Solution quality

The solution developed is able to solve the scheduling problem very efficiently, resulting in good and realistic schedules. Of course, the solution quality depends to a great deal on how well the parameter estimation matches with the production process. More illustrations on the solution can be found in [5]. 

In this section, the numerical solutions of the MINLP-model and of the MILP-model as presented in Sections 7.4 and 7.5 are compared with respect to their solution quality (measured by the objective values) and the required solution effort (measured by the computing time). In order to compare the MILP-solution with the MINLP-solution, the optimized values for the start times of polymerizations tn, the recipe assignments W, and the total holdups Mnr are inserted into the MINLP-model and the objective is calculated. To guarantee comparability of the results, the models were stated with identical initial conditions, namely t° = 0, = 2 Vk, pf = 0 Vs, and ra = 0.4 Vs (i.e., the variables defined at the beginning of the corresponding time axes are fixed to the indicated values). For the algorithmic solution procedure, all variables were initialized by 1 (i.e., the search for optimal values starts at values of 1 ), and none of the solvers was specifically customized. 

In numerical studies it turned out that the MILP problem can not only be solved much faster than the MINLP problem, but for most of the model instances it provides solutions of significantly higher solution quality. Certainly, the engineered linearization of the nonlinear problem causes a loss in model precision, but on the other hand it enables a globally optimal solution. Since the MILP solutions are feasible for the MINLP problem, it is clear that the inferior quality of the MINLP solutions originates from the fact that only local minima were found. 

Due to the campaign structure, the existing decomposition techniques in the SNP optimizer like time decomposition and product decomposition are not applicable. For problems with this structure it is possible to use the resource decomposition in case a good sequence of planning of the campaign resources can be derived. However, in our case, problem instances could be solved without decomposition on a Pentium IV with 2 GHz in one hour to a solution quality of which the objective value deviates at most one percent from the optimal objective function value. 

Mark, W.K., Morton, D.P., and Wood, R.K. (1999) Monte Carlo bounding techniques for determining solution quality in... 

Minimizing Cleaner Loss by Maintaining Solution Quality... 

Besides monitoring bulk solution qualities by conventional analytical methods, measurement of the phase transition may also be warranted. Slight differences in the nature of the formulation owing to aging, undetected by typical analytical methods, may influence the phase transition of the product formulation. For example, absorption of carbon dioxide from the air over an extended time period may cause a pH shift, consume one component of a buffering system, or promote degradation. For a peptide or protein with both a hydrophilic and hydrophobic nature, alterations to desired secondary, tertiary, or quaternary... 

For the CO2 capture system, the parameter cases update all significant equipment performance to match observed data. The primary performance of this system is the CO2 absorber slip and the energy required to regenerate the solution to semilean and lean solution quality. The model can be made to match observed performance in several ways. Measurements are available for the lean and semilean... 

Array fabrication Spot morphology, probe solutions (quality and quantity), array design, probing approach Replicate features, reference standards, batch quality control, DNA binding dyes... 

In a flattened design style, layout designers directly cany out the 2.5-D placement and routing tasks on a flatten netlist consisting of both standard cells and macros. Such a flow could usually accomplish superior solution quality, but at the cost of a longer turnaround time because of the inability to implement different blocks in parallel. 

Linearity of a method should be established or a series of standards selected for use with non-linear-method calibration. This can be checked by preparing and analyzing serial dilutions of aqueous reference standard solutions, quality control materials, enzyme solutions, or commercially available materials for demonstrating linearity (again, these are designed for use in human medicine) and comparing the determined values with the theoretical values calculated for the dilutions. The serial dilutions used for linearity checks can also help establish the analytical sensitivity when defined as the minimal detectable change from one concentration to another. 

These macroscopic viscosity measurements have been confirmed at the molecular level. For example, dynamic light-scattering methods show an average hydrodynamic diameter (D J of about 370 A for a 50/50 copolymer of NVP/SPE in low salt (<2%) and a of about 390 A in high-salt (20% NaCl) concentrations (18). Moreover, in solutions of water or low concentrations of salt, solvent quality (as measured by second virial coefficient, A2) decreases with increasing levels of SPE. LALLS measurements for NVP/SPE 80/20 and 10/90 copolymers in 2% NaCl solution yielded molecular weights of 1.1 X 10 and 1.4 x 10 g mol respectively. The same compositions yielded second virial coefficients of 9.0 X 10 and 0.6 X 10 , respectively. In this case, a higher virial coefficient means better solution quality. 

Validation of an analytical method is often done under the best of conditions such as use of a new column on dedicated equipment by an analyst experienced with the method. But what about routine analysis of commercial samples by many analysts in a busy Quality Control laboratory Robustness establishes the reliability of the method with respect to deliberate variations in the operating parameters, evaluates use of different column lots from the vendor, and also determines the stability of sample and standard solutions. Quality by Design (QbD) principles have begun to impact method development and validation activities to a wider extent and application of QbD concepts should result in higher quality and more robust analytical... 

A problem is the tendency of designers to be satisfiers rather than optimizers. That is, designers tend to stop as soon as they have one feasible solution. For example, when designing an assembly line, the designer may stop as soon as there is a solution. For an optimum solution, there must be a number of alternatives to select from. Alternatives tend to suggest further alternatives, so stopping too soon can limit solution quality and acceptance. 

Each algorithm has its own influential parameters that affect its performance in terms of solution quality and computational time. In order to increase the performance of the FA and GA, it is necessary to provide the adjustments of the parameters depending on the problem domain. With the appropriate choice of the algorithm settings the accuracy of the decisions and the execution time can be optimized. Parameters of the FA and GA are tuned on the basis of a large number of pre-tests according to the parameter identification problem, considered here. 

The polymeric solutions were made from two batches of master solution at 2% concentration. The polymer solution in this tank was allowed to remain at rest for 30 minutes prior to beginning a run in order to achieve a more homogeneous solution. The solution quality was checked during the experiments with an accurate turbulent rheometer. This instrument checked the friction reduction efficiency of the polymer in controlled measurements. 

Three solution algorithms based on the method of lines for systems of parabolic differential equations cire tested by simulation of a reversed flow reactor for exhaust air purification. The solutions are compared with regcird to solution quality and computing time needed. It will be shown, that only the fully adaptive method will guarantee a sufficient solution quality. 

---