Non-dominated sorting simplified swarm optimization for multi-objective omni-channel of pollution routing problem

The activities of the traffic department mainly contribute to the generation of greenhouse gas (GHG) emissions. The swift expansion of the traffic department results in a significant increase in global pollution levels, adversely affecting human health. To address GHG emissions and propose impactful solutions for reducing fuel consumption in vehicles, environmental considerations are integrated with the core principles of the Vehicle Routing Problem (VRP). This integration gives rise to the Pollution Routing Problem (PRP), which aims to optimize routing decisions with a focus on minimizing environmental impact. At the same time, the retail distribution system explores the use of an Omni-channel approach as a transportation mode adopted in this study. The objectives of this research include minimizing total travel costs and fuel consumption while aiming to reduce GHG emissions, promote environmental sustainability, and enhance the convenience of shopping and pickup for customers through the integration of online and offline modes. This problem is NP-Hard; therefore, the Non-dominated Sorting Simplified Swarm Optimization (NSSO) algorithm is employed. NSSO combines the non-dominated technique of Non-dominated Sorting Genetic Algorithm II (NSGA-II) with the update mechanism of SSO to obtain a set of Pareto optimal solutions. Moreover, the NSSO, a multi-objective evolutionary algorithm, is adopted to address multi-objective problems. The PRP benchmark dataset is utilized, and the results are compared with two other multi-objective evolutionary algorithms: NSGA-II and Non-dominated Sorting Particle Swarm Optimization (NSPSO). The findings of the study confirm that NSSO exhibits feasibility, provides good solutions, and achieves faster convergence compared to the other two algorithms, NSGA-II and NSPSO.