Python数学建模系列（二）：规划问题之整数规划

# 运行环境：Vs Code
import math
from scipy.optimize import linprog
import sys

def integerPro(c, A, b, Aeq, beq,t=1.0E-8):
    res = linprog(c, A_ub=A, b_ub=b, A_eq=Aeq, b_eq=beq)
    bestVal = sys.maxsize
    bestX = res.x
    if not(type(res.x) is float or res.status != 0): 
        bestVal = sum([x*y for x,y in zip(c, bestX)])
    if all(((x-math.floor(x))<=t or (math.ceil(x)-x)<=t) for x in bestX):
        return (bestVal,bestX)
    else:
        ind = [i for i, x in enumerate(bestX) if (x-math.floor(x))>t and (math.ceil(x)-x)>t][0]
        newCon1 = [0]*len(A[0])
        newCon2 = [0]*len(A[0])
        newCon1[ind] = -1
        newCon2[ind] = 1
        newA1 = A.copy()
        newA2 = A.copy()
        newA1.append(newCon1)
        newA2.append(newCon2)
        newB1 = b.copy()
        newB2 = b.copy()
        newB1.append(-math.ceil(bestX[ind]))
        newB2.append(math.floor(bestX[ind]))
        r1 = integerPro(c, newA1, newB1, Aeq, beq)
        r2 = integerPro(c, newA2, newB2, Aeq, beq)
        if r1[0] < r2[0]:
            return r1
        else:
            return r2
c = [3,4,1]
A = [[-1,-6,-2],[-2,0,0]]
b = [-5,-3]
Aeq = [[0,0,0]]
beq = [0]
print(integerPro(c, A, b, Aeq, beq))

(8.000000000001586, array([2., 0., 2.]))
# 或者
(8.000000000001586, array([2.00000000e+00, 1.83247535e-13, 2.00000000e+00]))

import pulp as pp

# 参数设置
c = [3,4,1]        #目标函数未知数前的系数

A_gq = [[1,6,2],[2,0,0]]   # 大于等于式子 未知数前的系数集合 二维数组 
b_gq = [5,3]         # 大于等于式子右边的数值 一维数组


# 确定最大最小化问题，当前确定的是最小化问题
m = pp.LpProblem(sense=pp.LpMinimize)

# 定义三个变量放到列表中 生成x1 x2 x3
x = [pp.LpVariable(f'x{i}',lowBound=0,cat='Integer') for i in [1,2,3]]

# 定义目标函数，并将目标函数加入求解的问题中 
m += pp.lpDot(c,x) # lpDot 用于计算点积 

# 设置比较条件
for i in range(len(A_gq)):# 大于等于
    m += (pp.lpDot(A_gq[i],x) >= b_gq[i])

# 求解
m.solve()

# 输出结果
print(f'优化结果：{pp.value(m.objective)}')
print(f'参数取值：{[pp.value(var) for var in x]}')

优化结果：8.0
参数取值：[2.0, 0.0, 2.0]