Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor

Luus, Rein; Dittrich, Joaichim; Keil, Frerich J.

doi:10.1002/cjce.5450700423

Cited by 53 publications

(35 citation statements)

References 13 publications

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“…A 6 A 7 A ~X 3~ k 8 10 2 k 7 k 3 9 1: ' k, :,1:, Al ~ This problem has been studied by Luus et al (1992), Bojkov and Luus (1993), and Luus and Bojkov (1994). Even though this example is relatively small (7 states and 1 control), it has been shown to exhibit a very large number of loeal minima.…”

Section: Datamentioning

confidence: 99%

Handbook of Test Problems in Local and Global Optimization

Floudas¹

1999

Nonconvex Optimization and Its Applications

476

352

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PrefaceSignificant research activities have taken place in the areas of local and global optimization in the last two decades. Many new theoretical, computational, algorithmic, and software contributions have resulted. It has been realized that despite these numerous contributions, there does not exist a systematic forum for thorough experimental computational testing and· evaluation of the proposed optimization algorithms and their implementations.Well-designed nonconvex optimization test problems are of major importance for academic and industrial researchers interested in algorithmic and software development. It is remarkable that eventhough nonconvex models dominate all the important application areas in engineering and applied sciences, there is only a limited dass of reported representative test problems. This book reflects our long term efforts in designing a benchmark database and it is motivated primarily from the need for nonconvex optimization test problems. The present collection of benchmarks indudes test problems from literature studies and a large dass of applications that arise in several branches of engineering and applied science. v C.A. Floudas

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Section: Datamentioning

confidence: 99%

Handbook of Test Problems in Local and Global Optimization

Floudas¹

1999

Nonconvex Optimization and Its Applications

476

352

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“…Let us now consider the optimization of a bifunctional catalyst in converting methylcyclopentane to benzene in a tubular reactor. It is extremely interesting to investigate this system because of its multitude of local optima and the inability of nonlinear programming to obtain the global optimum, even when using 100 different starting points as discussed by Luus et al (1992). Recently, Storey (1992) showed that for this system Simulated Annealing, Modified Controlled Random Search and Multilevel Single Linkage also were unable to yield the global optimum.…”

Section: Blendmentioning

confidence: 99%

“…n the investigation of design possibilities of engineering I systems, one is frequently confronted with problems of determining the optimal control of systems described by a large number of nonlinear differential equations. Although, there are numerous numerical methods that can be used, in many situations it is difficult to foresee the existence of local optima, thus rendering the search for the global optimum solution extremely difficult, as shown by Luus et al (1992) and Storey (1992). Even if one uses an optimization procedure that has been reliable for many problems, it is prudent to cross-check the solution of a new problem by using some different optimization method.…”

mentioning

confidence: 99%

Evaluation of the parameters used in iterative dynamic programming

Bojkov

Luus

1993

Can. J. Chem. Eng.

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To apply iterative dynamic programming (IDP) to optimal control problems having a very large number of control variables the use of randomly chosen values for control at each grid point is required. To gain insight into the effect of the number of allowable values for control, the region contraction factor, and the number of grid points for the state vector to be used, computational results are presented for two nonlinear systems, one of which possesses numerous local optima. The reliability of obtaining the global optimum for the bifunctional catalyst blend optimization problem was found to be somewhat higher by using randomly chosen values for control rather than by choosing the control values over a uniform distribution. The global optimum is obtained even when a small number of allowable values for control at each grid point and a small number of grid points for the states are used. There is a wide range of the region contraction factor for which rapid convergence to the optimum is obtained. Also the number of grid points for the state can be very small without adversely affecting convergence to the optimum.

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“…The nonlinearity can result in a highly nonconvex problem exhibiting many suboptimal local solutions. It is known that even small-scale dynamic systems can exhibit multiple suboptimal local solutions [12][13][14]. Unfortunately, a derivative-based optimization method can become trapped in any of these, which can lead to a suboptimal operation and loss of profit.…”

Section: Introductionmentioning

confidence: 99%

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

Sahlodin

Barton

2017

Processes

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Dynamic optimization offers a great potential for maximizing performance of continuous processes from startup to shutdown by obtaining optimal trajectories for the control variables. However, numerical procedures for dynamic optimization can become prohibitively costly upon a sufficiently fine discretization of control trajectories, especially for large-scale dynamic process models. On the other hand, a coarse discretization of control trajectories is often incapable of representing the optimal solution, thereby leading to reduced performance. In this paper, a new control discretization approach for dynamic optimization of continuous processes is proposed. It builds upon turnpike theory in optimal control and exploits the solution structure for constructing the optimal trajectories and adaptively deciding the locations of the control discretization points. As a result, the proposed approach can potentially yield the same, or even improved, optimal solution with a coarser discretization than a conventional uniform discretization approach. It is shown via case studies that using the proposed approach can reduce the cost of dynamic optimization significantly, mainly due to introducing fewer optimization variables and cheaper sensitivity calculations during integration.

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Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor

Cited by 53 publications

References 13 publications

Handbook of Test Problems in Local and Global Optimization

Handbook of Test Problems in Local and Global Optimization

Evaluation of the parameters used in iterative dynamic programming

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

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