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== Terminology == | == Terminology == | ||
| − | :{| cellpadding=" | + | :{| cellpadding="5" cellspacing="0" width="95%" border="1" |
|- | |- | ||
| ''solution'' | | ''solution'' | ||
| − | | The term solution is used in optimization. One solution ('''x''','''f''','''g''','''a''') consists of a vector of design variables '''x''', the evaluated objective(s) '''f'''('''x'''), constraint(s) '''g'''('''x''') | + | | The term solution is used in optimization. One solution ('''x''','''f''','''g''','''a''') consists of a vector of design variables '''x''', the evaluated objective(s) '''f'''('''x'''), constraint(s) '''g'''('''x'''), and optionally of additional values '''a'''. |
|- | |- | ||
| ''design variables'' | | ''design variables'' | ||
| The vector of design variables '''x''' may consist of real numbers (continuous variables), integers (discrete variables) or both (mixed variables). | | The vector of design variables '''x''' may consist of real numbers (continuous variables), integers (discrete variables) or both (mixed variables). | ||
|- | |- | ||
| − | |} | + | | ''objectives'' |
| + | | An optimization problem must have at least one objective or one constraint. OpenDino requires that the objective(s) '''f''' is/are to be minimized. A maximization of a function ''k'' can be converted into minimization by using ''f'' = -''k''. | ||
| + | |- | ||
| + | | ''constraints'' | ||
| + | | Constraints '''c''' are criteria that have to be fulfilled. OpenDino defines a constraint ''c'' as | ||
| + | * fulfilled, if ''c'' =< 0 | ||
| + | * violated, if ''c'' > 0. | ||
| + | |||
| + | The most simple constraint handling in optimization is to add a penalty to the objective function if the constraint is vialoted, resulting in | ||
| + | |||
| + | ''f'' + max(0, ''c''). | ||
| + | |-|} | ||
Version vom 21. Oktober 2015, 20:09 Uhr
Notation
As a math parser is currently not used, we write the math equations as formated text:
- Scalars are written as small italic letters, e.g. f
- Vectors are written as small bold letters, e.g. x.
- Matrices are written in capital bold letters, e.g. C.
Symbols
f, f objective function(s) x, x design variable(s) g, g constraint(s)
Terminology
solution The term solution is used in optimization. One solution (x,f,g,a) consists of a vector of design variables x, the evaluated objective(s) f(x), constraint(s) g(x), and optionally of additional values a. design variables The vector of design variables x may consist of real numbers (continuous variables), integers (discrete variables) or both (mixed variables). objectives An optimization problem must have at least one objective or one constraint. OpenDino requires that the objective(s) f is/are to be minimized. A maximization of a function k can be converted into minimization by using f = -k. constraints Constraints c are criteria that have to be fulfilled. OpenDino defines a constraint c as - fulfilled, if c =< 0
- violated, if c > 0.
The most simple constraint handling in optimization is to add a penalty to the objective function if the constraint is vialoted, resulting in
f + max(0, c).
