OR-Tools：获取每一个最优解

如何解决OR-Tools：获取每一个最优解

我正在使用 OR-Tools 通过 SCIP 解决 MIP。 OR-Tools 为我的问题的连续变量和整数（二进制）变量返回最佳值。

然后，当我将此 MIP 的二进制变量固定为 OR-Tools（对于 MIP）返回的最优值并使用 GLOP 求解相应的 LP 时，OR-Tools 返回连续变量最优值的新值.

我的理解是初始问题没有唯一的解决方案（就变量的最佳值而言）。

所以我的问题是：我怎样才能让 OR 工具返回每一个最佳解决方案，而不仅仅是一个？

请在下面找到代码：

from ortools.linear_solver import pywraplp

#Fixed parameters
K = 4
L = 3
J = {}
J[0,0] = 3
J[0,1] = 2
J[0,2] = 1
J[1,0] = 3
J[1,1] = 1
J[1,2] = 2
J[2,0] = 2
J[2,1] = 2
J[2,2] = 2
J[3,0] = 1
J[3,1] = 1
J[3,2] = 1

S_up = {}
S_lw = {}
U = {}

S_up[0,0] = 20
S_up[0,1,0] = 40
S_up[0,2,0] = 60
S_up[0,1] = 15
S_up[0,1] = 40
S_up[0,2] = 50

S_lw[0,0] = 0
S_lw[0,0] = 21
S_lw[0,0] = 41
S_lw[0,1] = 5
S_lw[0,1] = 16
S_lw[0,2] = 10

U[0,0] = 5
U[0,0] = 7
U[0,0] = 8
U[0,1] = 2
U[0,1] = 5
U[0,2] = 6

S_up[1,0] = 25
S_up[1,0] = 35
S_up[1,0] = 50
S_up[1,1] = 30
S_up[1,2] = 30
S_up[1,2] = 30

S_lw[1,0] = 5
S_lw[1,0] = 26
S_lw[1,0] = 36
S_lw[1,1] = 10
S_lw[1,2] = 5
S_lw[1,2] = 31

U[1,0] = 6
U[1,0] = 8
U[1,0] = 9
U[1,1] = 3
U[1,2] = 5
U[1,2] = 7

S_up[2,0] = 40
S_up[2,0] = 60
S_up[2,1] = 60
S_up[2,1] = 80
S_up[2,2] = 40
S_up[2,2] = 60

S_lw[2,0] = 5
S_lw[2,0] = 41
S_lw[2,1] = 5
S_lw[2,1] = 61
S_lw[2,2] = 5
S_lw[2,2] = 41

U[2,0] = 5
U[2,0] = 6
U[2,1] = 4
U[2,1] = 5
U[2,2] = 5
U[2,2] = 6

S_up[3,0] = 100
S_up[3,1] = 90
S_up[3,2] = 90

S_lw[3,0] = 0
S_lw[3,1] = 0
S_lw[3,2] = 0

U[3,0] = 5
U[3,1] = 4
U[3,2] = 5

D = [100,100,90]
P = [50,30,20]

Q_up = [0,1]
Q_lw = [0,0.1,0]

#Declare MIP solver
solver_mip = pywraplp.solver.CreateSolver('SCIP')

#Define variables
infinity = solver_mip.infinity()
y = {}
for k in range(K):
    for l in range(L):
        for j in range(J[k,l]):
            y[k,j,l] = solver_mip.NumVar(0,infinity,'')

x = {}
for k in range(K):
    for l in range(L):
        for j in range(J[k,l]):
            x[k,l] = solver_mip.Intvar(0,'')

print('Number of variables =',solver_mip.NumVariables())

#Define constraints
for k in range(K):
    for l in range(L):
        for j in range(J[k,l]):
            solver_mip.Add(y[k,l] <= x[k,l]*S_up[k,l])
            solver_mip.Add(x[k,l]*S_lw[k,l] <= y[k,l])

for k in range(K):
    for l in range(L):
        solver_mip.Add(sum([x[k,l] for j in range(J[k,l])]) <= 1)

for l in range(L):
    solver_mip.Add(sum([sum([y[k,l])]) for k in range(K)]) == D[l]) 

for k in range(K):
    solver_mip.Add(sum([sum([y[k,l]*P[l] for j in range(J[k,l])]) for l in range(L)]) <= Q_up[k]*sum([D[l]*P[l] for l in range(L)]))
    solver_mip.Add(Q_lw[k]*sum([D[l]*P[l] for l in range(L)]) <= sum([sum([y[k,l])]) for l in range(L)]))

print('Number of constraints =',solver_mip.NumConstraints())

#Define objective
solver_mip.Minimize(sum([sum([sum([y[k,l]*U[k,l])]) for k in range(K)]) for l in range(L)]))

#Call MIP solver
status = solver_mip.solve()

#display solution
if status == pywraplp.solver.OPTIMAL:
    print('Solution of MIP:')
    print('Objective value =',solver_mip.Objective().Value())
    x_opt = {} #store optimal values of binary variable
    for k in range(K):
        for l in range(L):
            for j in range(J[k,l]):
                x_opt[k,l] = x[k,l].solution_value()
                if x[k,l].solution_value() == 1:
                    print('y[',k,',l,']=',y[k,l].solution_value())
else:
    print('The problem does not have an optimal solution.')

print('\nAdvanced usage:')
print('Problem solved in %f milliseconds' % solver_mip.wall_time())
print('Problem solved in %d iterations' % solver_mip.iterations())
print('Problem solved in %d branch-and-bound nodes' % solver_mip.nodes())

#Primal problem with fixed binary variables to optimal value becomes a LP
#Declare LP solver
solver_lp = pywraplp.solver.CreateSolver('GLOP')

##Quantity variable
y_fixed_binary = {}
for k in range(K):
    for l in range(L):
        for j in range(J[k,l]):
            y_fixed_binary[k,l] = solver_lp.NumVar(0,'')

#Define constraints
##Quantity should be in bounds defined by reinsurer
for k in range(K):
    for l in range(L):
        for j in range(J[k,l]):
            solver_lp.Add(y_fixed_binary[k,l] <= x_opt[k,l])
            solver_lp.Add(x_opt[k,l] <= y_fixed_binary[k,l])

for l in range(L):
    solver_lp.Add(sum([sum([y_fixed_binary[k,l])]) for k in range(K)]) == D[l]) 

for k in range(K):
    solver_lp.Add(sum([sum([y_fixed_binary[k,l])]) for l in range(L)]) <= Q_up[k]*sum([D[l]*P[l] for l in range(L)]))
    solver_lp.Add(Q_lw[k]*sum([D[l]*P[l] for l in range(L)]) <= sum([sum([y_fixed_binary[k,l])]) for l in range(L)]))

#Define objective
solver_lp.Minimize(sum([sum([sum([y_fixed_binary[k,l])]) for k in range(K)]) for l in range(L)]))

status = solver_lp.solve()

if status == pywraplp.solver.OPTIMAL:
    print('Solution of LP:')
    print('Objective value =',solver_mip.Objective().Value())
    for k in range(K):
        for l in range(L):
            for j in range(J[k,l]):
                if x_opt[k,l] == 1:
                    print('y[',y_fixed_binary[k,l].solution_value())
else:
    print('The LP does not have an optimal solution.')

print('Advanced usage:')
print('Problem solved in %f milliseconds' % solver_lp.wall_time())

输出是

Solution of MIP:
Objective value = 1280.0
y[ 1,1 ]= 30.0
y[ 2,0 ]= 13.999999999999998
y[ 2,1 ]= 5.0
y[ 2,2 ]= 5.0
y[ 3,0 ]= 86.0
y[ 3,1 ]= 55.0
y[ 3,2 ]= 85.0

Solution of LP:
Objective value = 1280.0
y[ 1,0 ]= 40.0
y[ 2,1 ]= 60.0
y[ 2,2 ]= 40.0
y[ 3,0 ]= 60.0
y[ 3,1 ]= 0.0
y[ 3,2 ]= 50.0

解决方法

您可以通过在第一个 NextSolution() 之后调用 Solve() 来获得所有最优解