In parallel to the increase of computer sophistication, optimization techniques are finding wide applications in chemical process design. The chemical process synthesis problem can be stated as a mixed-integer nonline...
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In parallel to the increase of computer sophistication, optimization techniques are finding wide applications in chemical process design. The chemical process synthesis problem can be stated as a mixed-integer nonlinear programming problem, where the integer variables represent the process structure and the continuous variables refer to operating conditions of the process units. The formulation of a classical chemical engineering problem is presented in the first part on the paper. Three mathematical programming methods (GRG - branch and bound - and mixed-integer nonlinear programming) with increasing degree of sophistication are used to solve this problem, and the results are then compared. From this example, the mixed-integer nonlinear programming method appears to be the most powerful tool for solving chemical process synthesis problems, even though the branch and bound procedure is a well suitable approach for solving the particular problem of choosing configurations for a process. Finally it is shown that the introduction into the initial objective function of an outer penalty term on the number of process links may avoid equivalent process structures to be obtained.
An outer-approximation algorithm is presented for solving mixed-integer nonlinear programming problems of a particular class. Linearity of the integer (or discrete) variables, and convexity of the nonlinear functions ...
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An outer-approximation algorithm is presented for solving mixed-integer nonlinear programming problems of a particular class. Linearity of the integer (or discrete) variables, and convexity of the nonlinear functions involving continuous variables are the main features in the underlying mathematical structure. Based on principles of decomposition, outer-approximation and relaxation, the proposed algorithm effectively exploits the structure of the problems, and consists of solving an alternating finite sequence of nonlinearprogramming subproblems and relaxed versions of a mixed-integer linear master program. Convergence and optimality properties of the algorithm are presented, as well as a general discussion on its implementation. Numerical results are reported for several example problems to illustrate the potential of the proposed algorithm for programs in the class addressed in this paper. Finally, a theoretical comparison with generalized Benders decomposition is presented on the lower bounds predicted by the relaxed master programs.
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