A MIXED-INTEGER NONLINEAR PROGAMMING APPROACH FOR THE SYSTEMATIC SYNTHESIS OF ENGINEERING SYSTEMS (PROCESS SYNTHESIS, NONDIFFERENTIABLE OPTIMIZATION, HEAT INTEGRATION, OPERATIONS RESEARCH, COMPUTER-AIDED DESIGN)

This thesis addresses the development of a framework and optimization procedures to be used within a mixed-integer nonlinear programming (MINLP) approach to the synthesis of engineering systems. Based on a superstructure representation for alternative configurations, a general framework is presented that takes explicitly into account inherent nonlinearities and interactions in a system, and that allows the simultaneous structural and parameter optimization of processing systems. The underlying model corresponds to a MINLP program with a particular mathematical structure where the discrete variables are binary, which appear linearly and are separable from the continuous variables. Also, nonlinearities are only involved in inequality constraints and in the objective function.; For the solution of this class of problems, an outer-approximation algorithm is proposed that effectively exploits the particular mathematical structure. Based on the mathematical programming principles of decomposition, outer-approximation and relaxation, the proposed algorithm consists of solving an alternating finite sequence of nonlinear programming subproblems and relaxed versions of a mixed-integer linear master program. The theoretical study of the bounding, convergence and optimality properties of the algorithm is presented for the case of a convex continuous space in the MINLP programs addressed in this thesis. Also, the relationship between the proposed algorithm and the generalized Benders decomposition (GBD) method is established, and a proof is presented to show that the former method will always provide lower bounds that are either of the same quality or else tighter than the corresponding ones predicted by GBD.; To illusrate both the perfomance of the outer-approximation algorithm and the application of the proposed MINLP framework for synthesis, several example problems are solved including the optimal design of a gas transmission network, for which a MINLP formulation is derived.; To evaluate and compare alternatives based on more than one criterion when performing synthesis of processing systems, a method is presented for the simultaneous optimization and heat integration of process flowsheets. The method handles explicitly variable flowrates and temperatures of the process streams, and relies on a new representation of the minimum utility target for heat recovery networks. Finally, preliminary experience is reported on the synthesis of integrated processing systems.