Concept
OptimizationProbleM's general proposed method is to select a set of parameters (variables), under a series of related restrictions (constraints), Make the design indicator (target) to the optimal value. Therefore, optimization problems can generally represent the following mathematical planned forms.
For a set of variables represented by a group of available columns, our purpose is "abbreviation" "in
, indicating" under constraint conditions ". Eration refers to the maximum or minimum of the target function.
Therefore, in engineering optimization design, engineering design issues should be expressed as mathematical problems in the form of the above form, and then solve with optimized methods. This job is to establish a mathematical model of optimization design.
Basic principle
Design variables and design space
is one of the dimensional space (recorded) Vector, it consists of a component. It is the amount of design scheme to determine the design of the design in the optimization process, that is, a set of values that need to be selected in optimization, called design variable vector. From the geometric say, each variable vector is a point in the variable space of the coordinate axis with each variable component. At that time, there was only one variable component, which varies along the line; at that time, only two variable components, all points of this variable vector constitute a plane; at that time, the stereo space was constituted. When there are three variable components, the multidimensional space is constituted. Each design variable vector in design space corresponds to a design point, ie corresponding to a design. The design space contains all possible scenarios designed.
Target function
is called a target function. It is a conscious continuous function for designing variable vectors, usually assumed that it has a second-order continuous bias. The target function is the basis for more designed options for selection. The optimization is to make it a pole value. In the variable space, the target function is known as the equivalent surface of all points of a common value. That is, it is a point set that makes the target function as a constant value:
, that is, only two variable components are the contour.
The equivalents have the following properties:
(1) There is no intersection between the equivalents of different values. Because the target function is a single value function.
(2) In addition to the equivalence surface of the extreme point, it is not interrupted within the area. Because the target function is a continuous function.
(3) is densely dense, the target function value changes faster; the sparse places are slower.
(4) Generally, the equivalent surface near the extreme point is approximated as a communication elliptical facial group.