Selectivity optimization objective functions

The selectivity constraints are satisfied at the optimal final time of 42.8 min. The optimal objective functional is —6.35, which corresponds to the final product concentration of 6.35 g/cm . 

Select the objective function to optimize for the best design configuration for a fixed-bed reactor. 

One way to treat multiple criteria is to select one criterion as primary and the other criteria as secondary. The primary criterion is then used as the optimization objective function, while the secondary criteria are assigned acceptable minimum and maximum values and are treated as problem constraints. However, if careful considerations were not given while selecting the acceptable levels, a feasible solution that satisfies all the constraints may not exist. This problem is overcome by Goal Programming (GP), which has become a practical method for handling multiple criteria. 

Optimization should be viewed as a tool to aid in decision making. Its purpose is to aid in the selection of better values for the decisions that can be made by a person in solving a problem. To formulate an optimization problem, one must resolve three issues. First, one must have a representation of the artifact that can be used to determine how the artifac t performs in response to the decisions one makes. This representation may be a mathematical model or the artifact itself. Second, one must have a way to evaluate the performance—an objective function—which is used to compare alternative solutions. Third, one must have a method to search for the improvement. This section concentrates on the third issue, the methods one might use. The first two items are difficult ones, but discussing them at length is outside the scope of this sec tion. 

Objective Function This is the quantity for which a minimax is sought. For a complete manufacturing plant, it is related closely to the economy of the plant. Subsidiary problems may be to optimize conversion, production, selectivity, energy consumption, and so on in terms of temperature, pressure, catalyst, or other pertinent variables. 

FIG. 8-46 Diagram for selection of optimization techniques with algebraic constraints and objective function. 

Various criteria were proposed for the optimal selection of the equipment configuration and the number and sizes of units. In grass-root design, the capital cost of equipment is mostly used as the optimization criterion. In retrofit design a more appropriate objective function seems to be the net profit, which has to be maximized. Papageorgaki and Reklaitis (1993) formulated the criterion as follows ... 

The cycle time for the sequence, tc..K.uJS, should be minimized to find the optimal sequence of batches for the UIS policy. The form of the objective function implies that the optimization of a schedule for UIS with minimum cycle time simply reduces to selecting any sequence of batches with slack times of bottleneck stage(s) set to zero. 

Since we have a minimization problem, significant computational savings can be realized by noting in the implementation of the LJ optimization procedure that for each trial parameter vector, we do not need to complete the summation in Equation 5.23. Once the LS Objective function exceeds the smallest value found up to that point (S ), a new trial parameter vector can be selected. 

Different measures of the quality of the solution can be used for scheduling problems. However, the criterion selected to be optimized usually has a direct effect on the model computational performance. In addition, some objective functions can be very hard to implement for some event representations, requiring additional variables and complex constraints. 

From the different planning methods available within SNP, SNP optimization is selected because it offers the best fit to the customer requirements outlined above. The main reasons for this decision are the multisourcing characteristics of the supply network as well as the fact that the objective functions used by the SNP optimizer, profit maximization or cost minimization, correspond to the planning philosophy favored by the customer. In addition to SNP optimization with its cost-based approach, SNP offers several heuristic-based planning methods which follow a rule-based logic. 

Suppose you wanted to find the configuration that minimizes the capital costs of a cylindrical pressure vessel. To select the best dimensions (length L and diameter D) of the vessel, formulate a suitable objective function for the capital costs and find the optimal (LID) that minimizes the cost function. Let the tank volume be V, which is fixed. Compare your result with the design rule-of-thumb used in practice, (L/D)opt = 3.0. 

Another simple optimization technique is to select n fixed search directions (usually the coordinate axes) for an objective function of n variables. Then fix) is minimized in each search direction sequentially using a one-dimensional search. This method is effective for a quadratic function of the form... 

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