Solving a class of two-stage stochastic nonlinear integer programs using value functions

We propose a level-set characterization of the value function of a class of nonlinear integer programs with finite domain. We study the theoretical properties of this characterization and show the equivalence between the set of level-set minimal vectors and a set of non-dominated right-hand side vectors. We use these properties to develop a solution approach for two-stage nonconvex integer programs with stochastic right-hand sides. The proposed approach can solve problems with pure integer variables in both stages. We demonstrate the effectiveness of the proposed approach using a nonlinear generalized assignment problem with uncertain capacity. We also conduct computational experiments using two-stage quadratically-constrained quadratic integer programs with stochastic right-hand sides. The proposed value function-based approach can solve instances whose extensive forms are among the largest stochastic quadratic integer programs solved in the literature with respect to the number of rows and variables in extensive form, and with considerably more rows.