Large language models (LLMs) offer new opportunities for assisting with algorithm design.<n>We propose LLM4CMO, a novel CMOEA based on a dual-population, two-stage framework.<n>LLMs can serve as efficient co-designers in the development of complex evolutionary optimization algorithms.
  arXiv  Detail & Related papers  (2025-08-16T02:00:57Z)
• Pareto Multi-Objective Alignment for Language Models [7.9051473654430655]
  Large language models (LLMs) are increasingly deployed in real-world applications that require careful balancing of multiple, often conflicting, objectives.<n>We propose a principled and computationally efficient algorithm designed explicitly for multi-objective alignment (MOA) in LLMs.<n>PAMA transforms multi-objective RLHF into a convex optimization with a closed-form solution, significantly enhancing scalability.
  arXiv  Detail & Related papers  (2025-08-11T08:54:14Z)
• Pareto-Grid-Guided Large Language Models for Fast and High-Quality Heuristics Design in Multi-Objective Combinatorial Optimization [8.950269044886621]
  Multi-objective optimization problems (MOCOP) frequently arise in practical applications that require the simultaneous optimization of conflicting objectives.<n>We introduce Multi-heuristics for MOCOP via Pareto-Grid-guided Evolution of LLMs (MPaGE)<n>MPaGE utilizes LLMs to prioritize with semantically distinct logical structures during variation, thus promoting diversity and mitigating redundancy within the population.
  arXiv  Detail & Related papers  (2025-07-28T15:26:43Z)
• Improving LLM-based Global Optimization with Search Space Partitioning [40.61249592871905]
  Large Language Models (LLMs) have emerged as effective surrogate models and candidate generators within global optimization frameworks.<n>We propose HOLLM, a novel global optimization algorithm that enhances LLM-driven sampling by partitioning the search space into promising subregions.<n> Empirical evaluation on standard optimization benchmarks shows that HOLLM consistently matches or surpasses leading Bayesian optimization and trust-region methods.
  arXiv  Detail & Related papers  (2025-05-27T16:01:49Z)
• LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning [56.273799410256075]
  The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability.
  arXiv  Detail & Related papers  (2024-10-03T18:12:29Z)
• Self-Exploring Language Models: Active Preference Elicitation for Online Alignment [88.56809269990625]
  We propose a bilevel objective optimistically biased towards potentially high-reward responses to actively explore out-of-distribution regions. Our experimental results demonstrate that when fine-tuned on Zephyr-7B-SFT and Llama-3-8B-Instruct models, Self-Exploring Language Models (SELM) significantly boosts the performance on instruction-following benchmarks.
  arXiv  Detail & Related papers  (2024-05-29T17:59:07Z)
• Multi-Reference Preference Optimization for Large Language Models [56.84730239046117]
  We introduce a novel closed-form formulation for direct preference optimization using multiple reference models. The resulting algorithm, Multi-Reference Preference Optimization (MRPO), leverages broader prior knowledge from diverse reference models. Our experiments demonstrate that LLMs finetuned with MRPO generalize better in various preference data, regardless of data scarcity or abundance.
  arXiv  Detail & Related papers  (2024-05-26T00:29:04Z)
• Large Language Model-Aided Evolutionary Search for Constrained Multiobjective Optimization [15.476478159958416]
  We employ a large language model (LLM) to enhance evolutionary search for solving constrained multi-objective optimization problems. Our aim is to speed up the convergence of the evolutionary population.
  arXiv  Detail & Related papers  (2024-05-09T13:44:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.