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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.12106 |
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| _version_ | 1866918497117798400 |
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| author | Xu, Peipei Ma, SiYuan Liu, Yaohua Wu, Yu Liu, Guanliang Zhang, Yang Liu, Yong |
| author_facet | Xu, Peipei Ma, SiYuan Liu, Yaohua Wu, Yu Liu, Guanliang Zhang, Yang Liu, Yong |
| contents | Generating feasible Pareto fronts for constrained bi-objective continuous optimization is central to multi-criteria decision-making. Existing methods usually rely on iterative scalarization, evolutionary search, or problem-specific solvers, requiring repeated optimization for each instance. We introduce DIPS, an end-to-end framework that fine-tunes large language models as amortized Pareto-front generators for constrained bi-objective convex optimization. Given a textual problem description, DIPS directly outputs an ordered set of feasible continuous decision vectors approximating the Pareto front. To make continuous optimization compatible with autoregressive language modeling, DIPS combines a compact discretization scheme, Numerically Grounded Token Initialization for new numerical tokens, and Three-Phase Curriculum Optimization, which progressively aligns structural validity, feasibility, and Pareto-front quality. Across five families of constrained bi-objective convex problems, a fine-tuned 7B-parameter model achieves normalized hypervolume ratios of 95.29% to 98.18% relative to reference fronts. With vLLM-accelerated inference, DIPS solves one instance in as little as 0.16 seconds and outperforms general-purpose and reasoning LLM baselines under the evaluated setting. These results suggest that LLMs can serve as effective amortized generators for continuous Pareto-front approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12106 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large Language Models as Amortized Pareto-Front Generators for Constrained Bi-Objective Convex Optimization Xu, Peipei Ma, SiYuan Liu, Yaohua Wu, Yu Liu, Guanliang Zhang, Yang Liu, Yong Artificial Intelligence Generating feasible Pareto fronts for constrained bi-objective continuous optimization is central to multi-criteria decision-making. Existing methods usually rely on iterative scalarization, evolutionary search, or problem-specific solvers, requiring repeated optimization for each instance. We introduce DIPS, an end-to-end framework that fine-tunes large language models as amortized Pareto-front generators for constrained bi-objective convex optimization. Given a textual problem description, DIPS directly outputs an ordered set of feasible continuous decision vectors approximating the Pareto front. To make continuous optimization compatible with autoregressive language modeling, DIPS combines a compact discretization scheme, Numerically Grounded Token Initialization for new numerical tokens, and Three-Phase Curriculum Optimization, which progressively aligns structural validity, feasibility, and Pareto-front quality. Across five families of constrained bi-objective convex problems, a fine-tuned 7B-parameter model achieves normalized hypervolume ratios of 95.29% to 98.18% relative to reference fronts. With vLLM-accelerated inference, DIPS solves one instance in as little as 0.16 seconds and outperforms general-purpose and reasoning LLM baselines under the evaluated setting. These results suggest that LLMs can serve as effective amortized generators for continuous Pareto-front approximation. |
| title | Large Language Models as Amortized Pareto-Front Generators for Constrained Bi-Objective Convex Optimization |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2605.12106 |