Research on Vehicle Path Planning Method with Time Windows in Uncertain Environments

With the growing complexity of logistics and the demand for sustainability, the vehicle routing problem (VRP) has become a key research area. Classical VRPs now incorporate practical challenges such as time window constraints and carbon emissions. In uncertain environments, where many factors are stochastic or fuzzy, optimization models based on uncertainty theory have gained increasing attention. A single-objective optimization model is proposed in this paper to minimize the total cost of VRP in uncertain environments, including fixed costs, transportation costs, and carbon emission costs. Practical constraints like time windows and load capacity are incorporated, and uncertain variables, such as carbon emission factors, are modeled using normal distributions. Two uncertainty models, based on the expected value and chance-constrained criteria, are developed, and their deterministic forms are derived using the inverse distribution method. To solve the problem effectively, a hybrid ant colony–zebra optimization algorithm is proposed, integrating ant colony optimization, zebra optimization, and the 3-opt algorithm to enhance global search and local optimization. Numerical experiments demonstrate the superior performance of the hybrid algorithm, achieving lower total costs compared to standalone ant colony, zebra optimization, genetic algorithm, and particle swarm optimization algorithms. The results highlight its robustness and efficiency in addressing complex constraints.