The Vehicle Routing Problem (VRP) has been thoroughly studied in the last decades. However, the main
focus has been on the deterministic version where customer demands are fixed and known in advance.
Uncertainty in demand has not received enough consideration. When demands are uncertain, several
problems arise in the VRP. For example, there might be unmet customers’ demands, which eventually
lead to profit loss. A reliable plan and set of routes, after solving the VRP, can significantly reduce the
unmet demand costs, helping in obtaining customer satisfaction. This paper investigates a variant of
an uncertain VRP in which the customers’ demands are supposed to be uncertain with unknown distributions.
An advanced Particle Swarm Optimization (PSO) algorithm has been proposed to solve such a
VRP. A novel decoding scheme has also been developed to increase the PSO efficiency. Comprehensive
computational experiments, along with comparisons with other existing algorithms, have been provided
to validate the proposed algorithms.