The evolution of both optimization methods and application fields in chemical engineering are presented in this paper. The study was carried out on three Escape Conferences, ESCAPE 1, ESCAPE 4 and ESCAPE 8. The use of...
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The evolution of both optimization methods and application fields in chemical engineering are presented in this paper. The study was carried out on three Escape Conferences, ESCAPE 1, ESCAPE 4 and ESCAPE 8. The use of classical mathematical programming approaches, like NLP, MILP and MINLP has reached a cruising speed, even when Linear or Successive Linear programming methods are less and less used. Due to the highly combinatorial nature of many problems, Simulated Annealing and Genetic Algorithms begin to compete with mathematical programming approaches. For optimal control purposes, Neural Networks appear to be an efficient tool. Continuous and batch process optimization and design always constitute a privileged application field of optimization procedures, but some recent classes of problems, like batch plant scheduling, thermodynamics, kinetics, molecular modeling and aided mixture design appear to emerge as new application fields.
This paper illustrates the application of two decomposition algorithms, generalized Benders decomposition (GBD) and outer approximation (OA), to water resources problems involving cost functions with both discrete and...
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This paper illustrates the application of two decomposition algorithms, generalized Benders decomposition (GBD) and outer approximation (OA), to water resources problems involving cost functions with both discrete and nonlinear terms. Each algorithm involves the solution of an alternating finite sequence of nonlinearprogramming subproblems and relaxed versions of a mixed-integer linear programming master problem. Three example models, involving capacity expansion of a conjunctively managed surface and groundwater system, are formulated and solved to demonstrate the performance of the algorithms. The results show that OA obtains solutions in far fewer iterations than GBD, but OA requires more computational resources per iteration. As a result, depending on the mixed-integerprogramming and nonlinearprogramming solvers available, GBD may be better suited for solving larger planning problems. (C) 1997 Elsevier Science Limited. All rights reserved.
Process synthesis problems involving uncertainty can be mathematically represented as multiparametric mixed integer nonlinear programming(mp-MINLP) models. In this paper, we present an outer-approximation algorithm fo...
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Process synthesis problems involving uncertainty can be mathematically represented as multiparametric mixed integer nonlinear programming(mp-MINLP) models. In this paper, we present an outer-approximation algorithm for the solution of such mp-MINLPs, described by convex process models, linear in the vectors of binary variables and uncertain parameters. The algorithm follows decomposition principles, i.e., constructing a converging sequence of valid upper and lower bounds through the solution of parametric primal and master subproblems. The solution is characterized in different sub-domains of the uncertain parameter space by (i) linear parametric profiles, and (ii) the corresponding integer solutions. (C) 1998 Elsevier Science Ltd. All rights reserved.
A wide range of optimization problems arising from engineering applications can be formulated as mixed integer nonlinear programming problems (MINLPs). Duran and Grossmann (1986) suggest an outer approximation scheme ...
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A wide range of optimization problems arising from engineering applications can be formulated as mixed integer nonlinear programming problems (MINLPs). Duran and Grossmann (1986) suggest an outer approximation scheme for solving a class of MINLPs that are linear in the integer variables by a finite sequence of relaxed MILP master programs and NLP subproblems. Their idea is generalized by treating nonlinearities in the integer variables directly, which allows a much wider class of problem to be tackled, including the case of pure INLPs. A new and more simple proof of finite termination is given and a rigorous treatment of infeasible NLP subproblems is presented which includes all the common methods for resolving infeasibility in Phase I. The worst case performance of the outer approximation algorithm is investigated and an example is given for which it visits all integer assignments. This behaviour leads us to include curvature information into the relaxed MILP master problem, giving rise to a new quadratic outer approximation algorithm. An alternative approach is considered to the difficulties caused by infeasibility in outer approximation, in which exact penalty functions are used to solve the NLP subproblems. It is possible to develop the theory in an elegant way for a large class of nonsmooth MINLPs based on the use of convex composite functions and subdifferentials, although an interpretation for the l(1) norm is also given.
This thesis addresses two problems in aligning the recruiting structure for Navy Recruiting Command. The first problem involves two decisions affecting recruiting stations within a single recruiting district: which st...
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This thesis addresses two problems in aligning the recruiting structure for Navy Recruiting Command. The first problem involves two decisions affecting recruiting stations within a single recruiting district: which stations should remain open and how many recruiters should be assigned to each open station? The second problem is to decide how many recruiters and stations each district should have. The first problem is formulated as a nonlinearmixedintegerprogramming problem. To obtain a solution with readily available software, the problem is decomposed into four subproblems that are solved sequentially. This decomposition approach is empirically shown to yield near optimal solutions for problems of varied sizes. The second problem is formulated as a nonlinear resource allocation problem in which the objective function is not expressible in closed form. To efficiently solve this problem, the function is approximated in a piecewise linear fashion using the results from the first problem. To illustrate the applications of these optimization models, solutions were obtained for Navy Recruiting District Boston and Navy Recruiting Area 1, which consists of Albany, Boston, Buffalo. New York, Harrisburg, Philadelphia, Pittsburgh and New Jersey districts.
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