A novel Hybrid PSO-Heuristic Algorithm with Combinatorial Benders' Cuts for maximal evacuation planning in wildfire disasters

• Hybrid PSO-Heuristic Algorithm for solving complex nonlinear evacuation problems. • Developed a mathematical model with real-world constraints like road blockages. • Linearized model with Combinatorial Benders' Cuts (CBC) for enhanced solution efficiency. • Numerical experiments show practical application and rapid solutions using HPSO-HA. • New methodologies improve emergency evacuation planning during wildfire disasters. Natural disasters, such as floods and fires, affect various regions of the world every year. One of the most critical aspects of disaster management and planning is facilitating the evacuation of people. Therefore, this study develops a mathematical model for emergency evacuation, taking into account the constraints and limitations of transferring individuals to shelters. The model, called the maximal bus evacuation planning, considers constraints including road blockages, vehicle fuel, and passenger capacities. Given the Nondeterministic Polynomial-time hard complexity of this problem, a Hybrid Particle Swarm Optimization–Heuristic Algorithm, which combines the Particle Swarm Optimization Algorithm with a Heuristic Algorithm , is used to solve the nonlinear model. Furthermore, we linearize the model and solve it using the developed Combinatorial Benders' Cuts approach in three versions. Numerical computations are examined under various scenarios, and the outputs of the Hybrid Particle Swarm Optimization – Heuristic algorithm reach suitable solutions within a short timeframe. Additionally, the results from solving the linearized model using the Combinatorial Benders' Cuts show that, in most cases, the execution time of the second version is better than the other versions.