With the linear solver, can you create a new variable as the sum and/or product of other variables.

[Rhys Davies]

In Python, I have a set of BoolVars and I would like to create a new variable that is either the product or the sum of the boolean variables.

I would then like to use this new var in the objective.

I have attached a small example (that is not running to try and illustrate what I am trying to achieve.

I appreciate that I am probably being somewhat moronic...

Thanks for any help

[Laurent Perron]

Product no, sum should be:

solver.Add(new_var == sum([bool var array]))

Laurent Perron | Operations Research | lpe...@google.com | (33) 1 42 68 53 00

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[Rhys Davies]

Thanks.... :)

That helps greatly

[Rhys Davies]

Hi Laurent

I am still having an issue with the Boolean sum. The solver is essential converting the BoolVar into an integer.

For example:

    var1 = solver.BoolVar('var1')

    var2 = solver.BoolVar('var2')

    var3 = solver.BoolVar('var3')

    sum1 = solver.BoolVar('sum1')

    solver.Add(sum1 == solver.Sum([var1, var2, var3]))

sum1 has a max value of 1, so only one of the vars can be true at a time...

I can, of course, set sum1 as an IntVar.

    sum1 = solver.IntVar(0, 3, 'sum1')

but then I do not know how to set the coefficient in the objective function

objective = solver.Objective()

objective.SetCoefficient(sum1, 80)

This now sets all the vars to True, sum1 is three and the objective function comes out at 240.

I would like to add 80 if and only if sum1 is not 0.

Is there a way to do this? Or does break the linearity?

I was expecting the solver.Sum to obey Boolean Algebra:

0+0+0 = 0

1+0+0 = 1

1+1+0 = 1

1+1+1 = 0

Regards

Rhys

[Rhys Davies]

Lets try that algebra again :(

0+0+0 = 0

1+0+0 = 1

1+1+0 = 1

1+1+1 = 1

[Laurent Perron]

This is a linear solver, not a boolean one :-)

Just to sum1 >= var1; sum1 >= var2; sum3 >= var1; sum1 <= var1 + var2 + var3.

Laurent Perron | Operations Research | lpe...@google.com | (33) 1 42 68 53 00

[Laurent Perron]

Correct version:

just do: 

  sum1 >= var1; 

  sum1 >= var2;

  sum1 >= var3; 

  sum1 <= var1 + var2 + var3.

[Rhys Davies]

That works perfectly.

For anyone interested:

def boolean_linear_sum(solver, bool_vars, bool_sum):
    for var in bool_vars:
        solver.Add(bool_sum >= var)

    solver.Add(bool_sum <= solver.Sum(bool_vars))