Pulp之二：Pulp中幾個重要的概念

1. LpProblem類
   LpProblem(name='NoName', sense=LpMinimize)
   構造函數，用來構造一個LP問題實例，其中name指定問題名（輸出信息用)，
   sense值是LpMinimize或LpMaximize中的一個，用來指定目標函數是求極大值還是極小值。

solve(solver=None, **kwargs)
在對LpProblem添加完約束條件后，調用該函數進行求解，如果不是求解特定的整數規划問題，solver一般使用默認即可。

2. LpVariable類
   LpVariable(name, lowBound=None, upBound=None, cat='Continuous', e=None)
   構造函數，用來構造LP問題中的變量，name指定變量名，lowBound和upBound是下界和上界，
   默認分別是負無窮到正無窮,cat用來指定變量是離散(Integer,Binary)還是連續(Continuous)。

dicts(name, indexs, lowBound=None, upBound=None, cat='Continuous', indexStart=[])
用來構造變量字典，可以讓我們不用一個個地創建Lp變量實例。name指定所有變量的前綴,
index是列表，其中的元素會被用來構成變量名，后面三個參數和LbVariable中的一樣。

3. lpSum(vector)
   計算一個序列的值，使用lpSum求解比普通的sum函數要快得多。

4. pulp.allcombinations()方法
   allcombinations（list, k）: 返回list的所有元素組合，元素個數不超過k
   

Examples
See the examples directory for examples. PuLP requires Python 2.7 or Python >= 3.4.

The examples use the default solver (CBC). To use other solvers they must be available (installed and accessible). For more information on how to do that, see the guide on configuring solvers.

Documentation is found on https://coin-or.github.io/pulp/.

Use LpVariable() to create new variables. To create a variable 0 <= x <= 3:
x = LpVariable("x", 0, 3)

To create a variable 0 <= y <= 1:
y = LpVariable("y", 0, 1)

Use LpProblem() to create new problems. Create "myProblem":
prob = LpProblem("myProblem", LpMinimize)

Combine variables to create expressions and constraints, then add them to the problem:
prob += x + y <= 2

If you add an expression (not a constraint), it will become the objective:
prob += -4*x + y

To solve with the default included solver:
status = prob.solve()

To use another sovler to solve the problem:
status = prob.solve(GLPK(msg = 0))

Display the status of the solution:
LpStatus[status]

'Optimal'
You can get the value of the variables using value(). ex:
value(x)
2.0
Exported Classes:
LpProblem -- Container class for a Linear programming problem
LpVariable -- Variables that are added to constraints in the LP
LpConstraint -- A constraint of the general form

a1x1+a2x2 ...anxn (<=, =, >=) b
LpConstraintVar -- Used to construct a column of the model in column-wise modelling

Exported Functions:
value() -- Finds the value of a variable or expression
lpSum() -- given a list of the form [a1*x1, a2x2, ..., anxn] will construct a linear expression to be used as a constraint or variable
lpDot() --given two lists of the form [a1, a2, ..., an] and [ x1, x2, ..., xn] will construct a linear epression to be used as a constraint or variable
Comments, bug reports, patches and suggestions are welcome.
Comments and suggestions: https://github.com/coin-or/pulp/discussions

Bug reports: https://github.com/coin-or/pulp/issues
Patches: https://github.com/coin-or/pulp/pulls
Copyright J.S. Roy ([e-mail]), 2003-2005 Copyright Stuart A. Mitchell ([e-mail]) See the LICENSE file for copyright information.