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

2026-05-18

AI Summary

Existing neural combinatorial optimization methods struggle with dynamic multi-objective settings and complex constraints. This work proposes a relation-graph-based conditional diffusion solver that, for the first time, integrates conditional diffusion models with heterogeneous graph neural networks. By treating user-specified objectives as generation conditions and designing a constraint-aware message-passing mechanism over heterogeneous graphs, the approach enables controllable multi-objective solution generation. Without architectural modifications, the method generalizes across scheduling problems of varying structures and types, achieving 100% solution feasibility and a multi-objective mean absolute percentage error (MAPE) below 0.20% on FSP, JSP, and FJSP benchmarks. It outperforms NSGA-II and MOEA/D by up to 25× in both solution quality and inference speed.

Abstract

Existing neural combinatorial optimization solvers frame solution search as imitation of optimal decisions, inherently limiting their utility to single-objective minimization and static constraints. We propose GOAL, a conditioned diffusion solver over relational graph representations that enables controllable decision generations by conditioning on human-specified objectives. We introduce a heterogeneous graph encoding in which distinct edge types, corresponding to different classes of constraints, define the message passing structure of the graph neural network, which allows information to propagate selectively according to the ontology of each constraint. GOAL is instantiated and evaluated on three canonical scheduling benchmarks of various constraint complexity: the Flow Shop Problem (FSP), the Job Shop Scheduling Problem (JSP), and the Flexible Job Shop Scheduling Problem (FJSP). Generalization is demonstrated across structurally distinct constraint regimes and problem types without architectural modification. On all three benchmarks, GOAL achieves 100% solution feasibility and near-zero MAPE (below 0.20%) on multiple objectives for problem sizes up to 20 jobs and 60 operations, outperforming NSGA-II and MOEA/D in both solution quality and inference speed by up to 25x.

Problem

• Dynamic Multi-Objective Optimization
• Combinatorial Optimization
• Scheduling Problems
• Constraint Handling
• Neural Solvers

Innovation

• conditional diffusion
• heterogeneous graph encoding
• multi-objective optimization
• combinatorial optimization
• graph neural networks