本篇将介绍使用MindOpt来优化营养调配问题。（本例数据是假设的，决策值不能作为参考，仅为讲解决策算法用。）

营养调配问题的的目标是利用优化模型来设定每日饮食菜单，在满足各类营养的需求同时更能优化总成本．营养调配问题是可用线性优化来表达

决策变量为：以下食物调配多少量：起司汉堡 (Cheeseburger)、汉堡 (Hamburger)、火腿三明治 (Ham-sandwich)、鱼肉三民治 (Fish-sandwich)、鸡肉三民治 (Chicken-sandwich)、薯条 (Fries)、香肠比司吉 (Sausage biscuit)、低脂牛乳 (Low-fat milk)、和橙汁 (Orange juice)；
约束条件为：卡路里 (Cal.)、碳水化合物 (Carbo.)、蛋白质 (Portien)、维生素A/D (Vit. A/D)、铁 (Iron)和钙质 (Calc.)的每日摄取上/下限制，以及总量 (Volume) 限制；
目标函数则为：总成本的最小化．

问题定义

问题类型

线性优化问题，我们用先用集合和参数标明后面变量的取值关联信息。

集合

参数

然后这个线性规划问题定义如下：

决策变量

目标函数

约束条件

总结下这个模型的数学公式为：

数据

为简化表达，以下以食物的简称替代．

食物	Cheese burger	Ham sandwich	Ham-burger	Fish sandwich	Chicken sandwich	Fries	Sausage biscuit	Lowfat milk	Orange juice
简称	CB	HS	H	FS	CS	F	SB	LM	OJ

每单位食物的成本价

食物	CB	HS	H	FS	CS	F	SB	LM	OJ
成本	1.84	2.19	1.84	1.44	2.29	0.77	1.29	0.60	0.72

各营养的单日摄取上限和下限

营养	Cal	Carbo	Protein	VitA	VitC	Calc	Iron	Volume
下界	2000	355	55	100	100	100	100	-∞
上界	∞	375	∞	∞	∞	∞	∞	75

各种食物的营养含量与容积量

食物	CB	HS	H	FS	CS	F	SB	LM	OJ
Cal	510	370	500	370	400	220	345	110	80
Carbo	34	55	42	38	42	26	27	12	20
Protein	28	24	25	14	31	3	15	9	1
VitA	15	15	6	2	8	0	4	10	2
VitC	6	10	2	0	15	15	0	4	120
Calc	30	20	25	15	15	0	20	30	2
Iron	20	20	20	10	8	2	15	0	2
Volume	4	7.5	3.5	5	7.3	2.6	4.1	8	12

使用MindOpt求解器的API

直接采用求解器的API，需要查阅API文档来理解API的意思，没有建模语言可读性高。请参阅https://solver.damo.alibaba.com/doc/html/API%20reference/API-python/index.html来查看PythonAPI的使用说明。

关于Python的例子，在达摩院 MindOpt优化中文社区中有Python的示例。这里是个LP的问题，我们可以参考：https://developer.aliyun.com/article/1090860?spm=a2c6h.26396819.creator-center.8.14fb3e182y9iZl

下面我们分三种方式描述在本平台环境中的运行方法：

方法1：cell中直接输入代码运行

示例：进入官网>进入线上平台>创建项目>输入代码

云上平台运行python案例.gif

请运行下面cell中的代码，点击本窗口上面的播放△运行，或者摁shift+enter键运行:

# LP_2_diet.py

"""
/**
 *  example_2_py1.py
 *  Description 
 *  -----------
 *
 *  Linear optimization (diet problem).
 * 
 *  The goal is to select foods that satisfy daily nutritional requirements while minimizing the total cost. 
 *  The constraints in this problem limit the number of calories, the volume of good consumed, and the amount of 
 *  vitamins, protein, carbohydrates, calcium, and iron in the diet.
 *
 *  Note
 *  ----
 * 
 *  The model below will be inputted in a row-wise order.
 *
 *  Formulation
 *  -----------
 *
 * Minimize
 * Obj:        1.840000000 Cheeseburger + 2.190000000 HamSandwich + 1.840000000 Hamburger + 1.440000000 FishSandwich +
 *             2.290000000 ChickenSandwich + 0.770000000 Fries + 1.290000000 SausageBiscuit + 0.600000000 LowfatMilk + 
 *             0.720000000 OrangeJuice
 * Subject To
 * Cal:        510 Cheeseburger + 370 HamSandwich + 500 Hamburger + 370 FishSandwich +
 *             400 ChickenSandwich + 220 Fries + 345 SausageBiscuit + 110 LowfatMilk + 80 OrangeJuice >= 2000
 * Carbo:      34 Cheeseburger + 35 HamSandwich + 42 Hamburger + 38 FishSandwich + 42 ChickenSandwich + 
 *             26 Fries + 27 SausageBiscuit + 12 LowfatMilk + 20 OrangeJuice <= 375
 * Carbo_low:  34 Cheeseburger + 35 HamSandwich + 42 Hamburger + 38 FishSandwich + 42 ChickenSandwich + 
 *             26 Fries + 27 SausageBiscuit + 12 LowfatMilk + 20 OrangeJuice >= 350
 * Protein:    28 Cheeseburger + 24 HamSandwich + 25 Hamburger + 14 FishSandwich + 31 ChickenSandwich + 
 *             3 Fries + 15 SausageBiscuit + 9 LowfatMilk + OrangeJuice >= 55
 * VitA:       15 Cheeseburger + 15 HamSandwich + 6 Hamburger + 2 FishSandwich + 8 ChickenSandwich + 
 *             4 SausageBiscuit + 10 LowfatMilk + 2 OrangeJuice >= 100
 * VitC:       6 Cheeseburger + 10 HamSandwich + 2 Hamburger + 15 ChickenSandwich + 
 *             15 Fries + 4 LowfatMilk + 120 OrangeJuice >= 100
 * Calc:       30 Cheeseburger + 20 HamSandwich + 25 Hamburger + 15 FishSandwich + 
 *             15 ChickenSandwich + 20 SausageBiscuit + 30 LowfatMilk + 2 OrangeJuice >= 100
 * Iron:       20 Cheeseburger + 20 HamSandwich + 20 Hamburger + 10 FishSandwich + 
 *             8 ChickenSandwich + 2 Fries + 15 SausageBiscuit + 2 OrangeJuice >= 100
 * Volume:     4 Cheeseburger + 7.500000000 HamSandwich + 3.500000000 Hamburger + 5 FishSandwich + 
 *             7.300000000 ChickenSandwich + 2.600000000 Fries + 4.100000000 SausageBiscuit + 8 LowfatMilk + 12 OrangeJuice <= 75
 * Bounds
 * End
 */
"""
from mindoptpy import *


if __name__ == "__main__":

    MDO_INFINITY = MdoModel.get_infinity()

    req = \
    {   
        # requirement: ( lower bound,   upper bound)
        "Cal"        : (         2000, MDO_INFINITY), 
        "Carbo"      : (          350,          375),
        "Protein"    : (           55, MDO_INFINITY), 
        "VitA"       : (          100, MDO_INFINITY),
        "VitC"       : (          100, MDO_INFINITY),
        "Calc"       : (          100, MDO_INFINITY), 
        "Iron"       : (          100, MDO_INFINITY), 
        "Volume"     : (-MDO_INFINITY,           75)
    }

    food = \
    {
        # food            : ( lower bound,  upper bound, cost)
        "Cheeseburger"    : (           0, MDO_INFINITY, 1.84),
        "HamSandwich"     : (           0, MDO_INFINITY, 2.19),
        "Hamburger"       : (           0, MDO_INFINITY, 1.84),
        "FishSandwich"    : (           0, MDO_INFINITY, 1.44),
        "ChickenSandwich" : (           0, MDO_INFINITY, 2.29),
        "Fries"           : (           0, MDO_INFINITY, 0.77),
        "SausageBiscuit"  : (           0, MDO_INFINITY, 1.29),
        "LowfatMilk"      : (           0, MDO_INFINITY, 0.60),
        "OrangeJuice"     : (           0, MDO_INFINITY, 0.72)
    }
    
    req_value = \
    {  
        # (requirement, food              ) : value
        ( "Cal",        "Cheeseburger"    ) : 510,
        ( "Cal",        "HamSandwich"     ) : 370,
        ( "Cal",        "Hamburger"       ) : 500,
        ( "Cal",        "FishSandwich"    ) : 370,
        ( "Cal",        "ChickenSandwich" ) : 400,
        ( "Cal",        "Fries"           ) : 220,
        ( "Cal",        "SausageBiscuit"  ) : 345,
        ( "Cal",        "LowfatMilk"      ) : 110,
        ( "Cal",        "OrangeJuice"     ) : 80,

        ( "Carbo",      "Cheeseburger"    ) : 34,
        ( "Carbo",      "HamSandwich"     ) : 35,
        ( "Carbo",      "Hamburger"       ) : 42,
        ( "Carbo",      "FishSandwich"    ) : 38,
        ( "Carbo",      "ChickenSandwich" ) : 42,
        ( "Carbo",      "Fries"           ) : 26,
        ( "Carbo",      "SausageBiscuit"  ) : 27,
        ( "Carbo",      "LowfatMilk"      ) : 12,
        ( "Carbo",      "OrangeJuice"     ) : 20,

        ( "Protein",    "Cheeseburger"    ) : 28,
        ( "Protein",    "HamSandwich"     ) : 24,
        ( "Protein",    "Hamburger"       ) : 25,
        ( "Protein",    "FishSandwich"    ) : 14,
        ( "Protein",    "ChickenSandwich" ) : 31,
        ( "Protein",    "Fries"           ) : 3,
        ( "Protein",    "SausageBiscuit"  ) : 15,
        ( "Protein",    "LowfatMilk"      ) : 9,
        ( "Protein",    "OrangeJuice"     ) : 1,

        ( "VitA",       "Cheeseburger"    ) : 15,
        ( "VitA",       "HamSandwich"     ) : 15,
        ( "VitA",       "Hamburger"       ) : 6,
        ( "VitA",       "FishSandwich"    ) : 2,
        ( "VitA",       "ChickenSandwich" ) : 8,
        ( "VitA",       "Fries"           ) : 0,
        ( "VitA",       "SausageBiscuit"  ) : 4,
        ( "VitA",       "LowfatMilk"      ) : 10,
        ( "VitA",       "OrangeJuice"     ) : 2,

        ( "VitC",       "Cheeseburger"    ) : 6,
        ( "VitC",       "HamSandwich"     ) : 10,
        ( "VitC",       "Hamburger"       ) : 2,
        ( "VitC",       "FishSandwich"    ) : 0,
        ( "VitC",       "ChickenSandwich" ) : 15,
        ( "VitC",       "Fries"           ) : 15,
        ( "VitC",       "SausageBiscuit"  ) : 0,
        ( "VitC",       "OrangeJuice"     ) : 4,
        ( "VitC",       "LowfatMilk"      ) : 120,

        ( "Calc",       "Cheeseburger"    ) : 30,
        ( "Calc",       "HamSandwich"     ) : 20,
        ( "Calc",       "Hamburger"       ) : 25,
        ( "Calc",       "FishSandwich"    ) : 15,
        ( "Calc",       "ChickenSandwich" ) : 15,
        ( "Calc",       "Fries"           ) : 0,
        ( "Calc",       "SausageBiscuit"  ) : 20,
        ( "Calc",       "LowfatMilk"      ) : 30,
        ( "Calc",       "OrangeJuice"     ) : 2,

        ( "Iron",       "Cheeseburger"    ) : 20,
        ( "Iron",       "HamSandwich"     ) : 20,
        ( "Iron",       "Hamburger"       ) : 20,
        ( "Iron",       "FishSandwich"    ) : 10,
        ( "Iron",       "ChickenSandwich" ) : 8,
        ( "Iron",       "Fries"           ) : 2,
        ( "Iron",       "SausageBiscuit"  ) : 15,
        ( "Iron",       "LowfatMilk"      ) : 0,
        ( "Iron",       "OrangeJuice"     ) : 2,

        ( "Volume",     "Cheeseburger"    ) : 4,
        ( "Volume",     "HamSandwich"     ) : 7.5,
        ( "Volume",     "Hamburger"       ) : 3.5,
        ( "Volume",     "FishSandwich"    ) : 5,
        ( "Volume",     "ChickenSandwich" ) : 7.3,
        ( "Volume",     "Fries"           ) : 2.6,
        ( "Volume",     "SausageBiscuit"  ) : 4.1,
        ( "Volume",     "LowfatMilk"      ) : 8,
        ( "Volume",     "OrangeJuice"     ) : 12
    }

    # ----Step 1. Create a model and change the parameters.
    model = MdoModel()

    try:
        # ----Step 2. Input model.
        # Change to minimization problem.
        model.set_int_attr("MinSense", 1)
        
        # Add variables.
        var = {}
        for food_name, food_data in food.items():
            var[food_name] = model.add_var(food_data[0], food_data[1], food_data[2], None, food_name, False)

        # Add constraints.
        cons = {}
        for req_name, req_data in req.items():
            expr = MdoExprLinear()
            for food_name in food.keys():
                expr += req_value[req_name, food_name] * var[food_name]
            cons[req_name] = model.add_cons(req_data[0], req_data[1], expr, req_name)

        # ----Step 3. Solve the problem and populate the result.
        model.solve_prob()
        model.display_results()
        time.sleep(1) #for print
  
        status_code, status_msg = model.get_status()
        if status_msg == "OPTIMAL":
            print("----\n")
            print("The solver terminated with an OPTIMAL status (code {0}).".format(status_code))

            print("目标函数总收益是: {0}".format(model.get_real_attr("PrimalObjVal")))
            
            print("原始解是：")
            for var_name,var_val in var.items():
                primal_soln = var_val.get_real_attr("PrimalSoln")
                print("{0:>20} : {1}".format(var_name,primal_soln))
    
        else:
            print("Optimizer terminated with a(n) {0} status (code {1}).".format(status_msg, status_code))
     
    except MdoError as e:
        print("Received Mindopt exception.")
        print(" - Code          : {}".format(e.code))
        print(" - Reason        : {}".format(e.message))
    except Exception as e:
        print("Received exception.")
        print(" - Reason        : {}".format(e))
    finally:
        # Step 4. Free the model.
        model.free_mdl()

点击运行后，得到的结果如下：

Start license validation (current time : 17-JAN-2023 23:54:14).
License validation terminated. Time : 0.003s

Model summary.
 - Num. variables     : 9
 - Num. constraints   : 8
 - Num. nonzeros      : 67
 - Bound range        : [5.5e+01,2.0e+03]
 - Objective range    : [6.0e-01,2.3e+00]
 - Matrix range       : [1.0e+00,5.1e+02]

Presolver started.
Presolver terminated. Time : 0.000s

Simplex method started.
Model fingerprint: =IGYvFmb5d2dgF2dud3b

    Iteration       Objective       Dual Inf.     Primal Inf.     Time
            0     0.00000e+00      0.0000e+00      4.0937e+01     0.00s    
            3     1.48557e+01      0.0000e+00      0.0000e+00     0.00s    
Postsolver started.
Simplex method terminated. Time : 0.001s

Optimizer summary.
 - Optimizer used     : Simplex method
 - Optimizer status   : OPTIMAL
 - Total time         : 0.002s

Solution summary.       Primal solution
 - Objective          : 1.4855737705e+01 
----

The solver terminated with an OPTIMAL status (code 1).
目标函数总收益是: 14.855737704918033
原始解是：
        Cheeseburger : 4.385245901639344
         HamSandwich : 0.0
           Hamburger : 0.0
        FishSandwich : 0.0
     ChickenSandwich : 0.0
               Fries : 6.147540983606558
      SausageBiscuit : 0.0
          LowfatMilk : 3.422131147540985
         OrangeJuice : 0.0

方法2：命令行直接运行.py文件

上面是直接在cell中运行所有的脚本，我们也可以建立个新文档，将Python代码存在src/python_src文件夹的LP_2_diet.py文件。然后在Launcher中打开Terminal，执行python xx.py文件来运行。

您也可以下载本.py文件，在自己的电脑上安装MindOpt求解器，然后在自己电脑的环境运行。

Luancher可以点击左上角的+打方块打开，Terminal在最下方，如截图示意。打开的窗口可以拖动调整位置。

然后在Terminal命令行里运行如下指令:

cd src/python_src
python LP_2_diet.py

运行得到的结果同方法1：

方法3:复制案例广场的例子

这个例子已经在MindOpt的案例广场，可以直接复制：营养调配

直接点击复制项目，会将配置的文件全部复制过来，可以直接运行。（如上图所示）

求解结果

运行结果里面打印有：

目标函数总收益是: 14.855737704918033
原始解是：
        Cheeseburger : 4.385245901639344
         HamSandwich : 0.0
           Hamburger : 0.0
        FishSandwich : 0.0
     ChickenSandwich : 0.0
               Fries : 6.147540983606558
      SausageBiscuit : 0.0
          LowfatMilk : 3.422131147540985
         OrangeJuice : 0.0

代表求解结果的目标函数（每日饮食餐费）最低解为：$14.86元，包含了4.39份起司汉堡，6.15份薯条，以及3.42份低脂牛乳。

联系我们

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更多更新通知：https://solver.damo.alibaba.com

如何吃，少花钱又营养丰富？可用MindOpt线性规划求解来决策

问题定义

问题类型

集合

参数

决策变量

目标函数

约束条件

数据

使用MindOpt求解器的API

方法1：cell中直接输入代码运行

方法2：命令行直接运行.py文件

方法3:复制案例广场的例子

求解结果

联系我们

达摩院 MindOpt 优化

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如何吃，少花钱又营养丰富？可用MindOpt线性规划求解来决策

问题定义

问题类型

集合

参数

决策变量

目标函数

约束条件

数据

使用MindOpt求解器的API

方法1：cell中直接输入代码运行

方法2：命令行直接运行.py文件

方法3:复制案例广场的例子

求解结果

联系我们

达摩院 MindOpt 优化

热门文章

最新文章

相关课程

相关电子书

相关实验场景