Model is infeasible or unbounded
Answered
親愛的 Gurobi 社區。對於一項教育任務，我製作了一個數學模型並用 python 編寫，並嘗試使用 Gurobi 作為求解器。
儘管我認為我已經正確地實現了決策變量、約束和目標函數，但 Gurobi 似乎不同意這一點，因為它指出“模型不可行或無界”。
我已經嘗試了很多東西，並試圖通過閱讀文檔來找出問題，但到目前為止沒有成功。請注意，我是初學者，請原諒我的代碼中可能存在的愚蠢錯誤。
    
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ori_center(xorii,yorii) = [[104.5, 43.0], [18.5, 15.5], [103.5, 65.0], [17.5, 100.5], [75.0, 43.0], [49.0, 43.0], [52.0, 100.5], [48.0, 15.5], [77.0, 66.5], [109.5, 100.0]]
ori_ap(ai 和 bi) = [[31, 24], [37, 31], [33, 20], [35, 39], [28, 24], [24, 24], [34, 39], [22, 31], [20, 23], [21, 31]]
sta_p(xp,yp) = [[-20, 100] , [-20, 20], [140, 100], [140, 20]]
sta_m(xm,ym) = [[20, 140], [-20, 60], [20, -20], [100 , -20], [140, 60], [100, 140]]f_w = 120
f_l(L) = 120
f_w(W) = 120
seq2(fim) = [[0, 0, 0, 0, 0, 0 ],
[1, 1, 0, 1, 0, 1],
[1, 1, 1, 1, 0, 1],
[1, 1, 0, 0, 1, 1],
[1, 1, 1 ] , 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 1, 1, 0, 1, 0],
[0, 0, 1, 0, 0, 1],
[1, 1, 1, 0, 0, 0],
[1, 0, 1, 0, 1, 0]]
seq3(fip) = [[1, 1, 1, 1],
[0, 1, 1, 0],
[1, 0, 0, 0],
[0, 1, 0, 1],
[0, 1, 1, 1],
[1, 0, 1, 1],
[1, 0, 0, 0],
[0, 1, 0, 1],
[0, 0, 1, 0],
[0, 0, 1, 0]]
m=Model("final_project")
fim = []
for i in range(len(ori_center)):
fim.append([])
for j in range(len(sta_m)):
fim[i].append(m. addVar(vtype = GRB.CONTINUOUS,name="fim_%d_%d"%(i,j)))
fip = []
for i in range(len(ori_center)):
fip.append([])
for j in範圍(len(sta_p)):
fip[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="fip_%d_%d"%(i,j)))
L = m.addVar(vtype = GRB.CONTINUOUS,name="L")
W = m.addVar(vtype = GRB.CONTINUOUS,name="W")
ai = [m.addVar(vtype = GRB.CONTINUOUS,name="ai_%d"%i ) 對於範圍內的我 (len(ori_center))]
bi = [m.addVar(vtype = GRB.CONTINUOUS,name="bi_%d"%i) 對於範圍內的我(len(ori_center))]
Vi = m.addVar(vtype = GRB.CONTINUOUS,name="Vi")
Vp = m.addVar(vtype = GRB.CONTINUOUS,name="Vp")
Ti = m.addVar(vtype = GRB.CONTINUOUS,name= "Ti")
xorii = [m.addVar(vtype = GRB.CONTINUOUS,name="yorii_%d"%i) for i in range(len(ori_center))]
yorii = [m.addVar(vtype = GRB.CONTINUOUS ,name="yorii_%d"%i) for i in range(len(ori_center))]
xm = [m.addVar(vtype = GRB.CONTINUOUS,name="xm_%d"%i) for i in range( len(sta_m))]
ym = [m.addVar(vtype = GRB.CONTINUOUS,name="ym_%d"%i) for i in range(len(sta_m))]
xp = [m.addVar(vtype = GRB .CONTINUOUS,name="xp_%d"%i) for i in range(len(sta_p))]
yp = [m.addVar(vtype = GRB.CONTINUOUS,name="yp_%d"%i) for i in 範圍（len（sta_p））]
xnewi = [m.addVar(vtype = GRB.CONTINUOUS,name="xnewi_%d"%i) for i in range(len(ori_center))]
ynewi = [m.addVar(vtype = GRB.CONTINUOUS,name="ynewi_%d"%i) for i in range(len(ori_center))]
li = [m.addVar(vtype = GRB.CONTINUOUS,name="li_%d"%i) for i in range(len(ori_center))]
wi = [m.addVar(vtype = GRB.CONTINUOUS,name="wi_%d"%i) for i in range(len(ori_center))]
DXi = [m.addVar(vtype = GRB.CONTINUOUS,name="DXi_%d"%i) for i in range(len(ori_center))]
DYi = [m.addVar(vtype = GRB.CONTINUOUS,name="DYi_%d"%i) for i in range(len(ori_center))]
DXim = []
for i in range(len(ori_center)):
DXim.append([])
for j in range(len(sta_m)):
DXim[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="DXim_%d_%d"%(i,j)))
DYim = []
for i in range(len(ori_center)):
DYim.append([])
for j in range(len(sta_m)):
DYim[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="DYim_%d_%d"%(i,j)))
DXip = []
for i in range(len(ori_center)):
DXip.append([])
for j in range(len(sta_p)):
DXip[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="DXip_%d_%d"%(i,j)))
DYip = []
for i in range(len(ori_center)):
DYip.append([])
for j in range(len(sta_p)):
DYip[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="DYip_%d_%d"%(i,j)))
DXij = []
for i in range(len(ori_center)):
DXij.append([])
for j in range(len(ori_center)):
DXij[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="DXij_%d_%d"%(i,j)))
DYij = []
for i in range(len(ori_center)):
DYij.append([])
for j in range(len(ori_center)):
DYij[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="DYij_%d_%d"%(i,j)))
oi = [m.addVar(vtype = GRB.BINARY,name="oi_%d"%i) for i in range(len(ori_center))]
leftij = []
for i in range(len(ori_center)):
leftij.append([])
for j in range(len(ori_center)):
leftij[i].append(m.addVar(vtype = GRB.BINARY,name="leftij_%d_%d"%(i,j)))
belowij = []
for i in range(len(ori_center)):
belowij.append([])
for j in range(len(ori_center)):
belowij[i].append(m.addVar(vtype = GRB.BINARY,name="belowij_%d_%d"%(i,j)))
m.addConstrs((fim[i][j] == seq2[i][j] for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
m.addConstrs((fip[i][j] == seq3[i][j] for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
m.addConstr(L == f_l, name = "")
m.addConstr(W == f_w, name = "")
m.addConstrs((ai[i] == min_(ori_ap[0],ori_ap[1]) for i in range(len(ori_center))), name = "")
m.addConstrs((bi[i] == max_(ori_ap[0],ori_ap[1]) for i in range(len(ori_center))), name = "")
m.addConstr(Vi == 1/10, name = "")
m.addConstr(Vp == 1/5, name = "")
m.addConstr(Ti == 20, name = "")
m.addConstrs((xorii[i] == ori_center[i][0] for i in range(len(ori_center))), name = "")
m.addConstrs((yorii[i] == ori_center[i][1] for i in range(len(ori_center))), name = "")
m.addConstrs((xm[i] == sta_m[i][0] for i in range(len(sta_m))), name = "")
m.addConstrs((ym[i] == sta_m[i][1] for i in range(len(sta_m))), name = "")
m.addConstrs((xp[i] == sta_p[i][0] for i in range(len(sta_p))), name = "")
m.addConstrs((yp[i] == sta_p[i][1] for i in range(len(sta_p))), name = "")
m.addConstrs((xnewi[i] >= 0.5*li[i] for i in range(len(ori_center))), name = "")
m.addConstrs((xnewi[i] <= L - 0.5*li[i] for i in range(len(ori_center))), name = "")
m.addConstrs((ynewi[i] >= 0.5*wi[i] for i in range(len(ori_center))), name = "")
m.addConstrs((ynewi[i] <= W - 0.5*wi[i] for i in range(len(ori_center))), name = "")
m.addConstrs((li[i] == ai[i]*oi[i] + bi[i]*(1 - oi[i]) for i in range(len(ori_center))), name = "")
m.addConstrs((wi[i] == bi[i]*oi[i] + ai[i]*(1 - oi[i]) for i in range(len(ori_center))), name = "")
m.addConstrs((DXi[i] >= xnewi[i] - xorii[i] for i in range(len(ori_center))), name = "")
m.addConstrs((DXi[i] >= xorii[i] - xnewi[i] for i in range(len(ori_center))), name = "")
m.addConstrs((DYi[i] >= ynewi[i] - yorii[i] for i in range(len(ori_center))), name = "")
m.addConstrs((DYi[i] >= yorii[i] - ynewi[i] for i in range(len(ori_center))), name = "")
m.addConstrs((DXim[i][j] >= xnewi[i] - xm[j] for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
m.addConstrs((DXim[i][j] >= xm[j] - xnewi[i] for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
m.addConstrs((DYim[i][j] >= ynewi[i] - ym[j] for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
m.addConstrs((DYim[i][j] >= ym[j] - ynewi[i] for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
m.addConstrs((DXip[i][j] >= xnewi[i] - xp[j] for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
m.addConstrs((DXip[i][j] >= xp[j] - xnewi[i] for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
m.addConstrs((DYip[i][j] >= ynewi[i] - yp[j] for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
m.addConstrs((DYip[i][j] >= yp[j] - ynewi[i] for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
m.addConstrs((DXij[i][j] >= xnewi[i] - xnewi[j] for i in range(len(ori_center))
for j in range(i+1,len(ori_center))), name = "")
m.addConstrs((DXij[i][j] >= xnewi[j] - xnewi[i] for i in range(len(ori_center))
for j in range(i+1,len(ori_center))), name = "")
m.addConstrs((DYij[i][j] >= ynewi[i] - ynewi[j] for i in range(len(ori_center))
for j in range(i+1,len(ori_center))), name = "")
m.addConstrs((DYij[i][j] >= ynewi[j] - ynewi[i] for i in range(len(ori_center))
for j in range(i+1,len(ori_center))), name = "")
m.addConstrs((xnewi[i] + 0.5*li[i] - (xnewi[j] - 0.5*li[j]) <= L*(1 - leftij[i][j])
for i in range(len(ori_center)) for j in range(len(ori_center)) if j != i),name = "")
m.addConstrs((ynewi[i] + 0.5*wi[i] - (ynewi[j] - 0.5*wi[j]) <= W*(1 - belowij[i][j])
for i in range(len(ori_center)) for j in range(len(ori_center)) if j != i),name = "")
m.addConstrs((leftij[i][j] + leftij[j][i] + belowij[i][j] + belowij[j][i] == 1
for i in range(len(ori_center)) for j in range(len(ori_center)) if j != i),name = "")
m.addConstrs((xnewi[i] >=0 for i in range(len(ori_center))), name = "")
m.addConstrs((ynewi[i] >=0 for i in range(len(ori_center))), name = "")
m.addConstrs((li[i] >=0 for i in range(len(ori_center))), name = "")
m.addConstrs((wi[i] >=0 for i in range(len(ori_center))), name = "")
m.addConstrs((DXim[i][j] >=0 for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
m.addConstrs((DYim[i][j] >=0 for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
m.addConstrs((DXip[i][j] >=0 for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
m.addConstrs((DYip[i][j] >=0 for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
m.addConstrs((DXij[i][j] >= 0 for i in range(len(ori_center)) for j in range(len(ori_center)) if j != i),name = "")
m.addConstrs((DYij[i][j] >= 0 for i in range(len(ori_center)) for j in range(len(ori_center)) if j != i),name = "")
dis_xy_p = []
for i in range(len(ori_center)):
dis_xy_p.append([])
for j in range(len(sta_p)):
dis_xy_p[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="dis_xy_p_%d_%d"%(i,j)))
m.addConstrs((dis_xy_p[i][j] == 2*(DXip[i][j] + DYip[i][j])
for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
flow_dis_xy_p = []
for i in range(len(ori_center)):
flow_dis_xy_p.append([])
for j in range(len(sta_p)):
flow_dis_xy_p[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="flow_dis_xy_p_%d_%d"%(i,j)))
m.addConstrs((flow_dis_xy_p[i][j] == fip[i][j]*dis_xy_p[i][j]
for i in range(len(ori_center)) for j in range(len(sta_p))), name = "")
dis_xy_m = []
for i in range(len(ori_center)):
dis_xy_m.append([])
for j in range(len(sta_m)):
dis_xy_m[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="dis_xy_m_%d_%d"%(i,j)))
m.addConstrs((dis_xy_m[i][j] == 2*(DXim[i][j] + DYim[i][j])
for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
flow_dis_xy_m = []
for i in range(len(ori_center)):
flow_dis_xy_m.append([])
for j in range(len(sta_m)):
flow_dis_xy_m[i].append(m.addVar(vtype = GRB.CONTINUOUS,name="flow_dis_xy_m_%d_%d"%(i,j)))
m.addConstrs((flow_dis_xy_m[i][j] == fim[i][j]*dis_xy_m[i][j]
for i in range(len(ori_center)) for j in range(len(sta_m))), name = "")
m.update()
obj_p = quicksum((flow_dis_xy_p[i][j]*Vp) for i in range(len(ori_center)) for j in range(len(sta_p)))
obj_m = quicksum((flow_dis_xy_m[i][j]*Vi + fim[i][j]*2*Ti) for i in range(len(ori_center)) for j in range(len(sta_m)))
obj_new = quicksum((DXi[i] + DYi[i])*Vi for i in range(len(ori_center)))
objective = obj_p + obj_m + obj_new
m.setObjective(objective,GRB.MINIMIZE)
m.update()
m.optimize()
-------------------
Gurobi creates the following output:
Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (mac64[x86])
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 1730 rows, 1035 columns and 3500 nonzeros
Model fingerprint: 0x9287f22a
Model has 180 quadratic objective terms
Model has 300 quadratic constraints
Model has 20 general constraints
Variable types: 825 continuous, 210 integer (210 binary)
Coefficient statistics:
Matrix range [5e-01, 2e+00]
QMatrix range [1e+00, 1e+00]
QLMatrix range [5e-01, 1e+00]
Objective range [0e+00, 0e+00]
QObjective range [2e+00, 4e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e-01, 1e+02]
GenCon const rng [2e+01, 4e+01]
Presolve removed 915 rows and 220 columns
Presolve time: 0.00s
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 0
Model is infeasible or unbounded
Best objective -, best bound -, gap -
-
Please refer to the Knowledge Base articles How do I resolve the error "Model is infeasible or unbounded"? and How do I determine why my model is infeasible?
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