A topology-aware cooperative optimization framework: integrating heuristic beam search with adaptive NSGA-II for constrained port scheduling

Abstract In strongly coupled coal port environments, traditional scheduling models face a fundamental conflict between search efficiency and multi-objective global optimality. Existing methods often struggle because the feasible solution space is sparse, leading standard evolutionary algorithms to expend excessive computational resources on invalid solutions. To resolve this, this study proposes a Topology-Aware Cooperative Optimization Framework (HSA-ENSGA-II). Unlike simple hybridizations, this framework establishes a hierarchical ‘guidance-evolution’ mechanism. First, a specialized A*-Beam Search (A*BS-BFS) module constructs a high-quality feasible subspace by pruning invalid search branches in the task-resource graph. This process effectively projects the search onto a sparse subgraph of valid solutions, preventing the combinatorial explosion typical of constrained scheduling. Second, an enhanced NSGA-II, incorporating Adaptive Hierarchical Selection (AHS) and Variable Neighborhood Operators (VNOs), performs global optimization within this refined space. Crucially, a dynamic feedback mechanism reinjects unexplored heuristic branches when evolutionary stagnation occurs, distinguishing this approach from simple heuristic initialization. Theoretical complexity analysis and ablation studies confirm that the heuristic guidance acts as a computational catalyst, reducing total runtime by ∼20% not merely through initialization, but by actively reshaping the search landscape. Experimental validation on DTLZ benchmarks (IGD: 0.008) and proprietary port data demonstrates that the model achieves a hypervolume of 0.928. By reducing average waiting time to 29.8 min and fuel consumption to 603 l, the proposed framework successfully resolves the conflict between search efficiency and global optimality.