Multi-Cooperative Agricultural Machinery Scheduling with Continuous Workload Allocation: A Hybrid PSO Approach with Sparsity Repair

Scheduling agricultural machinery across multiple cooperatives is often inefficient because existing rigid, discrete assignment models fail to flexibly coordinate shared resources under tight time windows. To address this limitation, we develop a simulation-based framework for the Multi-cooperative Agricultural Machinery Scheduling Problem (MAMSP) underpinned by a Continuous Collaborative Workload Sharing (CWS) formulation. To mitigate the solution fragmentation inherent in continuous optimization, we propose a Hybrid Particle Swarm Optimization with Sparsity Repair (HPSO-SR). The algorithm integrates a stochastic initialization strategy to enhance global exploration, a mutation injection mechanism to avoid swarm stagnation, and a sparsity repair operator that prunes uneconomical fractional assignments, yielding operationally feasible sparse schedules. A real-world case study from Liyang, China, augmented by synthetic instances of varying scales (small, medium, and large), was conducted to benchmark the proposed approach against a rule-based heuristic, a Genetic Algorithm (GA-CWS), and Simulated Annealing (SA-CWS) under a unified decoding scheme. The results show that HPSO-SR consistently achieves the lowest objective values, reducing the total cost by 74.43% relative to GA-CWS and 59.20% relative to SA-CWS in the medium-scale case. By deliberately trading off minimal additional transfer cost against improved timeliness, the obtained schedules nearly eliminate delay penalties. Sensitivity analysis and mechanism ablation studies further confirm that the sparse solutions exhibit structural resilience and that the proposed repair strategy is essential for algorithmic convergence, supporting the reliability of the proposed approach for time-critical, high-stakes agricultural operations.