Enhanced Particle Swarm Algorithm Boosts Mixed Delivery Fleet Routing Efficiency

Researchers have developed an improved particle swarm optimization framework designed to optimize delivery scheduling for mixed commercial fleets operating under complex road traffic conditions. The study introduces an advanced metaheuristic system that coordinates dispatch plans for hybrid transport networks composed of both electric and conventional fuel-powered vehicles. Across four independent experiments using 29 modified Solomon datasets, the proposed algorithm achieved an average improvement of 38 percent in the obtained optimal solutions.

To address these operational constraints, the investigation examined the Mixed Fleet Vehicle Routing Problem with Time Windows considering Traffic Conditions, designated as MFVRPTW-TC. The routing model simultaneously evaluates distinct vehicle classifications, carrying capacities, dynamic vehicle velocities, customer demand levels, specific delivery time windows, customer service durations, and waiting intervals across the transportation network.

A critical component of the research is a dedicated mathematical method for calculating time-varying travel times across road segments.

To solve the combinatorial challenge, the authors adapted Particle Swarm Optimization, a computational technique widely recognized for resolving continuous numerical problems but traditionally challenging to apply to discrete logistics networks. The research team introduced an Improved Comprehensive Learning Particle Swarm Optimization with Local Search, abbreviated as ICLPSO-LS.

The algorithm structures the discrete routing space using a set-based representation where particle positions and velocities are defined through mathematical sets of arcs and probabilities. Customized operational rules govern how particle velocities and positions update across iterations. To prevent the computational search from stalling in suboptimal configurations, the researchers incorporated a perturbation mechanism known as Improved Dual-Center Particle Swarm Optimization.

The framework further integrates a specialized neighborhood search mechanism operating on the elite individual solutions identified by the search process. This local search phase applies a remove-reinsert neighborhood search mechanism to the elite individuals obtained by the algorithm. Finally, charging stations are inserted according to the constraints to repair infeasible solutions.

Computational evaluations were carried out across 29 modified Solomon benchmark datasets to determine the performance of the algorithm under rigorous operational criteria.

Subject of Research: Mixed fleet vehicle routing optimization under time-varying traffic conditions

Article Title: Improved comprehensive learning particle swarm optimization for solving mixed fleet vehicle routing problem with time windows considering traffic conditions

Article References: Qin, Z., & Pan, D. (2026). Improved comprehensive learning particle swarm optimization for solving mixed fleet vehicle routing problem with time windows considering traffic conditions. Cluster Computing, 29(16), Article 939. https://doi.org/10.1007/s10586-026-06648-y

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06648-y

Keywords: particle swarm optimization, mixed fleet vehicle routing, electric vehicles, vehicle routing problem, time windows, traffic conditions, metaheuristic algorithm, combinatorial optimization, ICLPSO-LS, fleet management, logistics planning, time-varying travel time, local search, Solomon benchmark, transportation analytics