A green time-dependent traveling salesman problem with intermediate node and multiple traffic states

The aim of this paper is to develop a new green time-dependent traveling salesman problem with intermediate node and multiple traffic states (GTDTSPIM), minimizing the amount of emission from goods transport. Several factors such as vehicle routing, level of speed in different routes, load in each route, as well as dispatching time a vehicle are considered to obtain the optimal value of objective function. The model is formulated as a mixed integer nonlinear programming (MINLP) in which the objective function is nonlinear whereas constraints are linear functions. The key parameters affecting the emissions level, except the fleet (due to the sales zoning policy), are considered in the model formulation. Note that the multiple traffic modes and intermediate node are formulated as an optimization problem for the first time in this paper. Also, we consider speed as a decision variable that has constant value (exogenous) in three congestion states while it varies in free-flow mode (indigenous). A real-life case study is provided to show the capability of the proposed model in which the distance between two nodes is not calculated based on Euclidean distance and distance matrix of all nodes asymmetrical. To solve the model, an enumeration method, a Particle Swarm Optimization (PSO) method with pbest, gbest, and lbest, as well as a new version of PSO, called GLN-PSO, and five new swarm-based metaheuristic methods i.e. Emperor Penguin Optimizer (EPO), Seagull Optimization Algorithm (SOA), Artificial Lizard Search Optimization (ALSO), Honey Badger Algorithm (HBA) and Mayfly Optimization Algorithm (MA) are adapted and their results be compared with each other. The results show that ALSO and PSO have the same efficiency for solving the proposed model and there is significant difference between the efficiency of the above algorithms with the rest algorithm.