I'm trying to implement a Gurobi model with multiple objective functions (specifically 2) that solves lexicographically (in a hierarchy) but I'm running into an issue where when optimizing the second objective function it degrades the solution to the first one, which should not happen with hierarchical optimizations. It is degrading the first solution up by 1, to decrease the second by 5, could this be an error in how I setup my model hierarchically? This is the code where I set up my model:
m = Model('lexMin Model')
m.ModelSense = GRB.MINIMIZE
variable = m.addVars(k.numVars, vtype=GRB.BINARY, name='variable')
m.setObjectiveN(LinExpr(quicksum([variable[j]*k.obj[0][j] for j in range(k.numVars)])),0)
m.setObjectiveN(LinExpr(quicksum([variable[j]*k.obj[1][j] for j in range(k.numVars)])),1)
for i in range(0,k.numConst):
m.addConstr(quicksum([k.const[i,j]*variable[j] for j in range(k.numVars)] <= k.constRHS[i]))
m.addConstr(quicksum([variable[j]*k.obj[0][j] for j in range(k.numVars)]) >= r2[0][0])
m.addConstr(quicksum([variable[j]*k.obj[0][j] for j in range(k.numVars)]) <= r2[1][0])
m.addConstr(quicksum([variable[j]*k.obj[1][j] for j in range(k.numVars)]) >= r2[1][1])
m.addConstr(quicksum([variable[j]*k.obj[1][j] for j in range(k.numVars)]) <= r2[0][1])
m.Params.ObjNumber = 0
m.ObjNPriority = 1
m.update()
m.optimize()
I've double checked and the priority of the second function is 0, the value for the objective functions are nowhere near where they'd be if I prioritized the wrong function. When optimizing the first function it finds the right value, even, but when it moves on to the second value it chooses values that degrade the first value.
The Gurobi output looks like this:
Optimize a model with 6 rows, 375 columns and 2250 nonzeros
Model fingerprint: 0xac5de9aa
Variable types: 0 continuous, 375 integer (375 binary)
Coefficient statistics:
Matrix range [1e+01, 1e+02]
Objective range [1e+01, 1e+02]
Bounds range [1e+00, 1e+00]
RHS range [1e+04, 1e+04]
---------------------------------------------------------------------------
Multi-objectives: starting optimization with 2 objectives ...
---------------------------------------------------------------------------
Multi-objectives: applying initial presolve ...
---------------------------------------------------------------------------
Presolve time: 0.00s
Presolved: 6 rows and 375 columns
---------------------------------------------------------------------------
Multi-objectives: optimize objective 1 () ...
---------------------------------------------------------------------------
Presolve time: 0.00s
Presolved: 6 rows, 375 columns, 2250 nonzeros
Variable types: 0 continuous, 375 integer (375 binary)
Root relaxation: objective -1.461947e+04, 10 iterations, 0.00 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 -14619.473 0 3 - -14619.473 - - 0s
H 0 0 -14569.00000 -14619.473 0.35% - 0s
H 0 0 -14603.00000 -14619.473 0.11% - 0s
H 0 0 -14608.00000 -14619.473 0.08% - 0s
H 0 0 -14611.00000 -14618.032 0.05% - 0s
0 0 -14617.995 0 5 -14611.000 -14617.995 0.05% - 0s
0 0 -14617.995 0 3 -14611.000 -14617.995 0.05% - 0s
H 0 0 -14613.00000 -14617.995 0.03% - 0s
0 0 -14617.995 0 5 -14613.000 -14617.995 0.03% - 0s
0 0 -14617.995 0 5 -14613.000 -14617.995 0.03% - 0s
0 0 -14617.995 0 7 -14613.000 -14617.995 0.03% - 0s
0 0 -14617.995 0 3 -14613.000 -14617.995 0.03% - 0s
0 0 -14617.995 0 4 -14613.000 -14617.995 0.03% - 0s
0 0 -14617.995 0 6 -14613.000 -14617.995 0.03% - 0s
0 0 -14617.995 0 6 -14613.000 -14617.995 0.03% - 0s
0 0 -14617.995 0 6 -14613.000 -14617.995 0.03% - 0s
0 0 -14617.720 0 7 -14613.000 -14617.720 0.03% - 0s
0 0 -14617.716 0 8 -14613.000 -14617.716 0.03% - 0s
0 0 -14617.697 0 8 -14613.000 -14617.697 0.03% - 0s
0 0 -14617.661 0 9 -14613.000 -14617.661 0.03% - 0s
0 2 -14617.661 0 9 -14613.000 -14617.661 0.03% - 0s
* 823 0 16 -14614.00000 -14616.351 0.02% 2.8 0s
Cutting planes:
Gomory: 6
Cover: 12
MIR: 4
StrongCG: 2
Inf proof: 6
Zero half: 1
Explored 1242 nodes (3924 simplex iterations) in 0.29 seconds
Thread count was 8 (of 8 available processors)
Solution count 6: -14614 -14613 -14611 ... -14569
No other solutions better than -14614
Optimal solution found (tolerance 1.00e-04)
Best objective -1.461400000000e+04, best bound -1.461400000000e+04, gap 0.0000%
---------------------------------------------------------------------------
Multi-objectives: optimize objective 2 () ...
---------------------------------------------------------------------------
Loaded user MIP start with objective -12798
Presolve removed 1 rows and 0 columns
Presolve time: 0.01s
Presolved: 6 rows, 375 columns, 2250 nonzeros
Variable types: 0 continuous, 375 integer (375 binary)
Root relaxation: objective -1.282967e+04, 28 iterations, 0.00 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 -12829.673 0 3 -12798.000 -12829.673 0.25% - 0s
0 0 -12829.378 0 4 -12798.000 -12829.378 0.25% - 0s
0 0 -12829.378 0 3 -12798.000 -12829.378 0.25% - 0s
0 0 -12828.688 0 4 -12798.000 -12828.688 0.24% - 0s
H 0 0 -12803.00000 -12828.688 0.20% - 0s
0 0 -12825.806 0 5 -12803.000 -12825.806 0.18% - 0s
0 0 -12825.193 0 5 -12803.000 -12825.193 0.17% - 0s
0 0 -12823.156 0 6 -12803.000 -12823.156 0.16% - 0s
0 0 -12822.694 0 7 -12803.000 -12822.694 0.15% - 0s
0 0 -12822.679 0 7 -12803.000 -12822.679 0.15% - 0s
0 2 -12822.679 0 7 -12803.000 -12822.679 0.15% - 0s
Cutting planes:
Cover: 16
MIR: 6
StrongCG: 3
Inf proof: 4
RLT: 1
Explored 725 nodes (1629 simplex iterations) in 0.47 seconds
Thread count was 8 (of 8 available processors)
Solution count 2: -12803 -12798
No other solutions better than -12803
Optimal solution found (tolerance 1.00e-04)
Best objective -1.280300000000e+04, best bound -1.280300000000e+04, gap 0.0000%
So it finds the values (-14613,-12803) instead of (-14614,-12798)
