Over the past decades, the Multicommodity Network Flow (MCNF) problem has grown
popular in the academic literature and a growing number of researchers are interested in …

The literature on k-splittable flows, see Baier et al.(2002), provides evidence on how
controlling the number of used paths enables practical applications of flows optimization in …

Single‐path multicommodity flow problem (SMCFP) is a well‐known combinatorial
optimization problem, in which the flow of each commodity can be transmitted using only …

The multicommodity flow problem (MCFP) considers the efficient routing of commodities
from their origins to their destinations subject to capacity restrictions and edge costs. Baier et …

In the literature on Network Optimization, k-splittable flows were introduced to enhance
modeling accuracy in cases where an upper bound on the number of supporting paths for …

The Multi-Commodity k-splittable Maximum Flow Problem consists in routing as much flow
as possible through a capacitated network such that each commodity uses at most k paths …

Vertical Take Off and Landing (VTOLs) vehichules are used to move passengers between
skyports in urban air mobility. Safety landing sites (SLSs) cover the trajectory of VTOLs for …

In the multiple protocol label-switched (MPLS) networks, the commodities (packets) are
transmitted by the label-switched paths (LSPs). For the sake of reducing the total cost and …

Abstract The Multi-Commodity k-splittable Maximum Flow Problem consists of maximizing
the amount of flow routed through a network such that each commodity uses at most k paths …

In the k-splittable flow problem, each commodity can only use at most k paths and the key
point is to find the suitable transmitting paths for each commodity. To guarantee the …