使用scipy.optimize.minimize编写目标函数的排障问题

问题背景 #

目标是将预制护栏拆分为最少数量的独特类型，分为普通护栏与带灯杆护栏两类（附三跨桥梁示意图）。

参数定义 #

• 带灯杆护栏宽度为w
• 带灯杆护栏的均匀间距为s
• 灯杆起始点由变量a定义
• 桥梁跨径为数组spans
• x为所有距离需满足整除的基准宽度

核心思路 #

尽可能多使用宽度为x的护栏，最小化跨径内的剩余填充长度。需确保数组m中的所有距离（含灯杆间间距s-w）均能被x整除，引入arr数组元素补偿非整除的剩余长度。

实现代码 #

from scipy.optimize import minimize
import numpy as np

s = 12500  
spans = np.array([25450, 25100, 25450])
ejs = np.zeros(len(spans)-1)  # expansion or separation joints . ignore for now

min_bw, max_bw  = 0, 1200  #light pole barrier width

consts = abs((len(spans) * 2 - 1))  # Number of distance elements [b,c,d...]
init = np.array([1500, 1500, 6250]) #x, w, a + w/2

n = (spans - s / 2) // s  # consecutive spacings of barriers for a given span. At times we have more 
m = np.ones(len(spans) * 2)  # the length of the equation array that has to be divisible

def objective(arr, n, s, spans, ejs):

    x = arr[0]
    w = arr[1]
    a =  arr[2] # (the offset is until the mid axis of the light pole)
    m = np.ones(len(spans) * 2 + 1) # We make room for the last constraint h=(s-w)
    m[0] = a - w / 2 

    for i in range(1, len(spans) * 2):
        j = (i - 1) // 2
        if i % 2 == 0:
            m[i] = (s - w) - (m[i - 1] + ejs[j] + arr[2 + i])
        else:
            m[i] = spans[j] - (m[i - 1] + n[j] * s + w + arr[2 + i])
    m[-1] = s - w  # We also need the light distance between two poles to be divisible by x
    #print(m)
    return np.sum(m%x)

#Bounds
bounds = np.array([(1500, 2100), (1500, 2600), (3000, s)])
extras = np.repeat([(min_bw, max_bw)], consts, axis=0) # Add the bounds for each additional element
all_bounds = np.concatenate((bounds, extras), axis=0)


initial = np.pad(init, (0, consts), 'constant', constant_values=min_bw)

sol = minimize(fun=objective, x0=initial, bounds=all_bounds, method='Nelder-Mead', args=(n, s, spans, ejs))
print(np.round(sol.x))

#m = [ 5500. , 5950.,  5050.  ,6050.  ,4950. , 6500. ,11000.] #the print m statment

当前问题 #

np.sum(m%x)无法返回0，整除约束未满足，但优化函数显示成功终止，希望得到解决思路。

内容的提问来源于stack exchange，提问作者Dragos Seculin