Rounding LinearExpr with google or-tools SAT solver

问题

I'm creating a constraint (in Java) using or-tools SAT solver:

IntVar x, y, z;
IntVar[] variables = new IntVar{x, y, z};
int[] multiplier = new int{2, 3, 3};
LinearExpr expression = LinearExpr.scalProd(variables, multiplier); //2x + 3y + 3z
model.addLessThan(expression, q);

Where q is some given integer.

The thing is that I need to round the expression result. Something like:

if(expression < 25) {
    expression = 0;
} else if(expression < 75) {
    expression = 50;
} else if(expression < 125) {
    expression = 100;
} else if(expression < 175) {
    expression = 150;
} else if(expression < 225) {
    expression = 200;
} else if(expression < 275) {
    expression = 250;
} else {
    expression = 300;
}

So that the value of the expression (which should be used in the addLessThan constraint) is one of the following:

0, 50, 100, 150, 200, 250, 300

Let's review 2 cases:

Case 1

q = 180 and expression = 176.

Although the condition 176 < 180 is true, after rounding up 176 to 200 the tested condition should be 200 < 180 which is false.

So for q = 180 and expression = 176 I would like the condition to return false.

Case 2

q = 210 and expression = 218.

Although the condition 218 < 210 is false, after rounding down 218 to 200 the tested condition should be 200 < 210 which is true.

So for q = 210 and expression = 218 I would like the condition to return true.

How can I achieve that?

回答1:

To elaborate on my comment (code in Python):

roundedExpr = model.NewIntVarFromDomain(cp_model.Domain.FromValues([0, 50, 100, 150, 200, 250, 300]), "roundedExpr")

b1 = model.NewBoolVar("< 25")
model.Add(expression < 25).OnlyEnforceIf(b1)
model.Add(roundedExpr == 0).OnlyEnforceIf(b1)
...
b7 = model.NewBoolVar(">= 275")
model.Add(expression >= 275).OnlyEnforceIf(b7)
model.Add(roundedExpr == 300).OnlyEnforceIf(b7)

model.AddBoolOr([b1, b2, b3, ..., b7])

来源：https://stackoverflow.com/questions/62646674/rounding-linearexpr-with-google-or-tools-sat-solver

标签

java

nonlinear-optimization

or-tools

sat