Gurobi Degrading Hierarchical Objective Functions
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I'm trying to run a Hierarchical multi-objective gurobi model without any degradation, but when it optimizes the second objective function it chooses a solution that degrades the first by 1. My code looks like this:
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()
And my 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%Instead of choosing (-14614,-12798) it chooses (-14613,-12803) which is a degraded solution.
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Gurobi Staff
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This is already answered on Stackoverflow.
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