Generalized disjunctive programming (GDP) has been introduced recently as an alternative model to MINLP for representing discrete/continuous optimization problems. The basic idea of GDP consists of representing discre...
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Generalized disjunctive programming (GDP) has been introduced recently as an alternative model to MINLP for representing discrete/continuous optimization problems. The basic idea of GDP consists of representing discrete decisions in the continuous space with disjunctions, and constraints in the discrete space with logic propositions. In this paper, we describe a new convex nonlinear relaxation of the nonlinear GDP problem that relies on the use of the convex hull of each of the disjunctions involving nonlinear inequalities. The proposed nonlinear relaxation is used to reformulate the GDP problem as a tight MINLP problem, and for deriving a branch and bound method. Properties of these methods are given, and the relation of this method with the logic based outer-approximation method is established. Numerical results are presented for problems in jobshop scheduling synthesis of process networks, optimal positioning of new products and batch process design. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper considers nonlinearly constrained tolerance allocation problems in which both tolerance and process selection are to be selected simultaneously so as to minimize the manufacturing cost. The tolerance alloca...
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This paper considers nonlinearly constrained tolerance allocation problems in which both tolerance and process selection are to be selected simultaneously so as to minimize the manufacturing cost. The tolerance allocation problem has been studied in the literature for decades, usually using mathematical programming or heuristic optimization approaches;The difficulties encountered for both methodologies are the number of constraints and the difficulty of satisfying the constraints. A penalty-guided genetic algorithm is presented for solving such mixed-integer tolerance allocation problems. It can efficiently and effectively search over promising feasible and infeasible regions to find the feasible optimal or near optimal solution. Genetic results are compared with the results obtained from 12 problems from the literature that dominate the previously mentioned solution techniques. Numerical examples indicate that the genetic algorithms perform well for the tolerance allocation problem considered in this paper. In particular, as reported, solutions obtained by genetic algorithms are as well as or better than the previously best-known solutions. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper presents a two-level strategy for stochastic synthesis of chemical processes under uncertainty with a fixed degree of flexibility by using the mixed-integer nonlinear programming (MINLP) approach. The objec...
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This paper presents a two-level strategy for stochastic synthesis of chemical processes under uncertainty with a fixed degree of flexibility by using the mixed-integer nonlinear programming (MINLP) approach. The objective is to develop an automated and robust strategy which could handle nontrivial optimization problems (about 1000 equations and variables with a considerable number of uncertain parameters - up to 30) that, at the present, cannot be solved in a reasonable period of time by using rigorous stochastic optimization methods. To accomplish the task, the nonlinear subproblems at fixed structures have been decomposed into design and operating optimization levels, the former being facilitated by using a direct search method and the latter by using the reduced dimensional stochastic procedure. Two examples are presented to illustrate the robustness and efficiency of the proposed strategy at solving medium- and large-scale problems. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper presents a two-level strategy for stochastic synthesis of chemical processes under uncertainty with a fixed degree of flexibility by using the mixed-integer nonlinear programming (MINLP) approach. The objec...
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This paper presents a two-level strategy for stochastic synthesis of chemical processes under uncertainty with a fixed degree of flexibility by using the mixed-integer nonlinear programming (MINLP) approach. The objective is to develop an automated and robust strategy which could handle nontrivial optimization problems (about 1000 equations and variables with a considerable number of uncertain parameters - up to 30) that, at the present, cannot be solved in a reasonable period of time by using rigorous stochastic optimization methods. To accomplish the task, the nonlinear subproblems at fixed structures have been decomposed into design and operating optimization levels, the former being facilitated by using a direct search method and the latter by using the reduced dimensional stochastic procedure. Two examples are presented to illustrate the robustness and efficiency of the proposed strategy at solving medium- and large-scale problems. (C) 2000 Elsevier Science Ltd. All rights reserved.
In the present paper some methods to transform a non-convex bilinear mixed-integerprogramming problem are considered in more detail. The methods have been applied in solving the trim-loss problem with MINLP methods a...
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In the present paper some methods to transform a non-convex bilinear mixed-integerprogramming problem are considered in more detail. The methods have been applied in solving the trim-loss problem with MINLP methods and even if the transformations lead to a global optimal solution, there are some variable properties that affect the solution performance. The properties are explored by systematically solving a set of example problems with modified transformation techniques and analyzing the results.
In the present paper some methods to transform a non-convex bilinear mixed-integerprogramming problem are considered in more detail. The methods have been applied in solving the trim-loss problem with MINLP methods a...
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In the present paper some methods to transform a non-convex bilinear mixed-integerprogramming problem are considered in more detail. The methods have been applied in solving the trim-loss problem with MINLP methods and even if the transformations lead to a global optimal solution, there are some variable properties that affect the solution performance. The properties are explored by systematically solving a set of example problems with modified transformation techniques and analyzing the results.
This paper presents an overview of mixed-integer nonlinear programming techniques by first providing a unified treatment of the Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane met...
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This paper presents an overview of mixed-integer nonlinear programming techniques by first providing a unified treatment of the Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The extension of these methods is also considered for logic based representations. Finally, an overview of the applications in many areas in process engineering is presented.
This paper presents the mixed-integer Non-linear programming (MINLP) optimization approach to structural synthesis. Non-linear continuous/discrete non-convex problems of structural synthesis are proposed to be solved ...
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This paper presents the mixed-integer Non-linear programming (MINLP) optimization approach to structural synthesis. Non-linear continuous/discrete non-convex problems of structural synthesis are proposed to be solved by means of simultaneous topology, parameter and standard dimension optimization. Part I of this three-part series of papers contains a general view of the MINLP approach to simultaneous topology and continuous parameter optimization. The MINLP optimization approach is performed through three steps. The first one includes the generation of a mechanical superstructure of different topology alternatives, the second one involves the development of an MINLP model formulation and the last one consists of a solution for the formulated MINLP problem. Some MINLP methods are also presented. A Modified OA/ER algorithm is applied to solve the MINLP problem and a simple example of a multiple cantilever beam is given to demonstrate the steps of the proposed MINLP optimization approach. As simultaneous optimization, extended to include also standard dimensions, requires additional effort, the development of suitable strategies to carry out the optimization is further discussed in Part II. The modelling of MINLP superstructures and the topology and parameter optimization of roller and sliding hydraulic steel gate structures are shown in Part III of the paper. An example of the synthesis of an already erected roller gate, i.e. the Intake Gate of Aswan II in Egypt, is presented as a comparative design research work. (C) 1998 John Wiley & Sons, Ltd.
A systematic procedure is presented to synthesize isothermal two-phase continuous stirred tank reactor networks. The interaction of reaction and transport phenomena is modelled using the two-film theory and the optima...
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A systematic procedure is presented to synthesize isothermal two-phase continuous stirred tank reactor networks. The interaction of reaction and transport phenomena is modelled using the two-film theory and the optimal reactor network is selected from a superstructure by means of a MINLP solver. The proposed synthesis is applied to a pseudo-first order reaction and to the nitration of an aromatic compound. (C) 1998 Elsevier Science Ltd. All rights reserved.
Cryogenic distillation cascades are proposed to be used today to separate hydrogen isotopes in the fuel cycle of a fusion reactor, It is necessary to design these cascades so that their tritium inventory, is minimal. ...
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Cryogenic distillation cascades are proposed to be used today to separate hydrogen isotopes in the fuel cycle of a fusion reactor, It is necessary to design these cascades so that their tritium inventory, is minimal. We have thus developed optimization tools in order to simultaneously optimize the structure and the operating parameters of these distillation sequences. This leads to the implementation of a mixed-integer nonlinear programming procedure in a process simulator The application concerns the International Thermonuclear Experimental Reactor (ITER) isotope separation system. Successive simulation and optimization studies have been carried out which show the accuracy of the simulation and lead to the suggestion of a new arrangement of units for the cascade, with a higher number of columns.
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