Purpose: This model aims to solve a Green Heterogeneous and Stochastic Capacitated Vehicle Routing Problem that considers risks and environmental hazards.

Research Methodology: Regarding an NP-hard and complex problem, and after confirming the accuracy of the problem-solving in smaller dimensions by GAMS software, the problem is solved by the metaheuristic algorithm of multi-objective particle swarm optimization (MOPSO) and its coding in MATLAB software.

Results: The results urge that using random sampling and probability The findings indicate that MOPSO effectively produces optimal or near-optimal solutions with significantly reduced computational time compared to GAMS. In small-scale cases, results matched the exact solutions, while larger-scale instances demonstrated the efficiency of the algorithm in handling complex routing problems. Sensitivity analyses revealed that prioritization of objectives—such as environmental impact, reliability, or routing cost—led to different but balanced routing strategies, confirming the model’s adaptability.

Conclusions: The proposed model ensures reliable and environmentally conscious waste transportation by integrating cost, risk, and time-window considerations. It demonstrates strong performance in optimizing multi-objective routing problems under uncertainty.

Limitation: The proposed method is a routing problem and has been applied for the Green Heterogeneous and Stochastic Capacitated Vehicle Routing Problem. Future researchers may work on real data sets and hazardous biomedical waste data.

Contribution: Based on the results presented, the model derived in this study can support decisions such as routing, prioritization, and time to reach each node, so that the costs of routing, system reliability, environmental issues, and penalties for violation of the priority and maximum time elapsed for vehicles are considered.