QMC DATA MINING PROGRAM for Windows Optimization Programs The main goal of optimization is to minimize variability of the process while maximizing quality and profit. With the optimization methods available in the QMC Program, it is possible to successfully determine the "best case" without actually testing all possible cases. It is known that no one method can be expected to uniformly solve all problems with equal efficiency. Here, the engineer has available multiple opportunities to adjust these methods against the characteristics of the problem. QMC Optimizers are used to solve user-defined equations by regression to a data set. Fits linear and non-linear equations. The QMC Optimizers include multivariable, multi-equation formats. Toggle between Excel and graphs. Save equations for future use. Equations that can be solved include kinetic, equilibrium, economic and other optimization routines for process improvement. This is the most powerful approach in determining the relationships in a process with data from a process. Given the equations that mathematically describe the system, the user can model the system for various operating scenarios with minimum risk in interpolation or extrapolation error. Technology based sample problems such as compressor, pump, separator, heat exchanger and unit conversions are included to assist your projects. Simple steps are to: 1) open an existing file or type in equation, 2) click to calculate, and 3) print or save displayed results. EquationSolver is used to solve simple or complex algebraic equations requiring numeric results. Cut and paste features allow equations and solutions to be inserted into spreadsheets, documents or other applications. Save or print results for further reference or research. Change a parameter, click and get instant results. This is an unprecedented feature of the EquationSolver. This program is applicable to science, engineering and mathematical disciplines. Direct Search Method uses function values and require only values of the objective to guide the search. It sequentially employs a regular pattern of points in the design space. The Direct Search Method is often slower than derivative based methods. Golden Section Search Method is a preferred optimization method due to its' computational efficiency and reliability. It is often used for strongly skewed or multi-modal functions. Quadratic Search Method is the simplest of polynomial approximations. It is based on observation of a function taking its minimum in the interior of an interval and be at least, quadratic. If linear, it assumes optimal value at one endpoint of the interval. It assumes that within the bound interval, the function can be approximated and that the approximation will improve as points approach the actual minimum. Cubic Search Method is a polynomial approximation in which a given function to be minimized is approximated by a third-order polynomial. With the function value and the derivative value available, .an approximating polynomial can be constructed using fewer points. Derivative Search Method depends on a starting point or initial approximation to the stationary point of the equation. A linear approximation is constructed and the point where the linear approximation vanishes is taken as the next approximation. It is possible for this method to diverge rather than converge. This method generates ideal search directions near the solution. Hooke-Jeeves' Search Method uses a fixed set of coordinate directions in a recursive manner. In other words, an entire set of points is condensed into a single vector difference that defines a direction. It is a combination of exploratory moves in a one-variable pattern regulated by heuristic rules. Exploratory moves examine the behavior and locate the direction of sloping valleys. Cauchy's Gradient Method is often referred to as the steepest descent optimization method. A single variable searching method is used to solve systems of linear equations and includes many essential ingredients. Cauchy's Gradient Method is a logical starting procedure for all gradient based methods but requires values of the objective and gradient at each of the iterations. Powell's Conjugate Direction Method uses a theoretically based method assuming a quadratic objective and converges in a finite number of iterations. It is probably the most successful of the direct search algorithms. It uses the history of the iterations to build up directions for acceleration. It also avoids degenerating to a sequence of coordinate searches. Newton's Gradient Method depends on a starting point or initial approximation to the stationary point of the equation. A linear approximation is constructed and the point where the linear approximation vanishes is taken as the next approximation. It is possible for this method to diverge rather than converge. This method generates ideal search directions near the solution. Marquardt's Gradient Method is a combination of Cauchy's and Newton's Methods but requires second order information. The search direction is specified and set to control both the direction of the search and the length of the step.
|
|
* * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * |