Improved Benders Decomposition and Feasibility Validation for Two-Stage Chance-Constrained Programs in Process Optimization

Abstract

The two-stage stochastic program with probabilistic constraints is studied by assuming normally distributed uncertain parameters. At stage I, the decision, represented by discrete variables, is made such that normal operations can be applied at stage II with high probability. At stage II, the uncertainty is realized and the optimal decision, represented by continuous variables, is determined accordingly. Different from the conventional two-stage decision process, recovery operations are introduced at stage II if normal operations are infeasible. This two-stage decision process can be approximately modeled by a scenario-based mixed-integer linear program (MILP). Two issues of this scheme are concerned. First, with more samples, the solution of the scenario-based MILP is closer to the original problem, but the computational demands increase significantly. Second, the feasibility of such a solution under unseen scenarios cannot be guaranteed. To overcome these two limitations, an improved Benders decomposition method is first proposed to calculate the globally optimal solution of the scenario-based MILP more efficiently than existing algorithms. Second, the probabilistic feasibility of a stage I solution from the improved Benders decomposition is rigorously evaluated through a chance-constrained program with linear decision rule. A refinery optimization problem is solved through the proposed scheme to verify the computational efficiency and probabilistic feasibility.

CVaR-Based Approximations of Wasserstein Distributionally Robust Chance Constraints with Application to Process Scheduling

“…Even with a small number of uncertain variables, solving the above optimization problem is computationally intensive. Although Li et al, − Rong et al, , Yang et al, , and Ostrovsky et al , have derived multivariate integration approaches and solution algorithms for CCP, none of them is universally applicable to all commonly used probability distributions. There are merely a few special cases under which chance constraints can be reformulated into tractable convex constraints.…”