/
Python_Pulp_GRACAR.txt
170 lines (163 loc) · 5.53 KB
/
Python_Pulp_GRACAR.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
"""
This is a Python Implementation for GRACAR (Group Role Assignment with Conflicting Agents on Roles) using Pulp, i.e., Problem 4 in [1].
Please cite:
[1] H. Zhu, "Group Role Assignment with Constraints (GRA+): A New Category of Assignment Problems," IEEE Trans. on Systems, Man, and Cybernetics: Systems (In Press), 2022, DOI: 10.1109/TSMC.2022.3199096.
[2] H. Zhu, E-CARGO and Role-Based Collaboration: Modeling and Solving Problems in the Complex World, Wiley-IEEE Press, NJ, USA, Dec. 2021.
[3] H. Zhu, M.C. Zhou, and R. Alkins, “Group Role Assignment via a Kuhn-Munkres Algorithm-based Solution”, IEEE Trans. on Systems, Man, and Cybernetics, Part A: Systems and Humans, vol. 42, no. 3, May 2012, pp. 739-750.
[4] H. Zhu, “Avoiding Conflicts by Group Role Assignment”, IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 46, no. 4, April 2016, pp. 535-547.
Authors: Haibin Zhu, Aug. 19, 2022
"""
import pulp
import time
class GRACAR:
def __init__(self, nagent, nrole, QM, RA, CA):
self.m = nagent
self.n = nrole
self.L = RA
self.Q = QM
self.AC = CA
@property
def resolve(self):
Agents = range(self.m)
Roles = range(self.n)
gra = pulp.LpProblem("GRA Model", pulp.LpMaximize)
Assignments = [i*n+j for i in Agents for j in Roles]
mn=self.m*self.n
vars = pulp.LpVariable.dicts("Assignment", range (mn), 0, 1, pulp.LpInteger)
# The objective function is added to 'prob' first
gra += (
pulp.lpSum([vars[index] * self.Q[int(index / n)][index % n] for index in Assignments]),
"Sum_of_Assignments",
)
for j in Roles:
gra += (
pulp.lpSum([vars[i*n+j] for i in Agents]) == self.L[j],
"each_role%s" % j,
)
for i in Agents:
gra += (
pulp.lpSum([vars[i*n+j] for j in Roles]) <= 1,
"each_agent%s" % i,
)
for i1 in Agents:
for i2 in Agents:
if 1 == self.AC[i1][i2]:
for j in Roles:
gra += (
pulp.lpSum([vars[i1*n+j] + vars[i2*n+j]]) <= 1,
"agent conflict_{}_{}_{}".format(i1, i2, j),
)
gra.solve()
T = [None]*mn
for v in gra.variables():
print(v.name, " ", v.varValue)
ind = int(v.name[11:len(v.name)])
if abs(1 - v.varValue) < 0.0001:
T[ind]=1
else:
T[ind]=0
return T
def printDMatrix(x, m, n):
txt = "{:.2f}"
for i in range(m):
for j in range(n):
print(txt.format(x[i][j]), " ", end='')
print()
def printIMatrix(x, m, n):
txt = "{:2}"
for i in range(m):
for j in range(n):
print(txt.format(x[i][j]), " ", end='')
print()
def sigmaL(L):
total = 0
for j in range(len(L)):
total += L[j]
return total
import copy
def getWQ(m, n, Q, W):
maxQ = 1
WQ = copy.deepcopy(Q)
for i in range(m):
for j in range(n):
WQ[i][j] = Q[i][j] * W[j]
if WQ[i][j] > maxQ:
maxQ = WQ[i][j]
for i in range(m):
for j in range(n):
WQ[i][j] = WQ[i][j] / maxQ
return WQ
m = 16
n = 4
L = [2, 3, 5, 2]
W = [4, 3, 2, 1]
Q = [
[0.35, 0.82, 0.58, 0.45],
[0.84, 0.88, 0.86, 0.36],
[0.96, 0.51, 0.45, 0.64],
[0.22, 0.33, 0.68, 0.33],
[0.35, 0.80, 0.58, 0.35],
[0.84, 0.85, 0.86, 0.36],
[0.96, 0.90, 0.88, 0.87],
[0.55, 0.23, 0.45, 0.58],
[0.65, 0.34, 0.78, 0.18],
[0.62, 0.78, 0.68, 0.31],
[0.96, 0.50, 0.10, 0.73],
[0.20, 0.50, 0.80, 0.96],
[0.38, 0.54, 0.72, 0.20],
[0.91, 0.31, 0.34, 0.15],
[0.45, 0.68, 0.53, 0.49],
[0.78, 0.67, 0.80, 0.62]]
C = [
[0,0,0,0,1, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 1,0,0,0,0, 0],
[0,0,0,0,0, 0,1,0,0,0, 0,0,0,0,0, 0],
[1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 0,0,0,1,0, 0],
[0,0,0,1,0, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 0,0,1,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,1,0,0, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,1,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 1,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0],
[0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0]]
"""
m = 9
n = 4
L = [2, 3, 2, 2]
Q = [
[0.35, 0.82, 0.58, 0.45],
[0.84, 0.88, 0.86, 0.36],
[0.96, 0.51, 0.45, 0.64],
[0.22, 0.33, 0.68, 0.33],
[0.35, 0.80, 0.58, 0.35],
[0.84, 0.85, 0.86, 0.36],
[0.96, 0.90, 0.88, 0.87],
[0.55, 0.23, 0.45, 0.58],
[0.78, 0.67, 0.80, 0.62]]
"""
t1 = int(round(time.time() * 1000))
PulpGRACAR = GRACAR(m, n, Q, L, C)
T = PulpGRACAR.resolve
t2 = int(round(time.time() * 1000))
diff1 = t2 - t1
print("Q=")
printDMatrix(Q, m, n);
print("C=")
printIMatrix(C, m, m);
mat = []
while T != []:
mat.append(T[:n])
T = T[n:]
printIMatrix(mat, m,n)
print("L=", L)
v1 = 0
for i in range(m):
for j in range(n):
v1+= Q[i][j] * mat[i][j]
print("Total GRACAR =", "{:.2f}".format(v1), " ", "Time = ", diff1, "ms")
del GRACAR