Hybrid evolutionary algorithms and Lagrangian relaxation for multi-period star hub median problem considering financial and service quality issues

Hub facilities are centralized locations that consolidate and distribute the commodities in transportation networks. In many real world applications, transport service providers may prefer to lease hub for a time horizon rather than being owned or constructed. this paper, modeling framework is proposed multi-period location problem arises design of star–star network with two types hubs links. It includes designated static central hub, some movable set nodes pairwise demands. A periodic growth amount budget considered at each period expand an interest rate also applied unused available during period. Since overall quality services spoke systems rely on length paths, upper bound constraints paths between nodes. Numerical experiments carried out show applicability model. Due computational complexity model, improved genetic algorithm (GA) hybrid particle swarm optimization (HPSO) utilized find near optimal solutions. Both algorithms employ caching strategy improve computation times. Moreover, HPSO benefits from operators local search methods update particles. order assess effectiveness methods, results compared pure GA proper lower achieved by Lagrangian relaxation method.