Large Language Models as Amortized Pareto-Front Generators for Constrained Bi-Objective Convex Optimization

TL;DR

This paper introduces DIPS, a framework that fine-tunes large language models to directly generate approximate Pareto fronts for constrained bi-objective convex optimization from textual descriptions, achieving high accuracy and speed.

Contribution

The paper presents a novel method that uses LLMs as amortized Pareto-front generators, combining discretization, token initialization, and curriculum optimization for efficient multi-criteria decision-making.

Findings

Fine-tuned 7B LLM achieves 95.29%-98.18% hypervolume ratio.

DIPS solves instances in as little as 0.16 seconds with vLLM acceleration.

Outperforms baseline methods in Pareto-front approximation quality.

Abstract

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.