用於着色問題[目標錯誤]的色數的精確 gurobi 求解器

Question

我試圖通過在 lp 設置中使用 gurobi 來解決着色問題。 但是，我做錯了什么，但不到底是什么。

`!pip 安裝 gurobipy'

import networkx as nx

  import gurobipy as gp
from gurobipy import *

import networkx as nx
# create test graph
n = 70
p = 0.6
G = nx.erdos_renyi_graph(n, p)

nx.draw(G, with_labels = True)


# compute chromatic number -- ILP solve
m = gp.Model('chrom_num', env =e)

# get maximum number of variables necessary
k = max(dict(nx.degree(G)).values()) + 1
TEST= range(k)


# create k binary variables, y_0 ... y_{k-1} to indicate whether color k is used
y = []
for j in range(k):
    y.append(m.addVar(vtype=gp.GRB.BINARY, name='y_%d' % j, obj=1))

# create n * k binary variables, x_{l,j} that is 1 if node l is colored with j
x = []
for l in range(n):
    x.append([])
    for j in range(k):
        x[-1].append(m.addVar(vtype=gp.GRB.BINARY, name='x_%d_%d' % (l, j), obj=0))

# objective function is minimize colors used --> sum of y_0 ... y_{k-1}
m.setObjective(gp.quicksum(y[j] for j in TEST), gp.GRB.MINIMIZE)
m.update()

# add constraint -- each node gets exactly one color (sum of colors used is 1)
for u in range(n):
    m.addConstr(gp.quicksum(x[u]) == 1, name='NC_%d')

# add constraint -- keep track of colors used (y_j is set high if any time j is used)
for l in range(n):
    for j in range(k):
        m.addConstr(x[u][j] <= y[j], name='SH_%d_%d')

# add constraint -- adjacent nodes have different colors
for u in range(n):
    for v in G[u]:
        if v > u:
            for j in range(k):
                m.addConstr(x[u][j] + x[v][j] <= 1, name='ADJ_%d_%d_COL_%d')



# update model, solve, return the chromatic number
m.update()
m.optimize()
chrom_num = m.objVal

Answer 1

通過為圖形着色問題添加額外的約束已經得到了答案。

for u in range(n):
    for v in G[u]:
        if v > u:
            for j in range(k):
                m.addConstr(x[u][j] + x[v][j] <= y[j], name='ADJ_%d_%d_COL_%d')