Optimizing a Fuzzy Green p-hub Centre Problem using Opposition Biogeography Based Optimization

Hub networks have always been acriticalissue in locating health facilities. Recently, a study has been investigated by Cocking et al. (2006)in Nouna health district in Burkina Faso, Africa, with a population of approximately 275,000 people living in 290 villages served by 23 health facilities. The travel times of the population to health services become extremely high during the rainy season, since many roads are unusable. In this regard, for many people, travelling to a health facility is a deterrent to seeking proper medical care. Furthermore, in real applications of hub networks, the travel times may vary due to traffic, climate conditions, and land or road type.To handle this challenge this paper considers the travel times are assumed to be characterized by trapezoidal fuzzy variables in order to present a fuzzy green capacitated single allocation p-hub center system (FGCSApHCP) with uncertain information. The proposed FGCSApHCP is redefined into its equivalent parametric integer nonlinear programming problem using credibility constraints. The aim is to determine the location of pcapacitated hubs and the allocation of center nodes to them in order to minimize the maximum travel time in a hub-and-center network in such uncertain environment. As the FGCSApHCP is NP-hard, a novel algorithmcalledoppositionbiogeography based optimizationis developed to solve that. This algorithm utilizes a binary oppositionbased learning mechanism to generate a diversity mechanism. At the end, both the applicability of the proposed approach and the solution methodologies are demonstrated using GAMS/BARON Software under severalkind of problems. Sensitivity analyses on the number of hubs and center nodes are conducted toprovide more insights as well.