I am using or-tools solve a non-linear mixed integer programming problem. It's unclear to me how the QuadraticSum feature works. The questions I have are: what does it do, and how do I use it?

In the basic example below, I code up the objective in two ways, but they seem to give a different result.

Anyone any idea?

Basic example:

from ortools.math_opt.python import mathopt

# Build the model.
model = mathopt.Model(name="getting_started_lp")
x = model.add_variable(lb=-1.0, ub=1.5, name="x")
y = model.add_variable(lb=0.0, ub=1.0, name="y")
# z = model.add_binary_variable(name="z")
model.add_linear_constraint(x + y <= 1.5)
objective1 = x * x + y * y
objective2 = mathopt.QuadraticSum([x, y])
model.maximize(objective1)
params = mathopt.SolveParameters(enable_output=True)
print(params)

result = mathopt.solve(model, mathopt.SolverType.GSCIP, params=params)
if result.termination.reason != mathopt.TerminationReason.OPTIMAL:
    raise RuntimeError(f"model failed to solve: {result.termination}")

I am using or-tools solve a non-linear mixed integer programming problem. It's unclear to me how the QuadraticSum feature works. The questions I have are: what does it do, and how do I use it?

In the basic example below, I code up the objective in two ways, but they seem to give a different result.

Anyone any idea?

Basic example:

from ortools.math_opt.python import mathopt

# Build the model.
model = mathopt.Model(name="getting_started_lp")
x = model.add_variable(lb=-1.0, ub=1.5, name="x")
y = model.add_variable(lb=0.0, ub=1.0, name="y")
# z = model.add_binary_variable(name="z")
model.add_linear_constraint(x + y <= 1.5)
objective1 = x * x + y * y
objective2 = mathopt.QuadraticSum([x, y])
model.maximize(objective1)
params = mathopt.SolveParameters(enable_output=True)
print(params)

result = mathopt.solve(model, mathopt.SolverType.GSCIP, params=params)
if result.termination.reason != mathopt.TerminationReason.OPTIMAL:
    raise RuntimeError(f"model failed to solve: {result.termination}")

• optimization
• or-tools

1 Answer 1

The QuadraticSum constructor takes in a heterogeneous list of numbers, linear expresisons and quadratic expressions, and adds them up. So objective_2 is just x+y in your code.

Generally, you do not need to invoke that constructor/use that type directly, just use operator overloads, QuadraticExpression(), and mathopt.fast_sum()

https://github/google/or-tools/blob/stable/ortools/math_opt/python/expressions.py#L27