An Investigation into the Rescue-Path Planning Algorithm for Multiple Mine Rescue Teams Based on FA-MDPSO and an Improved Force-Directed Layout

It is noted that existing mine emergency-rescue algorithms have overlooked the requirement for multi-route sharing at critical nodes and have offered limited network visualisation. Consequently, a multi-team rescue-path-planning algorithm based on FA-MDPSO (Firefly Algorithm-Multiple Constraints Discrete Particle Swarm Optimisation) was proposed, and a graph-structure optimisation method combining a Force-Directed Layout with Breadth-First Search was introduced for node arrangement and visualisation. Methodologically, the superiority of the improved DPSO (Discrete Particle Swarm Optimisation) in route-planning precision was first validated on the DIMACS dataset. Subsequently, the hyperparameters of MDPSO (Multiple Constraints Discrete Particle Swarm Optimisation) were optimised by means of four intelligent algorithms—ACO (Ant Colony Optimization), FA (Firefly Algorithm), GWO (Grey Wolf Optimizer) and WOA (Whale Optimization Algorithm). Finally, simulations of one to three rescue-team deployments were conducted within a mine-fire scenario, and node-importance analysis was performed. Results indicated that FA-MDPSO achieved comprehensive superiority in route precision, search efficiency and convergence speed, with FA-based hyperparameter optimisation proving most effective in comparative experiments. The graph-structure optimisation was found to substantially reduce crossings and enhance hierarchical clarity. Moreover, the three-team deployment yielded the shortest equivalent path (56,357.02), and node-visitation frequency was observed to be highly concentrated on a small number of key nodes. This not only significantly improves the collaborative rescue efficiency but also provides intuitive and practical technical support for intelligent mine rescue operations. It lays an important foundation for optimising mine emergency rescue plans, ensuring the safety of underground personnel, and promoting the intelligent development of mines.