OptimizationVariable - Variable for optimization - MATLAB (original) (raw)
Variable for optimization
Description
An OptimizationVariable
object contains variables for optimization expressions. Use expressions to represent an objective function, constraints, or equations. Variables are symbolic in nature, and can be arrays of any size.
Creation
Create an OptimizationVariable
object using optimvar.
Properties
Array-Wide Properties
This property is read-only.
Variable name, specified as a string or character vector.
Name
gives the variable label to be displayed, such as in show or write. Name
also gives the field names in the solution structure that solve returns.
Tip
To avoid confusion, set name
to be the MATLAB® variable name. For example,
metal = optimvar("metal")
Data Types: char
| string
Variable type, specified as 'continuous'
,'integer'
, 'semi-continuous'
, or'semi-integer'
.
'continuous'
— Real values.'integer'
— Integer values.'semi-continuous'
— Zero or real values between the lower and upper bounds, which must be strictly positive and cannot exceed1e5
. This type applies only to mixed-integer linear programming (intlinprog).'semi-integer'
— Zero or integer values between the lower and upper bounds, which must be strictly positive and cannot exceed1e5
. This type applies only to mixed-integer linear programming (intlinprog
).
Type
applies to the entire variable array. To have multiple variable types, create multiple variables.
Tip
To specify a binary variable, use the 'integer'
type and specify LowerBound
= 0
and UpperBound
= 1
.
Data Types: char
| string
Element-wise Properties
Lower bound, specified as a real scalar or as a real array having the same dimensions as the OptimizationVariable
object. Scalar values apply to all elements of the variable.
The LowerBound
property is always displayed as an array. However, you can set the property as a scalar that applies to all elements. For example,
Data Types: double
Upper bound, specified as a real scalar or as a real array having the same dimensions as the OptimizationVariable
object. Scalar values apply to all elements of the variable.
The UpperBound
property is always displayed as an array. However, you can set the property as a scalar that applies to all elements. For example
Data Types: double
Object Functions
show | Display information about optimization object |
---|---|
showbounds | Display variable bounds |
write | Save optimization object description |
writebounds | Save description of variable bounds |
Examples
Create a scalar optimization variable named dollars
.
dollars = optimvar("dollars")
dollars = OptimizationVariable with properties:
Name: 'dollars'
Type: 'continuous'
IndexNames: {{} {}}
LowerBound: -Inf
UpperBound: Inf
See variables with show. See bounds with showbounds.
Create a 3-by-1 optimization variable vector named x
.
x = 3×1 OptimizationVariable array with properties:
Array-wide properties: Name: 'x' Type: 'continuous' IndexNames: {{} {}}
Elementwise properties: LowerBound: [3×1 double] UpperBound: [3×1 double]
See variables with show. See bounds with showbounds.
Create an integer optimization variable vector named bolts
that is indexed by the strings "brass"
, "stainless"
, and "galvanized"
. Use the indices of bolts
to create an optimization expression, and experiment with creating bolts
using character arrays or in a different orientation.
Create bolts
using strings in a row orientation.
bnames = ["brass","stainless","galvanized"]; bolts = optimvar("bolts",bnames,Type="integer")
bolts = 1×3 OptimizationVariable array with properties:
Array-wide properties: Name: 'bolts' Type: 'integer' IndexNames: {{} {1×3 cell}}
Elementwise properties: LowerBound: [-Inf -Inf -Inf] UpperBound: [Inf Inf Inf]
See variables with show. See bounds with showbounds.
Create an optimization expression using the string indices.
y = bolts("brass") + 2bolts("stainless") + 4bolts("galvanized")
y = Linear OptimizationExpression
bolts('brass') + 2*bolts('stainless') + 4*bolts('galvanized')
Use a cell array of character vectors instead of strings to get a variable with the same indices as before.
bnames = {'brass','stainless','galvanized'}; bolts = optimvar("bolts",bnames,Type="integer")
bolts = 1×3 OptimizationVariable array with properties:
Array-wide properties: Name: 'bolts' Type: 'integer' IndexNames: {{} {1×3 cell}}
Elementwise properties: LowerBound: [-Inf -Inf -Inf] UpperBound: [Inf Inf Inf]
See variables with show. See bounds with showbounds.
Use a column-oriented version of bnames
, 3-by-1 instead of 1-by-3, and observe that bolts
has that orientation as well.
bnames = ["brass";"stainless";"galvanized"]; bolts = optimvar("bolts",bnames,Type="integer")
bolts = 3×1 OptimizationVariable array with properties:
Array-wide properties: Name: 'bolts' Type: 'integer' IndexNames: {{1×3 cell} {}}
Elementwise properties: LowerBound: [3×1 double] UpperBound: [3×1 double]
See variables with show. See bounds with showbounds.
Create a 3-by-4-by-2 array of optimization variables named xarray
.
xarray = optimvar("xarray",3,4,2)
xarray = 3×4×2 OptimizationVariable array with properties:
Array-wide properties: Name: 'xarray' Type: 'continuous' IndexNames: {{} {} {}}
Elementwise properties: LowerBound: [3×4×2 double] UpperBound: [3×4×2 double]
See variables with show. See bounds with showbounds.
You can also create multidimensional variables indexed by a mixture of names and numeric indices. For example, create a 3-by-4 array of optimization variables where the first dimension is indexed by the strings 'brass'
, 'stainless'
, and 'galvanized'
, and the second dimension is numerically indexed.
bnames = ["brass","stainless","galvanized"]; bolts = optimvar("bolts",bnames,4)
bolts = 3×4 OptimizationVariable array with properties:
Array-wide properties: Name: 'bolts' Type: 'continuous' IndexNames: {{1×3 cell} {}}
Elementwise properties: LowerBound: [3×4 double] UpperBound: [3×4 double]
See variables with show. See bounds with showbounds.
Create an optimization variable named x
of size 3-by-3-by-3 that represents binary variables.
x = optimvar("x",3,3,3,Type="integer",LowerBound=0,UpperBound=1)
x = 3×3×3 OptimizationVariable array with properties:
Array-wide properties: Name: 'x' Type: 'integer' IndexNames: {{} {} {}}
Elementwise properties: LowerBound: [3×3×3 double] UpperBound: [3×3×3 double]
See variables with show. See bounds with showbounds.
Create a semicontinuous optimization variable named x
with a lower bound of π/2 and an upper bound of 2π.
x = optimvar("x",Type="semi-continuous",... LowerBound=pi/2,UpperBound=2*pi)
x = OptimizationVariable with properties:
Name: 'x'
Type: 'semi-continuous'
IndexNames: {{} {}}
LowerBound: 1.5708
UpperBound: 6.2832
See variables with show. See bounds with showbounds.
Create a semi-integer 3-D variable named y
with lower bounds of [10,20,30]
and upper bounds of [20,40,60]
.
y = optimvar("y",3,Type="semi-integer",... LowerBound=[10,20,30],UpperBound=[20,40,60])
y = 3×1 OptimizationVariable array with properties:
Array-wide properties: Name: 'y' Type: 'semi-integer' IndexNames: {{} {}}
Elementwise properties: LowerBound: [3×1 double] UpperBound: [3×1 double]
See variables with show. See bounds with showbounds.
Semicontinuous and semi-integer variables must have strictly positive bounds that do not exceed 1e5
.
More About
An optimization variable reference is an optimization variable that is a subset of another optimization variable. The reference variable points to, meaning it is an alias of, the original variable. The reference variable does not have an independent existence.
For example, suppose x
is a 3-element optimization variable:
Take y
as the last two elements of x
.
Then y(1)
is an alias of x(2)
, andy(2)
is an alias of x(3)
. If you usey
in an optimization expression, the expression includesx
, not y
. For example,
expr =
OptimizationExpression
x(2) + 2*x(3)
Furthermore, any modification of y
produces a modification ofx
. For example,
y.LowerBound = 2; showbounds(x)
2 <= x(2, 1) 2 <= x(3, 1)
For mixed-integer linear programming problems, you can specifyType
="semi-continuous"
orType
="semi-integer"
for the variables. These variables must have strictly positive bounds that do not exceed1e5
.
Semicontinuous and semi-integer variables can take the value 0
or any value from the lower bound to the upper bound. Semi-integer variables can take only integer values within the bounds, whereas semicontinuous variables can take any real value within the bounds.
Tips
OptimizationVariable
objects have handle copy behavior. See Handle Object Behavior and Comparison of Handle and Value Classes. Handle copy behavior means that a copy of anOptimizationVariable
points to the original and does not have an independent existence. For example, create a variablex
, copy it toy
, then set a property ofy
. Note thatx
takes on the new property value.
x = optimvar('x','LowerBound',1);
y = x;
y.LowerBound = 0;
showbounds(x)
Version History
Introduced in R2017b