Local search heuristic for the discrete leader-follower problem with multiple follower objectives

Abstract

We study a discrete bilevel problem, called as well as leader-follower problem, with multiple objectives at the lower level. It is assumed that constraints at the upper level can include variables of both levels. For such ill-posed problem we define feasible and optimal solutions for pessimistic case. A central point of this work is a two stage method to get a feasible solution under the pessimistic case, given a leader decision. The target of the first stage is a follower solution that violates the leader constraints. The target of the second stage is a pessimistic feasible solution. Each stage calls a heuristic and a solver for a series of particular mixed integer programs. The method is integrated inside a local search based heuristic that is designed to find near-optimal leader solutions.