Named Index for Optimization Variables

Create Named Indices
Use Named Indices

Create Named Indices

Optimization variables can use names for indexing elements. You can give the names when you create a variable or afterward. For example, give the names while creating the variable.

x = optimvar('x',["United","Lufthansa","Virgin Air"])

x = 

  1×3 OptimizationVariable array with properties:

  Array-wide properties:
          Name: 'x'
          Type: 'continuous'
    IndexNames: {{}  {1×3 cell}}

  Elementwise properties:
    LowerBound: [-Inf -Inf -Inf]
    UpperBound: [Inf Inf Inf]

  See variables with showvar.
  See bounds with showbounds.

optimvar automatically maps the names you specify to index numbers in the order of your variables. For example, "United" corresponds to index 1, "Lufthansa" corresponds to index 2, and "Virgin Air" corresponds to index 3. Display this last variable for confirmation.

showvar(x(3))

    [ x(1, 'Virgin Air') ]

Index names enable you to address elements of x by the index names. For example:

route = 2*x("United") + 3*x("Virgin Air")

route = 

  OptimizationExpression

    2*x(1, 'United') + 3*x(1, 'Virgin Air')

You can create or change the index names after you create a variable. However, you cannot change the size of an optimization variable after construction. So you can change index names only by setting new names that index the same size as the original variable. For example:

x = optimvar('x',3,2);
x.IndexNames = { {'row1','row2','row3'}, {'col1','col2'} };

You can also set the index names for each dimension individually:

x.IndexNames{1} = {'row1', 'row2', 'row3'};
x.IndexNames{2} = {'col1', 'col2'};

You can set an index name for a particular element:

x.IndexNames{1}{2} = 'importantRow';

Examine the index names for the variable.

x.IndexNames{1}

ans =

  1×3 cell array

    {'row1'}    {'importantRow'}    {'row3'}

x.IndexNames{2}

ans =

  1×2 cell array

    {'col1'}    {'col2'}

Use Named Indices

You can create and debug some problems easily by using named index variables. For example, consider the variable x that is indexed by the names in vars:

vars = {'P1','P2','I1','I2','C','LE1','LE2','HE1','HE2',...
    'HPS','MPS','LPS','BF1','BF2','EP','PP'};
x = optimvar('x',vars,'LowerBound',0);

Create bounds, an objective function, and linear constraints for x by using the named indices.

x('P1').LowerBound = 2500;
x('I2').UpperBound = 244000;
linprob = optimproblem;
linprob.Objective = 0.002614*x('HPS') + 0.0239*x('PP') + 0.009825*x('EP');
linprob.Constraints.cons1 = x('I1') - x('HE1') <= 132000;

You can use strings (" ") or character vectors (' ') in index variables indiscriminantly. For example:

x("P2").LowerBound = 3000;
x('MPS').LowerBound = 271536;
showbounds(x)

      2500 <= x(1, 'P1')
      3000 <= x(1, 'P2')
         0 <= x(1, 'I1')
         0 <= x(1, 'I2')  <= 244000
         0 <= x(1, 'C')
         0 <= x(1, 'LE1')
         0 <= x(1, 'LE2')
         0 <= x(1, 'HE1')
         0 <= x(1, 'HE2')
         0 <= x(1, 'HPS')
    271536 <= x(1, 'MPS')
         0 <= x(1, 'LPS')
         0 <= x(1, 'BF1')
         0 <= x(1, 'BF2')
         0 <= x(1, 'EP')
         0 <= x(1, 'PP')

There is no distinction between variables you specified with a string, such as x("P2"), and variables you specified with a character vector, such as x('MPS').

Because named index variables have numeric equivalents, you can use ordinary summation and colon operators even when you have named index variable. For example, you can have constraints of these forms:

constr = sum(x) <= 100;
showconstr(constr)

x('P1') + x('P2') + x('I1') + x('I2') + x('C') + x('LE1') + x('LE2') + x('HE1') + x('HE2') + x('HPS') +
x('MPS') + x('LPS') + x('BF1') + x('BF2') + x('EP') + x('PP') <= 100

y = optimvar('y',{'red','green','blue'},{'plastic','wood','metal'},...
    'Type','integer','LowerBound',0);
constr2 = y("red",:) == [5,7,3];
showconstr(constr2)

(1, 1)

  y('red', 'plastic') == 5

(1, 2)

  y('red', 'wood') == 7

(1, 3)

  y('red', 'metal') == 3

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