Suboptimal solution returned as optimal in MIP

Hi,

I am running an MIP formulation (in Python) that ends with aprox. 0.01% optimality gap. However, I found the solution is not optimal. I tried then providing an initial starting point, and then (1), the log says "User MIP start did not produce a new incumbent solution", and (2) the obtained solution remains suboptimal. I was wondering if I am making a mistake, or if there is any setting that I should be using.

Find below the model and the output log. FYI, I tried with the pre solve off and it was the same solution.

Thanks!

#Model defitinion:

 # Create a new model
m = gp.Model("Baby Model")
m.Params.NonConvex = 2
m.Params.DUAL_REDUCTIONS = 0
m.Params.InfUnbdInfo = 1
m.Params.FuncPieces = -1
#m.Params.FuncPieceError = 0.0001
m.Params.FuncPieceError = 0.01
m.Params.FuncPieceRatio = 0
#m.Params.FeasibilityTol = 1e-2
m.Params.MIPFocus = 2
m.Params.Presolve = 1
m.Params.IntFeasRol = 1e-4
m.Params.timeLimit= 100000.0

    # Create variables
    
n = m.addVars(mobil, lb=0.1, ub=float('inf'), vtype=GRB.INTEGER, name="deliveries") 
d = m.addVar(lb=0.1, ub=float('inf'), vtype=GRB.INTEGER, name="openPODs") 
delta1 = m.addVars(mobil, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="delta1")
deltax = m.addVars(mobil, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="deltax")
alpha = m.addVars(populations, vtype=GRB.CONTINUOUS, name="alpha")
t = m.addVars(epoch_e,epoch_l,mobil, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="t")
rr = m.addVars(populations, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="rr")
h = m.addVars(pods,dcs, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="schd_delay")
hf = m.addVars(populations,dcs, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="schd_delay_f")
Q = m.addVars(pods,dcs,sub_e2, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="Q") #Relaxed
Qf = m.addVars(populations,dcs,sub_e2, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="Qf") #Relaxed
q = m.addVars(populations,mobil, lb=0.1, ub=float('inf'), vtype=GRB.CONTINUOUS, name="q") #Relaxed

xpod = m.addVars(pods, lb=0.0, ub=a, vtype=GRB.CONTINUOUS, name="xpod")
ypod = m.addVars(pods, lb=0.0, ub=b, vtype=GRB.CONTINUOUS, name="ypod")
x = m.addVars(populations,epoch_e,epoch_l, lb=0.0, ub=a, vtype=GRB.CONTINUOUS, name="x")
y = m.addVars(populations,epoch_e,epoch_l, lb=0.0, ub=b, vtype=GRB.CONTINUOUS, name="y")

bin_lambda = m.addVars(pods,dcs,sub_e2, vtype=GRB.BINARY, name="bin_lambda")
bin_tau = m.addVars(populations,pods, vtype=GRB.BINARY, name="bin_tau")

bin_rho = m.addVars(pods, vtype=GRB.BINARY, name="bin_rho")
bin_sigma = m.addVars(epoch_e,mobil, vtype=GRB.BINARY, name="bin_sigma")

bin_phif = m.addVars(populations,dcs,sub_e2, vtype=GRB.BINARY, name="bin_phif")

bina = m.addVars(populations, vtype=GRB.BINARY, name="binaryx")
binb = m.addVars(populations, vtype=GRB.BINARY, name="binaryy")

Ztran = m.addVar(vtype=GRB.CONTINUOUS, name="Ztran")
Zfixc = m.addVar(vtype=GRB.CONTINUOUS, name="Zfixc")
Zdepr = m.addVar(vtype=GRB.CONTINUOUS, name="Zdep")
Zwalk = m.addVar(vtype=GRB.CONTINUOUS, name="Zwalk")

zdep1 = m.addVars(populations,mobil, lb=0.0, ub=1000, vtype=GRB.CONTINUOUS, name="aux_dep_cost_funct_1")
zdepx = m.addVars(populations,mobil, lb=0.0, ub=1000, vtype=GRB.CONTINUOUS, name="aux_dep_cost_funct_1")
dist = m.addVars(pods,dcs, lb=0.0, ub=1000, vtype=GRB.CONTINUOUS, name="aux_distance")
distf = m.addVars(populations,dcs, lb=0.0, ub=1000, vtype=GRB.CONTINUOUS, name="aux_distancef")
aux1 = m.addVars(populations,mobil, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_delta1")
auxx = m.addVars(populations,mobil, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_deltax")
auxn = m.addVars(populations,mobil, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_deltax_n")
aux2 = m.addVars(pods,dcs, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_distance_2")
aux21 = m.addVar(lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_distance_2.1")
aux2f = m.addVars(populations,dcs, lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_distance_2f")
aux21f = m.addVar(lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_distance_2.1f")
aux3 = m.addVar(lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_location")
aux4 = m.addVars(populations,lb=0.0, ub=float('inf'), vtype=GRB.CONTINUOUS, name="aux_location_2")
A = m.addVars(populations,pods, vtype=GRB.CONTINUOUS, name="attractPODs")

    # Set objective: 
m.setObjective(Ztran + Zfixc + Zdepr + Zwalk, GRB.MINIMIZE)

    # Add constraints

m.addConstr(
    (Ztran>=(c/w)*aux21+(c/w)*aux21f), "Ztransport cost")

m.addConstrs(
    (aux2[j,k]==((xdc[k]-xpod[j])*(xdc[k]-xpod[j]))+((ydc[k]-ypod[j])*(ydc[k]-ypod[j]))
    for j in pods for k in dcs), "auxiliary distance 2")       
        
for j in pods:
    for k in dcs:
        m.addGenConstrPow(aux2[j,k], dist[j,k], 0.5)  

m.addConstr(
    (aux21==quicksum(dist[j,k]*bin_lambda[j,k,e] for j in pods for k in dcs for e in sub_e2)), "auxiliary distance 2.1")

m.addConstrs(
    (aux2f[i,k]==((xdc[k]-x_t0[i])*(xdc[k]-x_t0[i]))+((ydc[k]-y_t0[i])*(ydc[k]-y_t0[i]))
    for i in populations for k in dcs), "auxiliary distance 2 f")       
        
for i in populations:
    for k in dcs:
        m.addGenConstrPow(aux2f[i,k], distf[i,k], 0.5)  

m.addConstr(
    (aux21f==quicksum(distf[i,k]*bin_phif[i,k,e] for i in populations for k in dcs for e in sub_e2)), "auxiliary distance 2.1 f")

m.addConstr(
    (Zfixc>=cprim*d), "Zfix cost")

m.addConstr(
    (Zdepr>=quicksum(p[i,o]*beta1[i,o]*(zdep1[i,o]+auxn[i,o]) for i in populations for o in mobil)), "Zdeprivation cost")

m.addConstrs( 
    (aux1[i,o]==beta2[i,o]*delta1[o]
    for i in populations for o in mobil), "auxiliary delta1")

m.addConstrs(
    (auxx[i,o]==beta2[i,o]*deltax[o]
    for i in populations for o in mobil), "auxiliary deltax")

for i in populations:
    for o in mobil:
        m.addGenConstrExp(aux1[i,o], zdep1[i,o])
        m.addGenConstrExp(auxx[i,o], zdepx[i,o]) 

m.addConstrs(
    (auxn[i,o]==n[o]*zdepx[i,o]
    for i in populations for o in mobil), "auxiliary zdepx")

m.addConstr(
    (Zwalk>=quicksum(v[i]*g[i]*p[i,2]*rr[i] for i in populations) ), "Zwalking cost")





    
m.addConstrs(
    (deltax[o]*n[o] == T - delta1[o] - (n[o]*q[i,o]/(u*p[i,o]))
    for i in populations for o in mobil), "time conservation")

m.addConstrs(
    (Q.sum('*',k,'*') + Qf.sum('*',k,'*') <= s[k]
    for k in dcs), "supplies availabilitym")

###This one:
m.addConstrs(
    (q[i,o] >= u*f*p[i,o]
    for i in populations for o in mobil), "supply minimum")

m.addConstrs(
    (quicksum(q[i,2]*bin_tau[i,j] for i in populations) <= M*(1-bin_sigma[e+1,2]) + Q.sum(j,'*',e)
    for j in pods for e in sub_e2), "inventory conservation")

m.addConstrs(
    (q[i,1] <= M*(1-bin_sigma[e+1,1]) + Qf.sum(i,'*',e) 
    for i in populations for e in sub_e2), "inventory conservation f")

#Probably won't need this again
#m.addConstrs(
#    (q.sum('*') <= M*(1-bin_sigma[e+1]) + Q.sum('*','*',e)
#    for e in sub_e2), "inventory conservation2")

m.addConstrs(
    (Q[j,k,e] <= M*bin_lambda[j,k,e] 
    for j in pods  for k in dcs for e in sub_e2), "inventory conservation3")

m.addConstrs(
    (Q.sum(j,'*','*') <= M*bin_tau.sum('*',j) 
    for j in pods), "inventory conservation4")

m.addConstrs(
    (Qf[i,k,e] <= M*bin_phif[i,k,e] 
    for i in populations  for k in dcs for e in sub_e2), "inventory conservation5")

m.addConstrs(
    (p[i,1] >= bin_phif[i,k,e] 
    for i in populations  for k in dcs for e in sub_e2), "inventory conservation6")

m.addConstrs(
    (t[e,1,o]<=t[e,2,o]
    for e in epoch_e for o in mobil), "time conservation 1a")  

m.addConstrs(
    (t[e,2,o]<=t[e,3,o]
    for e in epoch_e for o in mobil), "time conservation 1b")

m.addConstrs(
    (t[1,1,2]<= rr[i]
    for i in populations), "arrival a")  

m.addConstrs(
    (t[1,2,2] >= rr[i]
    for i in populations), "arrival a")

m.addConstrs(
    (rr[i] <= vprim[i]
    for i in populations), "max walking time")

m.addConstrs(
    (t[1,2,o]==delta1[o]
     for o in mobil), "time conservation 2")  

###Thest the code without this one: it is not in the overleaf formulation
#m.addConstr(
#    (t[1,2]<=T), "time conservation 3")  
####

m.addConstrs(
    (bin_sigma[e,o]*(t[e,2,o]-t[e-1,3,o])==deltax[o]*bin_sigma[e,o]
    for e in sub_e for o in mobil), "time conservation 3")

m.addConstrs(
    (bin_sigma[e,o]*(t[e,3,o]-t[e,2,o])==(q[i,o]/(u*p[i,o]))*bin_sigma[e,o]
    for e in epoch_e for i in populations for o in mobil), "time conservation 4")

m.addConstrs(
    (vsq[i]*aux3==((x[i,1,1]-x_t0[i])*(x[i,1,1] - x_t0[i]))+((y[i,1,1]-y_t0[i])*(y[i,1,1]-y_t0[i]))
    for i in populations), "location t1")

m.addConstr((aux3==(t[1,1,2]*t[1,1,2])), "aux location t1")

m.addConstrs(
    (vsq[i]*aux4[i]==((x[i,1,2] - x[i,1,1])*((x[i,1,2] - x[i,1,1])) + ((y[i,1,2] - y[i,1,1])*(y[i,1,2] - y[i,1,1])))
    for i in populations), "location tao1")

m.addConstrs(
    (aux4[i]==(rr[i]-t[1,1,2])*(rr[i]-t[1,1,2])
    for i in populations), "aux location t1")

m.addConstrs(
    (bin_phi[i,k]*((ydc[k] - y_t0[i])*(x[i,1,1] - x_t0[i])) == bin_phi[i,k]*((y[i,1,1] - y_t0[i])*(xdc[k] - x_t0[i]))
    for i in populations for k in dcs), "trajectory t0 to t1")

m.addConstrs(
    (bin_phi[i,k]*bina[i]*(xdc[k] - x_t0[i]) >= 0
    for i in populations for k in dcs), "trajectory aux1")

m.addConstrs(
    (bin_phi[i,k]*(1-bina[i])*(xdc[k] - x_t0[i]) <= 0
    for i in populations for k in dcs), "trajectory aux2")

m.addConstrs(
    (x[i,1,1]>=bina[i]*x_t0[i]
    for i in populations), "trajectory aux3")

m.addConstrs(
    ((1-bina[i])*x[i,1,1]<=x_t0[i]
    for i in populations for k in dcs), "trajectory aux4")

m.addConstrs(
    (bin_phi[i,k]*binb[i]*(ydc[k] - y_t0[i]) >= 0
    for i in populations for k in dcs), "trajectory aux5")

m.addConstrs(
    (bin_phi[i,k]*(1-binb[i])*(ydc[k] - y_t0[i]) <= 0
    for i in populations for k in dcs), "trajectory aux6")

m.addConstrs(
    (y[i,1,1]>=binb[i]*y_t0[i]
    for i in populations), "trajectory aux7")

m.addConstrs(
    ((1-binb[i])*y[i,1,1]<=y_t0[i]
    for i in populations for k in dcs), "trajectory aux8")


######      Attractiveness      ######

m.addConstrs(
    (alpha[i] >= quicksum(A[i,j]*bin_tau[i,j] for j in pods)
    for i in populations), "attractiveness of pods 1")

m.addConstrs(
    (alpha[i] <= A[i,j]
    for i in populations for j in pods), "attractiveness of pods 2")

m.addConstrs(
    (A[i,j] == (((xpod[j]-x[i,1,1])*(xpod[j]-x[i,1,1]))+((ypod[j]-y[i,1,1])*(ypod[j]-y[i,1,1])))
    for i in populations for j in pods), "attractiveness of pods 23")

###############################

###This one:
m.addConstrs(
    (x[i,1,2]*bin_tau[i,j] == xpod[j]*bin_tau[i,j]
    for i in populations for j in pods), "location x pods")  

###This one:
m.addConstrs(
    (y[i,1,2]*bin_tau[i,j] == ypod[j]*bin_tau[i,j]
    for i in populations for j in pods), "location y pods")  

m.addConstrs(
    (xpod[j] <= M*quicksum(bin_tau[i,j] for i in populations)
    for j in pods), "location x pods2") 

m.addConstrs(
    (ypod[j] <= M*quicksum(bin_tau[i,j] for i in populations)
    for j in pods), "location y pods2") 

m.addConstrs(
    ((1/w) * dist[j,k] * bin_lambda[j,k,1] == (t[1,1,2] - h[j,k]) * bin_lambda[j,k,1]
    for j in pods for k in dcs), "shceduled delivery")

m.addConstrs(
    ((1/w) * distf[i,k] * bin_phif[i,k,1] == (t[1,2,1] - hf[i,k]) * bin_phif[i,k,1]
    for i in populations for k in dcs), "shceduled delivery")

m.addConstrs(
    (bin_tau.sum(i,'*') ==1
    for i in populations), "bin pop-pod")

########

m.addConstrs(
    (h[j,k] <= bin_rho[j]*M
    for j in pods for k in dcs), "rho1")

m.addConstrs(
    (Q[j,k,e] <= bin_rho[j]*M
    for j in pods for k in dcs for e in sub_e2), "rho2")

m.addConstrs(
    (xpod[j] <= bin_rho[j]*M
    for j in pods), "rho3")

m.addConstrs(
    (ypod[j] <= bin_rho[j]*M
    for j in pods), "rho4")

m.addConstrs(
    (bin_tau[i,j] <= bin_rho[j]*M
    for i in populations for j in pods), "rho5")

#m.addConstrs(
#    (bin_lambda[j,k,e] <= bin_rho[j]*M
#    for j in pods for k in dcs for e in sub_e2), "rho6")

m.addConstrs(
    (bin_rho[j-1] >= bin_rho[j]
    for j in sub_pods), "rhoa")

m.addConstr(
    (quicksum(bin_rho[j] for j in pods) == d), "rhob")

m.addConstrs(
    (t[e,l,o] <= bin_sigma[e,o]*M
    for e in epoch_e for l in epoch_l for o in mobil), "sigma1")

m.addConstrs(
    (Q[j,k,e] <= bin_sigma[e+1,2]*M
    for j in pods for k in dcs for e in sub_e2), "sigma2")

m.addConstrs(
    (Qf[i,k,e] <= bin_sigma[e+1,1]*M
    for i in populations for k in dcs for e in sub_e2), "sigma2f")

m.addConstrs(
    (x[i,e,l] <= bin_sigma[e,2]*M
    for i in populations for e in epoch_e for l in epoch_l), "sigma3")

m.addConstrs(
    (y[i,e,l] <= bin_sigma[e,2]*M
    for i in populations for e in epoch_e for l in epoch_l), "sigma4")

m.addConstrs(
    (bin_sigma[e-1,o] >= bin_sigma[e,o]
    for e in sub_e for o in mobil), "sigmaa")

m.addConstrs(
    (quicksum(bin_sigma[e,o] for e in epoch_e) == n[o]+1
    for o in mobil), "sigmab")

n[1].start=3
n[2].start=9


m.optimize()

______________________

Changed value of parameter NonConvex to 2
   Prev: -1  Min: -1  Max: 2  Default: -1
Changed value of parameter DUAL_REDUCTIONS to 0
   Prev: 1  Min: 0  Max: 1  Default: 1
Changed value of parameter InfUnbdInfo to 1
   Prev: 0  Min: 0  Max: 1  Default: 0
Changed value of parameter FuncPieces to -1
   Prev: 0  Min: -2  Max: 200000000  Default: 0
Changed value of parameter FuncPieceError to 0.01
   Prev: 0.001  Min: 1e-06  Max: 1000000.0  Default: 0.001
Changed value of parameter FuncPieceRatio to 0.0
   Prev: -1.0  Min: -1.0  Max: 1.0  Default: -1.0
Changed value of parameter MIPFocus to 2
   Prev: 0  Min: 0  Max: 3  Default: 0
Changed value of parameter Presolve to 1
   Prev: -1  Min: -1  Max: 2  Default: -1
No parameters matching 'IntFeasRol' found
Changed value of parameter timeLimit to 100000.0
   Prev: inf  Min: 0.0  Max: inf  Default: inf
Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (win64)
Optimize a model with 743 rows, 578 columns and 1591 nonzeros
Model fingerprint: 0x57b0b44f
Model has 170 quadratic constraints
Model has 11 general constraints
Variable types: 471 continuous, 107 integer (104 binary)
Coefficient statistics:
  Matrix range     [1e-01, 1e+04]
  QMatrix range    [6e-02, 2e+00]
  QLMatrix range   [1e+00, 1e+04]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e-01, 1e+03]
  RHS range        [1e+00, 1e+04]
  QRHS range       [1e+00, 1e+04]

Warning: Completing partial solution with 105 unfixed non-continuous variables out of 107
User MIP start did not produce a new incumbent solution

Presolve added 0 rows and 2037 columns
Presolve removed 83 rows and 0 columns
Presolve time: 0.04s
Presolved: 1520 rows, 2851 columns, 9974 nonzeros
Presolved model has 9 SOS constraint(s)
Presolved model has 25 bilinear constraint(s)
Variable types: 2753 continuous, 98 integer (96 binary)

Root relaxation: objective 5.544015e+03, 346 iterations, 0.01 seconds
Another try with MIP start

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 5544.01481    0   39          - 5544.01481      -     -    0s
     0     0 5688.79342    0   86          - 5688.79342      -     -    0s
     0     0 5806.27731    0   74          - 5806.27731      -     -    0s
     0     0 5813.89676    0   80          - 5813.89676      -     -    0s
     0     0 6034.03112    0   91          - 6034.03112      -     -    0s
     0     0 6065.66356    0   91          - 6065.66356      -     -    0s
     0     0 6237.90489    0   80          - 6237.90489      -     -    1s
     0     0 6241.68288    0   83          - 6241.68288      -     -    1s
     0     0 6309.42340    0   86          - 6309.42340      -     -    1s
     0     0 6315.98542    0   86          - 6315.98542      -     -    1s
     0     0 6390.46027    0   79          - 6390.46027      -     -    1s
     0     0 6396.00968    0   77          - 6396.00968      -     -    1s
     0     0 6466.54736    0   73          - 6466.54736      -     -    1s
     0     0 6475.12922    0   82          - 6475.12922      -     -    1s
     0     0 6530.18417    0   82          - 6530.18417      -     -    1s
     0     0 6537.74124    0   88          - 6537.74124      -     -    1s
     0     0 6551.85594    0   73          - 6551.85594      -     -    1s
     0     0 6560.48748    0   78          - 6560.48748      -     -    1s
     0     0 6597.61280    0   73          - 6597.61280      -     -    1s
     0     0 6599.37835    0   73          - 6599.37835      -     -    1s
     0     0 6608.22086    0   82          - 6608.22086      -     -    2s
     0     0 6609.10829    0   77          - 6609.10829      -     -    2s
     0     0 6626.15025    0   70          - 6626.15025      -     -    2s
     0     0 6628.36816    0   80          - 6628.36816      -     -    2s
     0     0 6698.97362    0   80          - 6698.97362      -     -    2s
     0     0 6705.50274    0   80          - 6705.50274      -     -    2s
     0     0 6718.12324    0   77          - 6718.12324      -     -    2s
     0     0 6728.21095    0   83          - 6728.21095      -     -    2s
     0     0 6738.24363    0   76          - 6738.24363      -     -    2s
     0     0 6743.84773    0   80          - 6743.84773      -     -    2s
     0     0 6773.61450    0   80          - 6773.61450      -     -    2s
     0     0 6774.91813    0   80          - 6774.91813      -     -    2s
     0     0 6784.04247    0   83          - 6784.04247      -     -    2s
     0     0 6784.04247    0   83          - 6784.04247      -     -    2s
     0     2 6784.04247    0   83          - 6784.04247      -     -    2s
  1034   686 14384.8076   18   60          - 9952.89104      -  12.9    5s
* 2159   874              58    28894.280474 9952.89104  65.6%  13.4    5s
H 2227   815                    28893.374778 9952.89104  65.6%  13.2    6s
* 3285   929              47    25347.066269 10565.6386  58.3%  11.2    7s
* 3521  1000              51    25346.516587 10648.6407  58.0%  11.1    7s
* 3526   999              53    25346.337160 10648.6407  58.0%  11.0    7s
* 3528   999              53    25346.298861 10648.6407  58.0%  11.0    7s
* 5348  1498              54    24926.139783 10911.7472  56.2%   9.5    8s
* 5349  1497              54    24925.519470 10911.7472  56.2%   9.5    8s
* 7213  2073              60    24907.378887 11234.1390  54.9%   8.6    9s
H 7492  1994                    23757.556933 11278.8271  52.5%   8.5    9s
  7519  2011 16863.7731   24   13 23757.5569 11278.8271  52.5%   8.5   10s
 14638  3436 infeasible   30      23757.5569 12512.1660  47.3%   7.4   15s
*16564  3832              85    23530.904517 12885.1354  45.2%   7.3   16s
*16565  3832              85    23530.902241 12885.1354  45.2%   7.3   16s
*16566  3832              84    23530.899842 12885.1354  45.2%   7.3   16s
*16567  3832              83    23530.897315 12885.1354  45.2%   7.3   16s
*16568  3832              82    23530.894656 12885.1354  45.2%   7.3   16s
*19009  4221              50    23355.730582 13155.9584  43.7%   7.1   17s
 22752  4817 14151.4527   26   13 23355.7306 13395.4596  42.6%   6.8   20s
 31189  5956 15755.0571   28   12 23355.7306 13816.8647  40.8%   6.5   25s
 40485  7190 21394.0706   32   16 23355.7306 14162.5339  39.4%   6.3   30s
*40926  7135              62    23128.678047 14176.8797  38.7%   6.3   30s
*43716  7479              64    23015.966057 14250.8943  38.1%   6.2   31s
*45822  7737              72    23010.309911 14300.4162  37.9%   6.2   33s
*49080  8129              67    23002.271049 14380.4729  37.5%   6.1   34s
 49710  8209 14445.2161   28   10 23002.2710 14391.9058  37.4%   6.1   35s
 58745  9285 15210.6247   29   14 23002.2710 14619.0750  36.4%   6.0   40s
*68187 10219              66    22926.527633 14899.3675  35.0%   5.9   44s
 68866 10259 14997.1826   29   16 22926.5276 14918.7946  34.9%   5.9   45s
 77277 10867 infeasible   35      22926.5276 15192.8803  33.7%   5.9   50s
 86401 11756 18410.3639   28   16 22926.5276 15452.7230  32.6%   5.9   55s
*91288 12115              64    22873.532433 15571.5403  31.9%   5.8   57s
 96403 12360 20703.0099   35   12 22873.5324 15732.2383  31.2%   5.8   60s
 105657 12886 17901.8325   27    8 22873.5324 15978.6237  30.1%   5.8   65s
 114004 13055 infeasible   28      22873.5324 16230.9210  29.0%   5.8   70s
 122315 13144 22303.9815   34    8 22873.5324 16468.0075  28.0%   5.8   75s
 129725 13193     cutoff   35      22873.5324 16665.1068  27.1%   5.9   80s
 137485 13301 21300.7452   35   13 22873.5324 16822.2013  26.5%   5.8   85s
 144871 13393     cutoff   27      22873.5324 16946.5411  25.9%   5.8   90s
 150906 13441 18762.5704   27   10 22873.5324 17064.7649  25.4%   5.8   95s
 157352 13389 17213.1779   27   13 22873.5324 17213.1779  24.7%   5.7  100s
 161692 13364 20000.8178   17   11 22873.5324 17331.5252  24.2%   5.7  105s
 168360 13281     cutoff   36      22873.5324 17496.9437  23.5%   5.7  110s
 173902 13115 infeasible   30      22873.5324 17635.6487  22.9%   5.7  115s
*178803 12998              63    22871.197256 17731.9327  22.5%   5.7  118s
*178807 12998              64    22871.197104 17731.9327  22.5%   5.7  118s
 180312 13017 infeasible   37      22871.1971 17763.5573  22.3%   5.7  120s
 186632 12986 17886.8643   28   10 22871.1971 17886.8643  21.8%   5.7  125s
 193006 12950 18008.2093   32   10 22871.1971 18008.2093  21.3%   5.6  130s
 199239 12732 20421.5142   30   13 22871.1971 18131.9273  20.7%   5.6  135s
 204380 12597 18245.1857   32   10 22871.1971 18245.1857  20.2%   5.6  140s
 210588 12468     cutoff   34      22871.1971 18393.1956  19.6%   5.6  145s
 215991 12265 20814.5248   28   10 22871.1971 18501.4464  19.1%   5.5  150s
 222037 12087 infeasible   34      22871.1971 18635.6635  18.5%   5.5  155s
 228245 11953 18743.5855   26    9 22871.1971 18743.5855  18.0%   5.5  160s
 233521 11739 19069.3630   31   14 22871.1971 18871.1331  17.5%   5.5  165s
 239766 11499     cutoff   29      22871.1971 19004.6010  16.9%   5.4  170s
 244786 11250 19097.2989   29   10 22871.1971 19097.2989  16.5%   5.4  175s
 250125 10960 infeasible   38      22871.1971 19215.5869  16.0%   5.4  180s
 255419 10716 infeasible   34      22871.1971 19339.0480  15.4%   5.4  185s
 260571 10402     cutoff   26      22871.1971 19446.9218  15.0%   5.3  190s
 265421 10106 19551.4153   29   10 22871.1971 19551.4153  14.5%   5.3  195s
 269835  9767 19671.9962   29   13 22871.1971 19671.9962  14.0%   5.3  200s
 274187  9375 19845.8157   29   12 22871.1971 19781.3743  13.5%   5.3  205s
 278535  9013 20194.8078   19   13 22871.1971 19885.3520  13.1%   5.3  210s
 283848  8577     cutoff   32      22871.1971 19997.5115  12.6%   5.3  215s
 288397  7997 21257.5445   34   12 22871.1971 20173.5093  11.8%   5.3  220s
 291948  7336 infeasible   24      22871.1971 20342.2819  11.1%   5.3  225s
 295624  6691 infeasible   34      22871.1971 20541.0609  10.2%   5.3  230s
*296408  6527              69    22856.454879 20575.6517  10.0%   5.3  231s
*296410  6527              70    22856.454853 20575.6517  10.0%   5.3  231s
 298664  6030 21162.3697   30   10 22856.4549 20694.0302  9.46%   5.3  235s
 301722  5285 infeasible   27      22856.4549 20877.5152  8.66%   5.3  240s
 305531  4375 infeasible   31      22856.4549 21139.2608  7.51%   5.3  245s
 308661  3681 infeasible   36      22856.4549 21380.9499  6.46%   5.3  250s
 311837  2865     cutoff   30      22856.4549 21652.3544  5.27%   5.3  255s
 315652  1985 22497.4404   44   12 22856.4549 22017.4032  3.67%   5.3  261s
 318672  1400 22530.0737   42   13 22856.4549 22294.9389  2.46%   5.3  265s
*321943   972              66    22856.369995 22549.5557  1.34%   5.3  268s
*322528   943              72    22855.884193 22591.0019  1.16%   5.3  269s
*322529   943              72    22855.864959 22591.0019  1.16%   5.3  269s
 323250   876 22633.6560   44   16 22855.8650 22632.5928  0.98%   5.3  270s
*327034   436              75    22855.168540 22790.6060  0.28%   5.2  274s
*327044   432              79    22855.050942 22790.6060  0.28%   5.2  274s
*327045   432              79    22855.044936 22790.6060  0.28%   5.2  274s
*327046   430              78    22855.038619 22790.6060  0.28%   5.2  274s
 328824   230     cutoff   56      22855.0386 22839.8348  0.07%   5.2  275s
*328922   230              77    22855.034849 22839.8348  0.07%   5.2  275s
*328924   230              75    22855.009242 22839.8348  0.07%   5.2  275s
*330323   203              80    22854.957680 22848.6399  0.03%   5.2  276s
*330327   203              82    22854.957672 22848.6399  0.03%   5.2  276s
*330329   203              83    22854.957666 22848.6399  0.03%   5.2  276s
*330342   203              90    22854.957133 22848.6399  0.03%   5.2  276s

Cutting planes:
  Gomory: 9
  Cover: 25
  Implied bound: 99
  Projected implied bound: 2
  Clique: 7
  MIR: 14
  Flow cover: 95
  RLT: 37
  Relax-and-lift: 26
  BQP: 2

Explored 331712 nodes (1727866 simplex iterations) in 277.19 seconds
Thread count was 8 (of 8 available processors)

Solution count 10: 22855 22855 22855 ... 22855.2

Optimal solution found (tolerance 1.00e-04)
Warning: max constraint violation (2.9212e-03) exceeds tolerance
Warning: max general constraint violation (2.9212e-03) exceeds tolerance
         (model may be infeasible or unbounded - try turning presolve off)
Best objective 2.285495713262e+04, best bound 2.285462660876e+04, gap 0.0014%