Location: JHE 326H
Process systems engineering is concerned with decision-making problems for the discovery, design, manufacture and distribution of chemical products. These problems are often cast as mathematical programming problems, which can be very difficult to solve due to two major reasons. One is large problem size that comes from the consideration of uncertainty and/or the large-scale of the physical system. The other is nonconvexity that usually comes from nonlinear relationships in the physical system.
This presentation discusses some recent advances in overcoming the computational challenges through decomposition strategies. In the first part of the presentation, a new cross decomposition method is introduced, which integrates the classical Benders decomposition and Dantzig-Wolfe decomposition in a novel way, for efficient solution of stochastic mixed-integer linear programming (MILP) problems. The new cross decomposition method shows significant advantages over classical decomposition methods and commercial MILP solvers. In addition, an extension of the method can handle more complex decomposable structures and address a wider class of MILPs. In the second part of the talk, an industrial natural gas production system design problem, which is cast as a stochastic nonconvex mixed-integer nonlinear programming (MINLP) problem, is used to demonstrate how classical Bender decomposition can be extended to achieve global optimal solutions in spite of the nonconvexity of the problem, and how an alternative modeling approach can reduce the nonconvexity of the problem and enable further decomposition for even faster solution.
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