PULP：用Python替代AMPL建模语言
数学建模简单的说就是求最大化最小化问题，现在大学都有数学建模比赛，另外做科研的时候其实也经常用到。一般要么是用Lingo，要么是用matlab，其实AMPL是比较通用的描述及数学建模的语言，不过比较贵，记得我以前发神经买过一年的license花了我快2000块钱。
现在cplex或者ampl都有破解版的可以下到，不过毕竟不知道什么时候就不能用了，其实也有免费的软件可以用，glpk就可以解LP或者MIP的问题，而且还自带一个简单的模型描述语言，不过有时候要描述复杂一点的场景就有点不行了。
PULP是用python写的建模描述语言，自带的例子里面就带有column generation的例子，显然是比glpk自带的那个强不少，下面就用一个例子来说明一个简单建模的流程吧。
# Import PuLP modeler functions
from pulp import *
# A new LP problem
prob = LpProblem("test1", LpMinimize)
# Variables
# 0 <= x <= 4
x = LpVariable("x", 0, 4)
# -1 <= y <= 1
y = LpVariable("y", -1, 1)
# 0 <= z
z = LpVariable("z", 0)
# Use None for +/- Infinity, i.e. z <= 0 -> LpVariable("z", None, 0)
# Objective
prob += x + 4*y + 9*z, "obj"
# (the name at the end is facultative)
# Constraints
prob += x+y <= 5, "c1"
prob += x+z >= 10, "c2"
prob += -y+z == 7, "c3"
# (the names at the end are facultative)
# Write the problem as an LP file
prob.writeLP("test1.lp")
# Solve the problem using the default solver
prob.solve()
# Use prob.solve(GLPK()) instead to choose GLPK as the solver
# Use GLPK(msg = 0) to suppress GLPK messages
# If GLPK is not in your path and you lack the pulpGLPK module,
# replace GLPK() with GLPK("/path/")
# Where /path/ is the path to glpsol (excluding glpsol itself).
# If you want to use CPLEX, use CPLEX() instead of GLPK().
# If you want to use XPRESS, use XPRESS() instead of GLPK().
# If you want to use COIN, use COIN() instead of GLPK(). In this last case,
# two paths may be provided (one to clp, one to cbc).
# Print the status of the solved LP
print "Status:", LpStatus[prob.status]
# Print the value of the variables at the optimum
for v in prob.variables():
print v.name, "=", v.varValue
# Print the value of the objective
print "objective=", value(prob.objective)