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.

翻译：摘要：现有的神经组合优化求解器将解搜索框架化为对最优决策的模仿，本质上将其效用限制在单目标最小化和静态约束中。我们提出GOAL，一种基于关系图表示的条件扩散求解器，通过对人类指定目标进行条件控制，实现可调控的决策生成。我们引入一种异构图编码，其中不同类型的边对应不同类别的约束，定义了图神经网络的消息传递结构，使得信息能根据每个约束的本体论选择性传播。GOAL在三种不同约束复杂度的经典调度基准上进行了实例化与评估：流水车间问题（FSP）、作业车间调度问题（JSP）和柔性作业车间调度问题（FJSP）。在无需架构修改的情况下，模型在结构不同的约束区间和问题类型上展示了泛化能力。在全部三个基准测试中，对于多达20个作业和60个操作的问题规模，GOAL实现了100%的解可行性和多目标上的近零MAPE（低于0.20%），在解质量和推理速度上均优于NSGA-II和MOEA/D，速度提升高达25倍。