An improved L-shaped method for two-stage convex 0–1 mixed integer nonlinear stochastic programs
•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...
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| Veröffentlicht in: | Computers & chemical engineering Jg. 112; S. 165 - 179 |
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06.04.2018
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| ISSN: | 0098-1354, 1873-4375 |
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| Abstract | •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. |
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| AbstractList | •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. |
| Author | Li, Can Grossmann, Ignacio E. |
| Author_xml | – sequence: 1 givenname: Can surname: Li fullname: Li, Can – sequence: 2 givenname: Ignacio E. orcidid: 0000-0002-7210-084X surname: Grossmann fullname: Grossmann, Ignacio E. email: grossmann@cmu.edu |
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