An improved L-shaped method for two-stage convex 0–1 mixed integer nonlinear stochastic programs. (6th April 2018)

• Record Type: Journal Article
• Authors: Li, Can; Grossmann, Ignacio E.
• Is Part Of: Computers & chemical engineering. Volume 112(2018)
• Page Start: 165
• Page End: 179
• Publication Date: 2018-04-06
• Subjects: Stochastic programming -- L-shaped method -- Convex MINLP -- Integer recourse; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2018.01.017
• Languages: English
• ISSNs: 0098-1354

Abstract

Highlights: 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. Abstract: 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.