An improved L-shaped method for two-stage convex 0–1 mixed integer nonlinear stochastic programs - Li, Can; Grossmann, Ignacio E. (Computers & chemical engineering, 2018)
•Algorithm for convex nonlinear stochastic programs with mixed-integer recourse.•Combination of Lagrangean cuts and (strengthened) Benders cuts in L-shaped method.•Application to a planning and a batch plant design problem under uncertainty.•The proposed algorithm outperforms the commercial solvers for large problems. In this paper, we propose an improved L-shaped method to solve large-scale two-stage convex 0–1 mixed-integer nonlinear stochastic programs with mixed-integer variables in both first and second stage decisions and with relatively complete recourse. To address the difficulties in solving large problems, we propose a Benders-like decomposition algorithm that includes both (strengthened) Benders cuts and Lagrangean cuts in the Benders master problem. The proposed algorithm is applied to solve a batch plant design problem under demand uncertainty, and a planning problem under demand and price uncertainty. It is shown that the proposed algorithm outperforms the commercial solvers, DICOPT, SBB, Alpha-ECP, and BARON, for the problems with a large number of scenarios. Also, although the proposed algorithm cannot close the duality gap, it is proved that it can yield a lower bound that is at least as tight as the one from Lagrangean decomposition.