Exact Algorithms for Generating the Efficient Set of Multi-Objective Stochastic Integer Linear Programs

In this paper, we propose two new methods for generating the set of all efficient solutions to a discrete multi-objective optimization problem under uncertainty, also known as stochastic multiple objective integer linear programming problem. The suggested approaches follows the standard state-of-the-art formulation requiring a two-stage integer stochastic formulation with fixed recourse and using the L-shaped method as a main framework. Furthermore, the suggested method can be perceived as adaptations of deterministic discrete multi-objective optimization methods to the stochastic context. Finally, the obtained computational results show that our methods can solve large-scale randomly generated instances. A comprehensive computational study on structured benchmark problems, including the well known George B. Dantzig (GBD) benchmark instances and the newly introduced stochastic bi-objective knapsack problem (SBKP) benchmark instances, further demonstrates the practical efficiency of the proposed approaches.