GOAL: Graph-based Objective-Aligned Diffusion Solvers for Dynamic Multi-Objective Optimization

2026-05-20 · Source: cs.NE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

Xingyu Li from Purdue University introduces GOAL (Graph-based Objective-Aligned Diffusion Solvers), a novel conditioned diffusion solver designed for dynamic multi-objective optimization problems (DMOPs) in scheduling. Unlike existing neural combinatorial optimization methods that are limited to single-objective minimization and static constraints, GOAL utilizes a heterogeneous graph encoding with distinct edge types to represent various constraint classes, enabling selective information propagation through a graph neural network. Evaluated on three canonical scheduling benchmarks—Flow Shop Problem (FSP), Job Shop Scheduling Problem (JSP), and Flexible Job Shop Scheduling Problem (FJSP)—GOAL achieves 100% solution feasibility and near-zero Mean Absolute Percentage Error (MAPE) (below 0.20%) on multiple objectives for problem sizes up to 20 jobs and 60 operations. It significantly outperforms traditional evolutionary algorithms like NSGA-II and MOEA/D in both solution quality and inference speed, demonstrating up to a 25x speedup on $\epsilon$-feasible decisions and strong generalization across structurally distinct constraint regimes and problem types without architectural modifications.

Key takeaway

For AI Scientists and Machine Learning Engineers working on complex scheduling or resource allocation, GOAL offers a robust solution for dynamic multi-objective optimization. Its ability to achieve 100% feasibility and significant speedups (up to 25x) over traditional methods, even with unseen constraints, means you can deploy more adaptable and efficient scheduling systems. Consider integrating graph-based diffusion models for problems where both dynamic constraints and multiple, human-specified objectives are critical.

Key insights

GOAL is a graph-based diffusion solver for dynamic multi-objective optimization, achieving high feasibility and speed.

Principles

• Heterogeneous graph encoding improves constraint reasoning.
• Conditional diffusion models can directly target objectives.
• Classifier-free guidance enables controllable generation.

Method

GOAL uses a discrete diffusion process over binary precedence relations, a relational graph neural network (RGNN) with type-specific message passing, and classifier-free guidance to generate feasible schedules conditioned on objectives and dynamic constraints.

In practice

• Apply GOAL to dynamic scheduling with evolving constraints.
• Use heterogeneous graphs for complex constraint modeling.
• Employ classifier-free guidance for objective-aligned solutions.

Topics

• Dynamic Multi-Objective Optimization
• Diffusion Models
• Graph Neural Networks
• Job Shop Scheduling
• Relational Graph Neural Networks

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.