Incorrect answer

[chenYanbin0218]

When I solve the following simple questions using HiGHS through pyoptinterface, the output is different from the answer using Gurobi

Using HiGHS

import pyoptinterface as poi
from pyoptinterface import highs
model = highs.Model()
x = model.add_variable(domain=poi.VariableDomain.Binary, name="x")
y = model.add_variable(domain=poi.VariableDomain.Binary, name="y")
z = model.add_variable(lb=0,ub=100, name="z")
con1=model.add_linear_constraint(2*y+3*z, poi.ConstraintSense.LessEqual, 12, name="con1")
con2=model.add_linear_constraint(x+y, poi.ConstraintSense.LessEqual, 1, name="con2")
obj =3*y+x*z
model.set_objective(obj, poi.ObjectiveSense.Maximize)
model.optimize()

print("x = ", model.get_value(x))
print("y = ", model.get_value(y))
print("z = ", model.get_value(z))
print("obj = ", model.get_value(obj))

Output of HiGHS

Presolving model
2 rows, 1 cols, 2 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve: Optimal

Solving report
  Status            Optimal
  Primal bound      3
  Dual bound        3
  Gap               0% (tolerance: 0.01%)
  Solution status   feasible
                    3 (objective)
                    0 (bound viol.)
                    0 (int. viol.)
                    0 (row viol.)
  Timing            0.00 (total)
                    0.00 (presolve)
                    0.00 (postsolve)
  Nodes             0
  LP iterations     0 (total)
                    0 (strong br.)
                    0 (separation)
                    0 (heuristics)
x =  0.0
y =  1.0
z =  0.0
obj =  3.0

Using Gurobi

import pyoptinterface as poi
from pyoptinterface import gurobi
 model = gurobi.Model()
x = model.add_variable(domain=poi.VariableDomain.Binary, name="x")
y = model.add_variable(domain=poi.VariableDomain.Binary, name="y")
z = model.add_variable(lb=0,ub=100, name="z")
con1=model.add_linear_constraint(2*y+3*z, poi.ConstraintSense.LessEqual, 12, name="con1")
con2=model.add_linear_constraint(x+y, poi.ConstraintSense.LessEqual, 1, name="con2")
obj =3*y+x*z
model.set_objective(obj, poi.ObjectiveSense.Maximize)
model.optimize()

print("x = ", model.get_value(x))
print("y = ", model.get_value(y))
print("z = ", model.get_value(z))
print("obj = ", model.get_value(obj))

Output of Gurobi

Optimal solution found (tolerance 1.00e-04)
Best objective 4.000000000000e+00, best bound 4.000000000000e+00, gap 0.0000%
x =  1.0
y =  0.0
z =  4.0
obj =  4.0

[jajhall]

This is because your problem is mixed-integer quadratic programming, and HiGHS can't solve such problems -
README.md

At one point, HiGHS used to ignore the Hessian matrix and just solve the mixed-integer linear programming (MIP) problem, but I'm struggling to find a version in which that happens! Now, all that happens is that HiGHS gives the message

ERROR: Cannot solve MIQP problems with HiGHS

What version of HiGHS is used by pyoptinterface?

Since the HiGHS solution that you quote corresponds to ignoring the Hessian, could it be that pyoptinterface doesn't pass the Hessian to HiGHS once it knows that there are integer variables?

[chenYanbin0218]

Thank you very much for your reply! The version is 1.7.1 and I think it's pyoptinerface that results such situation, missing the error.

[metab0t]

@jajhall I want to ensure that HiGHS accepts Hessian matrix in the lower triangular form or upper triangular form?

The docstring in C API says HiGHS accepts upper triangular form but the test codes in repo show that we should use lower triangle.

HiGHS/src/interfaces/highs_c_api.h

Lines 532 to 533 in 5ce7a27

	* @param start The Hessian matrix is provided to HiGHS as the upper
	* triangular component in compressed sparse column form. The

[jajhall]

@jajhall I want to ensure that HiGHS accepts Hessian matrix in the lower triangular form or upper triangular form?

The docstring in C API says HiGHS accepts upper triangular form but the test codes in repo show that we should use lower triangle.

HiGHS/src/interfaces/highs_c_api.h

Lines 532 to 533 in 5ce7a27

	* @param start The Hessian matrix is provided to HiGHS as the upper
	* triangular component in compressed sparse column form. The

Indeed, this should say "lower triangular component". Fixed by #1879

[metab0t]

Thanks! I have pushed a fix of PyOptInterface to use the lower triangular of Hessian.