Lead optimization desirability functions

The initial design phase for combinatorial compound collections focuses on computer-generation of a virtual library and selecting a subset of compounds for chemical synthesis on the basis of specific characteristics, such as maximum diversity, desired lipophilicity, and lack of toxic and reactive functionality [13]. When combinatorial compounds are used for lead optimization, collections can be designed on the basis of a reference structure with the collection chosen to represent the desired degree of diversity. Software for the design of such combinatorial reactions is commercially available. An alternative ap-... 

Besides interesting simulations, optimization tasks can also be performed, if, for instance there is a need to achieve an optimal result with minimal negative factors - harmful side products, costs, etc. The various goals are often contradictory and lead to a multitarget optimization task. Typically, the objective function has to be specified by the user, which means that while the objective functions for parameter estimation and optimal design are usually built-in routines in software like ModEst 6.1, the optimization task requires a user written subroutine. The desirability function technique is especially easy to implement and in many cases sufficient for multicriteria optimization. 

The simplest approach, of course, is to maintain the minimum-determinantal description and reoptimize all of the orbitals. In practice, however, such an approach is practical only in instances where die ground-state and the excited-state wave functions belong to different incduciblc representations of die molecular point group (cf. Section 6.3.3). Otherwise, the variational soludon for die excited-state wave function is simply to collapse back to the ground-state wave function And, even if the two states do differ in symmetry, the desired excited state may not be the lowest energy such state widiiii its irrep, to which variational optimization will nearly always lead. 

In general, an objective function in the optimization problem can be chosen, depending on the nature of the problem. Here, two practical optimization problems related to batch operation maximization of product concentration in a fixed batch time and minimization of batch operation time given amount of desired product, are considered to determine an optimal reactor temperature profile. The first problem formulation is applied to a situation where we need to increase the amount of desired product while batch operation time is fixed. This is due to the limitation of complete production line in a sequential processing. However, in some circumstances, we need to reduce the duration of batch run to allow the operation of more runs per day. This requirement leads to the minimum time optimization problem. These problems can be described in details as follows. 

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