Task Decomposition Method for a Multi-Agent Collaborative Decision-Making System in Coal Mines

Task decomposition is a fundamental challenge in multi-agent collaborative maintenance systems, where unstructured natural language instructions must be precisely translated into logically coherent, executable sub-task sequences. This paper formulates task decomposition as a constrained optimal path search problem on a heterogeneous knowledge graph that encodes coal mine equipment topology, fault causality, and maintenance procedures. We construct a composite cost function that systematically integrates semantic similarity from graph neural network embeddings, relation-type weights, and structural path length, transforming instruction parsing into a mathematically tractable combinatorial optimization. The cost function is derived from the principles of shortest-path reasoning in knowledge graphs: the relational weights capture domain-specific association strengths, the semantic similarity term promotes contextually coherent chains, and the path-length penalty prevents unnecessarily long derivations. A multi-hop reasoning algorithm coupling heterogeneous graph convolution with beam search is developed to solve this problem efficiently, achieving high-quality approximate solutions while ensuring computational tractability. The reasoning process is inherently interpretable, as the optimal path directly maps to a traceable atomic task sequence with explicit dependency relations. A formal complexity analysis shows the algorithm scales as O(b·K·dmax), where b is the beam width and dmax is the maximum node degree. Several theoretical properties of the proposed framework are further derived: the cost function is non-negative and strictly monotonic, optimal paths satisfy the optimal substructure property, cycle-free optimal paths always exist, and beam search can yield globally optimal solutions given a sufficiently large beam width. These theoretical conclusions establish mathematical guarantees for the presented decomposition framework. Experiments on 200 composite maintenance instructions with gold-standard annotations (inter-annotator agreement Cohen’s κ=0.88) demonstrate that the proposed method achieves 94.3% task sequence accuracy (95% CI: 91.2–96.8%) and 96.4% dependency accuracy (95% CI: 93.5–98.1%), substantially outperforming both a rule-augmented baseline (58.6%, 62.1%) and a GPT-4o few-shot chain-of-thought baseline (73.2%, 70.5%); McNemar’s test yields p < 0.001 for both comparisons. The average inference time is 29.7 ms (SD 2.1 ms), meeting stringent industrial real-time constraints. Ablation studies quantify the contribution of each cost function component and confirm the robustness of the chosen beam width and hyperparameters. When integrated into a full multi-agent system, the framework delivers end-to-end response time within 3 s (P50: 1.87 s, P95: 2.83 s) and maintains an 86.7% task success rate even under dual agent failures, validating the robustness of the proposed mathematical formulation. This work establishes a rigorous graph-theoretic foundation for instruction decomposition in multi-agent systems, with direct applicability to safety-critical industrial environments.