What is criterion function

What is criterion function

Function which connects the purpose with the operated variables in tasks of optimization is called criterion. Creation of this function is an integral part of carrying out calculations in various production fields of activity.

Instruction

1. Criterion function has an appearance: u = f (x1, x2..., xn) where u is area of decisions (purpose) for a certain set of design parameters (x), each of which has the dimension (n). Creation of this function is necessary when performing economic and engineering calculations, for example, for calculation of durability or mass of a design, power of installation, volume of production, cost of transport of cargoes, arrived, etc.

2. If the task provides the choice of an optimal solution or comparison of two alternative decisions, in this case not to do without some dependent size determined by design parameters. This size is also criterion function. At the solution of tasks of optimization it is necessary to find such design parameters at which criterion function has a minimum or a maximum. Thus, function represents model of optimality by means of which economic or engineering tasks are described.

3. In the presence of one design parameter when n = 1, criterion function has one variable, and some curve lying on the plane undertakes its schedule. If n = 2, function has two variables, and its schedule will be a surface in three-dimensional space.

4. Criterion function is optional presented in the formula form. When it accepts only discrete values, it can be set in the form of the table. Anyway, in all cases it represents unambiguous function of design parameters.

5. Creation of criterion function – an obligatory step at the solution of tasks of optimization. Optimization is called process of the choice of the most suitable option from possible. For example, when performing engineering calculations by method of optimization it is possible to define what option of a design is the best as it is rational to distribute resources.

6. The solution of tasks of optimization provides search of optimum values which define this task. In engineering tasks they are called design parameters, and in economic - plan parameters. Values of the sizes of an object, temperature, weight, etc. can act as design parameters.

7. For the solution of some tasks the creation of several criterion functions can be performed at once. For example, it is necessary to find optimum values of the maximum reliability, the minimum material consumption, the maximum net volume, etc. in a designing process of products of mechanical engineering.

Author: «MirrorInfo» Dream Team


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