Mehdi Khadem - Department of Industrial Management, Faculty of Management and Economics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Akbar Khadem - Department of Electrical and Electronic Engineering, Garmsar Branch, Islamic Azad University, Garmsar, Iran
Alireza Khadem - Department of Civil Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
Shahram Khadem - Department of English language and Literature, Central Tehran Branch, Islamic Azad University, Tehran, Iran

The vehicle routing problem (VRP) is one of the most well-known topics in complex combinatorial optimization problems. In the current research, several warehouses send goods to customers. The start time of the service has two timed windows, hard and soft, and each customer has a request for delivery and loading at the same time. The main goal of solving the minimization problem is to minimize system costs, including displacement, fixed cost of vehicles, cost of not respecting the soft time window, and additional cost due to depreciation caused by the amount of load on the vehicle. In this research, first, the conceptual model of the problem is defined and modelled, and then, considering the complexity of the problem, a hybrid genetic algorithm is used. In this hybrid genetic algorithm, the particle swarm algorithm first creates the initial population, and neighbourhood search is used in each step after mutation.The vehicle routing problem (VRP) is one of the most well-known topics in complex combinatorial optimization problems. In the current research, several warehouses send goods to customers. The start time of the service has two timed windows, hard and soft, and each customer has a request for delivery and loading at the same time. The main goal of solving the minimization problem is to minimize system costs, including displacement, fixed cost of vehicles, cost of not respecting the soft time window, and additional cost due to depreciation caused by the amount of load on the vehicle. In this research, first, the conceptual model of the problem is defined and modelled, and then, considering the complexity of the problem, a hybrid genetic algorithm is used. In this hybrid genetic algorithm, the particle swarm algorithm first creates the initial population, and neighbourhood search is used in each step after mutation.

Hybrid Genetic Algorithm, Route Type, Multiple Warehouses, Time window, Vehicle Routing Problem