A hybrid path-relinking method for solving two-stage stochastic integer problems

Abstract

Path relinking has been used for solving deterministic problems by exploring the neighborhood of elite solutions in an intelligent way. We present an algorithm that combines a mixed-integer linear solver with a truncated path-relinking method in order to solve two-stage stochastic integer problems with complete recourse and first-stage integer variables. This method takes advantage of a possible scenario-based decomposition in an innovative way. Therefore, path relinking is used to combine optimized solutions from different scenarios in order to pursue good stochastic solutions. To assess the computational performance of this method, we use the stochastic lot sizing and scheduling problem dealing with perishable products. In this problem, first-stage decision variables are linked to production sequences and production quantities. After the uncertain demand is unveiled, the second-stage variables decide on the inventory usage. Computational results show a clear advantage of the proposed method when compared to a state-of-the-art mixed-integer linear solver.