python - 如何使用 PuLP 的 Gurobi 求解器设置 MIP 启动(初始解决方案)？

我在 Python 中使用 PuLP 模块来制定混合整数程序。我正在尝试解决如何通过 MIP start 接口(interface)设置 PuLP(即程序启动的可行解决方案)。

here 中给出了如何设置 MIP start 的详细信息
PuLP 包的开发者声称可以通过 PuLP 接口(interface) here 访问完整的 Gurobi 模型

下面粘贴的是两个完整的模型。我已经使这些尽可能小，同时防止 gurobi 求解器使用启发式方法找到最佳值。

我试图在两个模型中设置初始解决方案(为最佳值)，但在 PuLP 模型中它被忽略，但在 gurobipy 模型中它按预期工作。

您如何通过 PuLP 接口(interface)为 Gurobi 求解设置初始解？

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)

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])

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

最佳答案

您正在设置这样的起始值

prob.solverModel.getVars()[0].start = 1

然后你用这个调用解决模型

prob.solve().

最初的 prob 不会改变，如果你打电话

prob.solver.callSolver(prob)

Gurobi 将使用起始向量。

关于python - 如何使用 PuLP 的 Gurobi 求解器设置 MIP 启动(初始解决方案)？，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/40144122/