Optimisation Algorithms

Optimisation may be used, for example, to minimise the cost of reactor operation or to maximise conversion. Having set up a mathematical model of a reactor system, it is only necessary to define a cost or profit functionOptimisation and then to minimise or maximise this by variation of the operational parameters, such as temperature, feed flow rate or coolant flow rate. The extremum can then be found either manually by trial and error or by the use of a numerical optimisation algorithms. The first method is easily applied with ISIM, or with any other simulation software, if only one operational parameter is allowed to vary at any one time. If two or more parameters are to be optimised this method however becomes extremely cumbersome. 

Famulari, A., Gianinetti, E., Raimondi, M. and Sironi, M. (1998) Implementation of gradient optimisation algorithms and force constant computations in BSSE free direct and conventional SCF... 

Two-Stage Optimisation Algorithm for Freshwater and Reusable Water Storage Minimisation... 

J. Schneider, I. Morgenstern, and J. M. Singer. Bouncing towards the optimum Improving the results of monte carlo optimisation algorithms. Phys. Rev. E,... 

Catalyst preparation and activation conditions are included as parameters of importance in the optimisation algorithm. The preparation and activation procedures are very relevant aspects since minor variations in such conditions would cause major changes to the final phase of the solid and, consequently, to its catalytic properties. Typical preparation variables are promoter precursors, type of impregnation, calcination atmosphere, time and temperature, time and temperature for metal reduction and so forth. 

For each outer loop function and gradient evaluation 4 and 14 inner loop problems were solved respectively (a total of 124 inner loop problems). For the inner loop problems 12-14 iterations for Tasks 1 and 3 and 5-7 iterations for Tasks 2 and 4 were usually required. For this problem size and detail of dynamic and physical properties models the computation time of slightly over 5 hrs (using SPARC-1 Workstation) is acceptable. It is to note that the optimum number of plates and optimum recovery for Task 1 (Table 7.2) are very close to initial number of plates and recovery (Table 7.1). This is merely a coincidence. However, during function evaluation step the optimisation algorithm hit lower and upper bounds of the variables (shown in Table 7.1) a number of times. Note that the choices of variable bounds were done through physical reasoning as explained in detail in Chapter 6 and Mujtaba and Macchietto (1993). 

The Ab Initio Valence Bond program TURTLE has been under development for about 12 years and is now becoming useful for the non-specialist computational chemist as is exemplified by its incorporation in the GAMESS-UK program. We describe here the principles of the matrix evaluation and orbital optimisation algorithms and the extensions required to use the Valence Bond wavefunctions in analytical (nuclear) gradient calculations. For the applications, the emphasis is on the selective use of restrictions on the orbitals in the Valence Bond wavefunctions, to investigate chemical concepts, in particular resonance in aromatic systems. 

The weightings w, in the neural network are determined by an optimisation algorithm using the error between the measured outputs and the outputs predicted by the neural network. The work of Rumelhart et.al. (1985) is recommended for more details about this type of neural networks and examples. 

In theory one hidden layer neural network is sufficient to describe all input/output relations. More hidden layers can be introduced to reduce the number of neurons compared to the number of neurons in a single layer neural network. The same argument holds for the type of activation function and the choice of the optimisation algorithm. However, the emphasis of this work is not directed on the selection of the best neural network structure, activation function and training protocol, but to the application of neural networks as a means of non-linear function fit. 

The process model was built using PETROX, a proprietary sequential-modular process simulator from PETROBRAS. The simulation comprises 53 components and pseudocomponents and 64 unit operation modules, including 7 distillation columns and a recycle stream. All modules are built with rigorous, first-principles models. For optimization applications, PETROX was linked to NPSOL, an SQP optimisation algorithm. 

All the four PSO algorithms can find the global optimal solutions whereas the gradient based optimisation algorithm from the MATLAB Optimisation Toolbox, fminunc, fails to find the global optimal solutions when the initial values are not close to the global optimal solutions. 

In this section we present our reduced input/output optimisation algorithm which is built around steady-state simulators which solve equations of the form ... 

R.S. Honorato, M.C.U. Araujo, R.A.C. Lima, E.A.G. Zagatto, R.A.S. Lapa, J.L.F.C. Lima, A flow-batch titrator exploiting a one-dimensional optimisation algorithm for end point search, Anal. Chim. Acta 396 (1999) 91. 

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