An interactive fuzzy satisficing method for multiobjective stochastic defensive location problems

This paper extends the defensive location problem (DLP), proposed by Uno and Katagiri, considering the situations that the defender locates defensive facilities for preventing invaders from reaching some important vertices in a network. Their DLPs assumed that invaders, with a given energy, exist on a given vertex in it. On the other hand, this paper considers a new DLP that invaders´ sites and energies are given uncertainly. By representing their existing vertices and energies as random variables with scenarios, the new DLP can be formulated as a multiobjective bilevel stochastic programming problem. In order to find a satisficing solution of the decision maker for the multiobjective DLP, an interactive fuzzy satisficing method with tabu search algorithm based on strategic oscillation is proposed. The efficiency of the proposed method is shown by applying it to numerical examples of the DLPs.