简介
建模是一种解决复杂问题的强大方法。依据图书Modeling Languages in Mathematical Optimization(参阅参考资料)的叙述，模型用于：
解释现象
进行预测
评估关键因素
识别极限
分析折衷方法
入门
首先要安装 Pyomo。Pyomo 是 Coopr 的一个中心组件，而 Coopr 是 Python 软件包的集合。您可以下载 coopr_install 脚本，在使用 Python 解释器运行它时，它会创建一个 Python 虚拟环境。
创建一个名为 “coopr” 的相对目录：
noahs-MacBook-Air% python coopr_installShow moreShow more icon
使用下面的命令启动 Pyomo，这会将该相对目录和它的可执行文件放在您的路径中：
noahs-MacBook-Air% source coopr/bin/activateShow moreShow more icon
使用 Pyomo “–help” 命令获取使用 pyomo 的帮助：
(coopr)noahs-MacBook-Air% pyomo –helpShow moreShow more icon
您需要一个编译器来使用虚拟 Python 环境构建器 (virtualenv) 和 Pyomo。在 OS X 上，使用 XCode Developer Tools 命令行工具。在 Linux 上，使用 GNU Compiler Collection (GCC)。初始化这个虚拟环境后，可通过以下两种方式之一使用 Pyomo 解决问题：
使用 Pyomo 命令行工具：
(coopr)noahs-MacBook-Air% pyomo my_problem.py –solver=glpkShow moreShow more icon
或者，将初始化代码嵌入您的脚本中，通过 Python 解释器运行它：
在一个脚本中调用 Pyomo
#This is an optional code path that allows the script to be run outside of
#pyomo command-line. For example: python wyndor.py
if __name__ == ‘__main__’:
#This replicates what the pyomo command-line tools does
from coopr.opt import SolverFactory
opt = SolverFactory(“glpk”)
instance = model.create()
results = opt.solve(instance)
#sends results to stdout
results.write()Show moreShow more icon
Pyomo 假设您至少安装了一个解算器 (solver)。GNU Linear Programming Kit (glpk) 是默认的解算器。请参阅您希望使用的解算器的安装说明。然后确保 Pyomo 能够在它的路径上找到此解算器。
建模策略
可通过两种方式使用 Pyomo 创建数据模型：抽象方式和具体方式。二者的关键区别在于是否将模型与数据分开。
在抽象模型中，模型与数据是分开的。
从总体上讲，Pyomo 模型由变量(variables)、目标(objectives)和约束(constraints)组成。
变量是在优化期间计算的值。
目标是获取数据和变量的 Python 函数，它要么是最大值，要么是最小值。
约束是定义表达式来限制变量可使用的值的一种方式。
在创建 Pyomo 模型时，需要了解表示代数表达式的 Python 方法。下面的摘要简单对比了电子表格、代数和 Python 中的表达式：
图 1. 符 对比表
您需要另一种方法来查找良好的结果。通常，通过运行模拟，然后获取这些模拟的最佳结果，可以实现良好但不一定最佳的解决方案。此方法的一个示例如下面的 Python 代码所示。随机选择一个开始城市，然后贪婪地选择下一个具有最短距离的城市。这种模拟然后可运行多次，然后将得到这些模拟中的最短路径。
贪婪最短距离选择
noahs-MacBook-Air% python tsp_greedy_random_start.py 20
Running simulation 20 times
Shortest Distance: 128
Optimal Route: [
(‘PCG’, ‘GPS’, 1),
(‘GPS’, ‘URS’, 1),
(‘URS’, ‘WFC’, 0),
(‘WFC’, ‘MCK’, 2),
(‘MCK’, ‘SFO’, 16),
(‘SFO’, ‘ORCL’, 20),
(‘ORCL’, ‘HPQ’, 12),
(‘HPQ’, ‘GOOG’, 6),
(‘GOOG’, ‘AAPL’, 11),
(‘AAPL’, ‘INTC’, 8),
(‘INTC’, ‘CSCO’, 6),
(‘CSCO’, ‘EBAY’, 0),
(‘EBAY’, ‘SWY’, 32),
(‘SWY’, ‘CVX’, 13)
]Show moreShow more icon
TSP 贪婪随机起点
#!/usr/bin/env python
“””
Traveling salesman solution with random start and greedy path selection
You can select how many iterations to run by doing the following:
python tsp_greedy_random_start.py 20 #runs 20 times
“””
import sys
from random import choice
import numpy as np
from routes import values
dt = np.dtype([(‘city_start’, ‘S10’), (‘city_end’, ‘S10’), (‘distance’, int)])
data_set = np.array(values,dtype=dt)
def all_cities(mdarray):
“””Takes a multi-dimensional array in this format and finds unique cities
array([[“A”, “A”],
[“A”, “B”]])
“””
cities = {}
city_set = set(data_set[‘city_end’])
for city in city_set:
cities[city] = “”
return cities
def randomize_city_start(all_cities):
“””Returns a randomized city to start trip”””
return choice(all_cities)
def get_shortest_route(routes):
“””Sort the list by distance and return shortest distance route”””
route = sorted(routes, key=lambda dist: dist[2]).pop(0)
return route
def greedy_path():
“””Select the next path to travel based on the shortest, nearest path”””
itinerary = []
cities = all_cities(data_set)
starting_city = randomize_city_start(cities.keys())
#print “starting_city: %s” % starting_city
cities_visited = {}
#we want to iterate through all cities once
count = 1
while True:
possible_routes = []
distance = []
#print “starting city: %s” % starting_city
for path in data_set:
if starting_city in path[‘city_start’]:
#we can’t go to cities we have already visited
if path[‘city_end’] in cities_visited:
continue
else:
#print “path: “, path
possible_routes.append(path)
if not possible_routes:
break
#append this to itinerary
route = get_shortest_route(possible_routes)
#print “Route(%s): %s ” % (count, route)
count += 1
itinerary.append(route)
#add this city to the visited city list
cities_visited[route[0]] = count
#print “cities_visited: %s ” % cities_visited
#reset the starting_city to the next city
starting_city = route[1]
#print “itinerary: %s” % itinerary
return itinerary
def get_total_distance(complete_itinerary):
distance = sum(z for x,y,z in complete_itinerary)
return distance
def lowest_simulation(num):
routes = {}
for i in range(num):
itinerary = greedy_path()
distance = get_total_distance(itinerary)
routes[distance] = itinerary
shortest_distance = min(routes.keys())
route = routes[shortest_distance]
return shortest_distance, route
def main():
“””runs everything”””
if len(sys.argv) == 2:
iterations = int(sys.argv[1])
print “Running simulation %s times” % iterations
distance, route = lowest_simulation(iterations)
print “Shortest Distance: %s” % distance
print “Optimal Route: %s” % route
else:
#print “All Routes: %s” % data_set
itinerary = greedy_path()
print “itinerary: %s” % itinerary
print “Distance: %s” % get_total_distance(itinerary)
if __name__ == ‘__main__’:
main()Show moreShow more icon
包含城市间路线的 NumPy 多维数组
values = [
(“AAPL”, “CSCO”, 14),
(“AAPL”, “CVX”, 44),
(“AAPL”, “EBAY”, 14),
(“AAPL”, “GOOG”, 14),
(“AAPL”, “GPS”, 59),
(“AAPL”, “HPQ”, 14),
(“AAPL”, “INTC”, 8),
(“AAPL”, “MCK”, 60),
(“AAPL”, “ORCL”, 26),
(“AAPL”, “PCG”, 59),
(“AAPL”, “SFO”, 46),
(“AAPL”, “SWY”, 37),
(“AAPL”, “URS”, 60),
(“AAPL”, “WFC”, 60),
(“CSCO”,”AAPL” ,14),
(“CSCO”, “CVX”, 43),
(“CSCO”, “EBAY”,0),
(“CSCO”, “GOOG”,21),
(“CSCO”, “GPS”,67),
(“CSCO”, “HPQ”,26),
(“CSCO”, “INTC”,6),
(“CSCO”, “MCK”,68),
(“CSCO”, “ORCL”,37),
(“CSCO”, “PCG”,68),
(“CSCO”, “SFO”,57),
(“CSCO”, “SWY”,32),
(“CSCO”, “URS”,68),
(“CSCO”, “WFC”,68),
(“CVX”,”AAPL” ,44),
(“CVX”, “CSCO”,43),
(“CVX”, “EBAY”,43),
(“CVX”, “GOOG”,36),
(“CVX”, “GPS”,43),
(“CVX”, “HPQ”,40),
(“CVX”, “INTC”,41),
(“CVX”, “MCK”,46),
(“CVX”, “ORCL”,39),
(“CVX”, “PCG”,44),
(“CVX”, “SFO”,45),
(“CVX”, “SWY”,13),
(“CVX”, “URS”,44),
(“CVX”, “WFC”,44),
(“EBAY”,”AAPL” ,14),
(“EBAY”, “CSCO”,0),
(“EBAY”, “CVX”,43),
(“EBAY”, “GOOG”,21),
(“EBAY”, “GPS”,67),
(“EBAY”, “HPQ”,26),
(“EBAY”, “INTC”,6),
(“EBAY”, “MCK”,68),
(“EBAY”, “ORCL”,37),
(“EBAY”, “PCG”,68),
(“EBAY”, “SFO”,57),
(“EBAY”, “SWY”,32),
(“EBAY”, “URS”,68),
(“EBAY”, “WFC”,68),
(“GOOG”,”AAPL”,11),
(“GOOG”, “CSCO”,21),
(“GOOG”, “CVX”,36),
(“GOOG”, “EBAY”,21),
(“GOOG”, “GPS”,48),
(“GOOG”, “HPQ”,6),
(“GOOG”, “INTC”,15),
(“GOOG”, “MCK”,49),
(“GOOG”, “ORCL”,16),
(“GOOG”, “PCG”,48),
(“GOOG”, “SFO”,36),
(“GOOG”, “SWY”,32),
(“GOOG”, “URS”,49),
(“GOOG”, “WFC”,49),
(“GPS”,”AAPL” ,59),
(“GPS”, “CSCO”,67),
(“GPS”, “CVX”,43),
(“GPS”, “EBAY”,67),
(“GPS”, “GOOG”,48),
(“GPS”, “HPQ”,45),
(“GPS”, “INTC”,62),
(“GPS”, “MCK”,03),
(“GPS”, “ORCL”,34),
(“GPS”, “PCG”,01),
(“GPS”, “SFO”,18),
(“GPS”, “SWY”,53),
(“GPS”, “URS”,01),
(“GPS”, “WFC”,01),
(“HPQ”,”AAPL” ,14),
(“HPQ”, “CSCO”,26),
(“HPQ”, “CVX”,40),
(“HPQ”, “EBAY”,26),
(“HPQ”, “GOOG”,6),
(“HPQ”, “GPS”,45),
(“HPQ”, “INTC”,20),
(“HPQ”, “MCK”,46),
(“HPQ”, “ORCL”,12),
(“HPQ”, “PCG”,46),
(“HPQ”, “SFO”,32),
(“HPQ”, “SWY”,37),
(“HPQ”, “URS”,46),
(“HPQ”, “WFC”,46),
(“INTC”,”AAPL”,8),
(“INTC”,”CSCO”,6),
(“INTC”, “CVX”,41),
(“INTC”, “EBAY”,6),
(“INTC”, “GOOG”,15),
(“INTC”, “GPS”,62),
(“INTC”, “HPQ”,20),
(“INTC”, “MCK”,63),
(“INTC”, “ORCL”,31),
(“INTC”, “PCG”,62),
(“INTC”, “SFO”,51),
(“INTC”, “SWY”,32),
(“INTC”, “URS”,63),
(“INTC”, “WFC”,63),
(“MCK”, “AAPL”,60),
(“MCK”, “CSCO”,68),
(“MCK”, “CVX”,46),
(“MCK”, “EBAY”,68),
(“MCK”, “GOOG”,49),
(“MCK”, “GPS”,03),
(“MCK”, “HPQ”,46),
(“MCK”, “INTC”,63),
(“MCK”, “ORCL”,34),
(“MCK”, “PCG”,3),
(“MCK”, “SFO”,16),
(“MCK”, “SWY”,56),
(“MCK”, “URS”,3),
(“MCK”, “WFC”,2),
(“ORCL”, “AAPL”,22),
(“ORCL”, “CSCO”,37),
(“ORCL”, “CVX”,39),
(“ORCL”, “EBAY”,37),
(“ORCL”, “GOOG”,16),
(“ORCL”, “GPS”,34),
(“ORCL”, “HPQ”,12),
(“ORCL”, “INTC”,31),
(“ORCL”, “MCK”,34),
(“ORCL”, “PCG”,35),
(“ORCL”, “SFO”,20),
(“ORCL”, “SWY”,40),
(“ORCL”, “URS”,35),
(“ORCL”, “WFC”,35),
(“PCG”, “AAPL”,59),
(“PCG”, “CSCO”,68),
(“PCG”, “CVX”,44),
(“PCG”, “EBAY”,68),
(“PCG”, “GOOG”,48),
(“PCG”, “GPS”,01),
(“PCG”, “HPQ”,46),
(“PCG”, “INTC”,62),
(“PCG”, “MCK”,03),
(“PCG”, “ORCL”,35),
(“PCG”, “SFO”,18),
(“PCG”, “SWY”,54),
(“PCG”, “URS”,01),
(“PCG”, “WFC”,01),
(“SFO”, “AAPL”,46),
(“SFO”, “CSCO”,57),
(“SFO”, “CVX”,45),
(“SFO”, “EBAY”,57),
(“SFO”, “GOOG”,36),
(“SFO”, “GPS”,18),
(“SFO”, “HPQ”,32),
(“SFO”, “INTC”,51),
(“SFO”, “MCK”,16),
(“SFO”, “ORCL”,20),
(“SFO”, “PCG”,18),
(“SFO”, “SWY”,52),
(“SFO”, “URS”,18),
(“SFO”, “WFC”,18),
(“SWY”, “AAPL”,37),
(“SWY”, “CSCO”,32),
(“SWY”, “CVX”,13),
(“SWY”, “EBAY”,32),
(“SWY”, “GOOG”,32),
(“SWY”, “GPS”,53),
(“SWY”, “HPQ”,37),
(“SWY”, “INTC”,32),
(“SWY”, “MCK”,56),
(“SWY”, “ORCL”,40),
(“SWY”, “PCG”,54),
(“SWY”, “SFO”,52),
(“SWY”, “URS”,54),
(“SWY”, “WFC”,54),
(“URS”, “AAPL”,60),
(“URS”, “CSCO”,68),
(“URS”, “CVX”,44),
(“URS”, “EBAY”,68),
(“URS”, “GOOG”,49),
(“URS”, “GPS”,01),
(“URS”, “HPQ”,46),
(“URS”, “INTC”,63),
(“URS”, “MCK”,03),
(“URS”, “ORCL”,35),
(“URS”, “PCG”,01),
(“URS”, “SFO”,18),
(“URS”, “SWY”,54),
(“URS”, “WFC”,0),
(“WFC”, “AAPL”,60),
(“WFC”, “CSCO”,68),
(“WFC”, “CVX”,44),
(“WFC”, “EBAY”,68),
(“WFC”, “GOOG”,49),
(“WFC”, “GPS”,01),
(“WFC”, “HPQ”,46),
(“WFC”, “INTC”,63),
(“WFC”, “MCK”,02),
(“WFC”, “ORCL”,35),
(“WFC”, “PCG”,01),
(“WFC”, “SFO”,18),
(“WFC”, “SWY”,54),
(“WFC”, “URS”,0),
]Show moreShow more icon
结束语
致谢
相关资源：翠雨方工作备忘录工具v2.31中文绿色版-其它代码类资源-CSDN文库
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