如何使用 PuLP 的 Gurobi 求解器设置 MIP 启动（初始解决方案）？
How to set MIP start (initial solution) with Gurobi solver from PuLP?
我正在使用 Python 中的 PuLP 模块来制定混合整数程序。我正在尝试通过 PuLP 接口设置 MIP start（即程序启动的可行解决方案）。
关于如何设置 MIP start 的详细信息已给出 here
并且 PuLP 包的开发者声称您可以通过 PuLP 接口访问完整的 Gurobi 模型 here
下面粘贴了两个完整的模型。我已将它们做得尽可能小，同时防止 gurobi 求解器使用启发式算法找到最佳值。
我试图在两个模型中设置一个初始解（最优值），但在 PuLP 模型中它被忽略了，但在 gurobipy 模型中它按预期工作。
如何通过 PuLP 界面设置 Gurobi 求解的初始解？
from pulp import *
prob = LpProblem("min example",LpMinimize)
x1=LpVariable("x1",0,None,LpInteger)
x2=LpVariable("x2",0,None,LpInteger)
x3=LpVariable("x3",0,None,LpInteger)
x4=LpVariable("x4",0,None,LpInteger)
# Objective function
prob += 3*x1 + 5*x2 + 6*x3 + 9*x4
# A constraint
prob += -2*x1 + 6*x2 -3*x3 + 4*x4 >= 2, "Con1"
prob += -5*x1 + 3*x2 + x3 + 3*x4 >= -2, "Con2"
prob += 5*x1 - x2 + 4*x3 - 2*x4 >= 3, "Con3"
# Choose solver, and set it to problem, and build the Gurobi model
solver = pulp.GUROBI()
prob.setSolver(solver)
prob.solver.buildSolverModel(prob)
# Attempt to set an initial feasible solution (in this case to an optimal solution)
prob.solverModel.getVars()[0].start = 1
prob.solverModel.getVars()[1].start = 1
prob.solverModel.getVars()[2].start = 0
prob.solverModel.getVars()[3].start = 0
# Solve model
prob.solve()
# Status of the solution is printed to the screen
print "Status:", LpStatus[prob.status]
# Each of the variables is printed with it's resolved optimum value
for v in prob.variables():
print v.name, "=", v.varValue
# Optimised objective function value is printed to the screen
print "OF = ", value(prob.objective)
哪个returns:
Optimize a model with 3 rows, 4 columns and 12 nonzeros
Coefficient statistics:
Matrix range [1e+00, 6e+00]
Objective range [3e+00, 9e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e+00, 3e+00]
Found heuristic solution: objective 12
Presolve removed 0 rows and 1 columns
Presolve time: 0.00s
Presolved: 3 rows, 3 columns, 9 nonzeros
Variable types: 0 continuous, 3 integer (0 binary)
Root relaxation: objective 7.400000e+00, 1 iterations, 0.00 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 7.40000 0 1 12.00000 7.40000 38.3% - 0s
H 0 0 8.0000000 7.40000 7.50% - 0s
Explored 0 nodes (1 simplex iterations) in 0.00 seconds
Thread count was 8 (of 8 available processors)
Optimal solution found (tolerance 1.00e-04)
Best objective 8.000000000000e+00, best bound 8.000000000000e+00, gap 0.0%
('Gurobi status=', 2)
Status: Optimal
x1 = 1.0
x2 = 1.0
x3 = -0.0
x4 = -0.0
OF = 8.0
其次，我可以使用 gurobipy 模块实现相同的模型，但在这种情况下，实际使用的是 MIP 启动：
from gurobipy import *
m = Model("min example")
m.modelSense = GRB.MINIMIZE
objFcnCoeffs = [3, 5, 6, 9]
xVars = []
for i in range(4):
xVars.append(m.addVar(vtype=GRB.INTEGER, obj=objFcnCoeffs[i], name="Open%d" % i))
# Update model to integrate new variables
m.update()
# Constraints
m.addConstr(-2*xVars[0] + 6*xVars[1] -3*xVars[2] + 4*xVars[3] >= 2, "Con1")
m.addConstr(-5*xVars[0] + 3*xVars[1] + xVars[2] + 3*xVars[3] >= -2, "Con2")
m.addConstr(5*xVars[0] - xVars[1] + 4*xVars[2] - 2*xVars[3] >= 3, "Con3")
# Attempt to set an initial feasible solution (in this case to an optimal solution)
startValues = [1, 1, 0, 0]
for i in range(4):
xVars[i].start = startValues[i]
# Solve model
m.optimize()
# Print solution
print('\nTOTAL COSTS: %g' % m.objVal)
for i in range(4):
print('\n xVar[%s] = %g' % i, xVars[i])
哪个returns:
Optimize a model with 3 rows, 4 columns and 12 nonzeros
Coefficient statistics:
Matrix range [1e+00, 6e+00]
Objective range [3e+00, 9e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e+00, 3e+00]
Found heuristic solution: objective 12
Presolve removed 0 rows and 1 columns
Presolve time: 0.00s
Presolved: 3 rows, 3 columns, 9 nonzeros
Loaded MIP start with objective 8
Variable types: 0 continuous, 3 integer (0 binary)
Root relaxation: infeasible, 0 iterations, 0.00 seconds
Explored 0 nodes (0 simplex iterations) in 0.00 seconds
Thread count was 8 (of 8 available processors)
Optimal solution found (tolerance 1.00e-04)
Best objective 8.000000000000e+00, best bound 8.000000000000e+00, gap 0.0%
TOTAL COSTS: 8
xVar[0] = 1
xVar[1] = 1
xVar[2] = 0
xVar[3] = 0
您正在像这样设置起始值
prob.solverModel.getVars()[0].start = 1
然后您将通过此调用求解模型
prob.solve().
原来的prob不变，如果调用
prob.solver.callSolver(prob)
Gurobi 将使用起始向量。
这个问题来晚了，但希望这对新访客有所帮助。从 PuLP 2.3 版本开始，通用的 warmStart 接口支持 GUROBI api。按照说明进行操作 here 您应该能够热启动 gurobi 求解器，而无需修补纸浆内部结构或 gurobi 包。
我正在使用 Python 中的 PuLP 模块来制定混合整数程序。我正在尝试通过 PuLP 接口设置 MIP start（即程序启动的可行解决方案）。
关于如何设置 MIP start 的详细信息已给出 here
并且 PuLP 包的开发者声称您可以通过 PuLP 接口访问完整的 Gurobi 模型 here
下面粘贴了两个完整的模型。我已将它们做得尽可能小，同时防止 gurobi 求解器使用启发式算法找到最佳值。
我试图在两个模型中设置一个初始解（最优值），但在 PuLP 模型中它被忽略了，但在 gurobipy 模型中它按预期工作。
如何通过 PuLP 界面设置 Gurobi 求解的初始解？
from pulp import *
prob = LpProblem("min example",LpMinimize)
x1=LpVariable("x1",0,None,LpInteger)
x2=LpVariable("x2",0,None,LpInteger)
x3=LpVariable("x3",0,None,LpInteger)
x4=LpVariable("x4",0,None,LpInteger)
# Objective function
prob += 3*x1 + 5*x2 + 6*x3 + 9*x4
# A constraint
prob += -2*x1 + 6*x2 -3*x3 + 4*x4 >= 2, "Con1"
prob += -5*x1 + 3*x2 + x3 + 3*x4 >= -2, "Con2"
prob += 5*x1 - x2 + 4*x3 - 2*x4 >= 3, "Con3"
# Choose solver, and set it to problem, and build the Gurobi model
solver = pulp.GUROBI()
prob.setSolver(solver)
prob.solver.buildSolverModel(prob)
# Attempt to set an initial feasible solution (in this case to an optimal solution)
prob.solverModel.getVars()[0].start = 1
prob.solverModel.getVars()[1].start = 1
prob.solverModel.getVars()[2].start = 0
prob.solverModel.getVars()[3].start = 0
# Solve model
prob.solve()
# Status of the solution is printed to the screen
print "Status:", LpStatus[prob.status]
# Each of the variables is printed with it's resolved optimum value
for v in prob.variables():
print v.name, "=", v.varValue
# Optimised objective function value is printed to the screen
print "OF = ", value(prob.objective)
哪个returns:
Optimize a model with 3 rows, 4 columns and 12 nonzeros
Coefficient statistics:
Matrix range [1e+00, 6e+00]
Objective range [3e+00, 9e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e+00, 3e+00]
Found heuristic solution: objective 12
Presolve removed 0 rows and 1 columns
Presolve time: 0.00s
Presolved: 3 rows, 3 columns, 9 nonzeros
Variable types: 0 continuous, 3 integer (0 binary)
Root relaxation: objective 7.400000e+00, 1 iterations, 0.00 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 7.40000 0 1 12.00000 7.40000 38.3% - 0s
H 0 0 8.0000000 7.40000 7.50% - 0s
Explored 0 nodes (1 simplex iterations) in 0.00 seconds
Thread count was 8 (of 8 available processors)
Optimal solution found (tolerance 1.00e-04)
Best objective 8.000000000000e+00, best bound 8.000000000000e+00, gap 0.0%
('Gurobi status=', 2)
Status: Optimal
x1 = 1.0
x2 = 1.0
x3 = -0.0
x4 = -0.0
OF = 8.0
其次，我可以使用 gurobipy 模块实现相同的模型，但在这种情况下，实际使用的是 MIP 启动：
from gurobipy import *
m = Model("min example")
m.modelSense = GRB.MINIMIZE
objFcnCoeffs = [3, 5, 6, 9]
xVars = []
for i in range(4):
xVars.append(m.addVar(vtype=GRB.INTEGER, obj=objFcnCoeffs[i], name="Open%d" % i))
# Update model to integrate new variables
m.update()
# Constraints
m.addConstr(-2*xVars[0] + 6*xVars[1] -3*xVars[2] + 4*xVars[3] >= 2, "Con1")
m.addConstr(-5*xVars[0] + 3*xVars[1] + xVars[2] + 3*xVars[3] >= -2, "Con2")
m.addConstr(5*xVars[0] - xVars[1] + 4*xVars[2] - 2*xVars[3] >= 3, "Con3")
# Attempt to set an initial feasible solution (in this case to an optimal solution)
startValues = [1, 1, 0, 0]
for i in range(4):
xVars[i].start = startValues[i]
# Solve model
m.optimize()
# Print solution
print('\nTOTAL COSTS: %g' % m.objVal)
for i in range(4):
print('\n xVar[%s] = %g' % i, xVars[i])
哪个returns:
Optimize a model with 3 rows, 4 columns and 12 nonzeros
Coefficient statistics:
Matrix range [1e+00, 6e+00]
Objective range [3e+00, 9e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e+00, 3e+00]
Found heuristic solution: objective 12
Presolve removed 0 rows and 1 columns
Presolve time: 0.00s
Presolved: 3 rows, 3 columns, 9 nonzeros
Loaded MIP start with objective 8
Variable types: 0 continuous, 3 integer (0 binary)
Root relaxation: infeasible, 0 iterations, 0.00 seconds
Explored 0 nodes (0 simplex iterations) in 0.00 seconds
Thread count was 8 (of 8 available processors)
Optimal solution found (tolerance 1.00e-04)
Best objective 8.000000000000e+00, best bound 8.000000000000e+00, gap 0.0%
TOTAL COSTS: 8
xVar[0] = 1
xVar[1] = 1
xVar[2] = 0
xVar[3] = 0
您正在像这样设置起始值
prob.solverModel.getVars()[0].start = 1
然后您将通过此调用求解模型
prob.solve().
原来的prob不变，如果调用
prob.solver.callSolver(prob)
Gurobi 将使用起始向量。
这个问题来晚了，但希望这对新访客有所帮助。从 PuLP 2.3 版本开始，通用的 warmStart 接口支持 GUROBI api。按照说明进行操作 here 您应该能够热启动 gurobi 求解器，而无需修补纸浆内部结构或 gurobi 包。