Heuristic Solution for the p-hub Problem

The hub location problem is important in the selection of technological networks, such as computer, cellular, or wireless sensor networks. These modern communication networks must be dynamically set as triggered by changes in external conditions; the nodes deplete their batteries and go out of service. For this reason, it is necessary to update the available data in order to determine which nodes can be used as hubs. The dynamic location problem requires a short solution time in despite of optimality. Heuristic methods are used for their simplicity and they are easy to package in the firmware. The central aim of this work is to design a heuristic method that will obtain a good feasible solution in a reasonable amount of time. The methodology proposed for the heuristic method consists of obtaining the optimum solution of the relaxed problem, followed by rounding this solution to a 0 or 1 value. The strategy developed for rounding the calculations is to first use a measure, called attractive force, for each node and then to define those nodes more attractive as hubs. Finally, an integer programming model is solved for assigning the nodes to the selected hubs. An interesting result is that the hubs selected by the optimal solution of the relaxed problem are always between the nodes that have the major attractive force. The heuristic algorithm is well established for problems with 10, 20, 25, 50 and 100 nodes. So, mixing two levels of difficulty we obtain four problems. Key–Words: Hubs, location, networks, integer programming, heuristics.