Variable neighborhood tabu search and its application to the median cycle problem

The Variable Neighborhood Tabu Search consists of a constructive phase and a series of local searches that use tabu tools. When the local search stops at a nontabu local minimum, a shake procedure starts a new local search. The local searches and the shake procedure are based on a series of standard moves. The local search consists of applying the best possible move until no such move exists. The shake procedure consists of applying a number of random moves. Since the shake could provide an infeasible solution, the local search considers as possible moves those providing a feasible solution or reducing the infeasibility. A location/allocation problem consists of selecting the location for some facilities and the allocation of the users to them. Two functions to be minimized are considered: the length of the solution, as a measure of the set of locations, and the total cost of the allocations. The standard moves for these problems are the add, drop and add/drop moves. The heuristic procedure is tested on the Median Cycle Problem.