接上篇學(xué)會(huì)了如何用python調(diào)用gurobipy之后，這篇總結(jié)一些學(xué)到的基本操作。

tuplelist、tupledict、multidict、創(chuàng)建list、

1.tuplelist方法：

tuplelist是Python list的擴(kuò)展對(duì)象，使用tuplelist()不能忘記from gurobipy import *，tuplelist增加了快速篩選select功能，比傳統(tǒng)的if...else...篩選速度快。

from gurobipy import * import timeT1 = time.time() Cities=[("A","B"),("A","C"),("B","C"),("B","D"),("C","D")] Routes=tuplelist(Cities) print(Routes.select("A","*")) T2 =time.time()print('程序運(yùn)行時(shí)間:%s毫秒' % ((T2 - T1)*1000))

tuplelist運(yùn)行結(jié)果：

C:\Users\xzr\.conda\envs\py310gurobi\python.exe F:\PycharmProjects\workspace\untitled\jizulunban\caogao.py <gurobi.tuplelist (2 tuples, 2 values each):( A , B )( A , C ) > 程序運(yùn)行時(shí)間:1.9958019256591797毫秒進(jìn)程已結(jié)束,退出代碼0

for...else...方法：

from gurobipy import * import timeT1 = time.time() Cities=[("A","B"),("A","C"),("B","C"),("B","D"),("C","D")] Result=[] for i,j in Cities:if i=="A":Result.append((i,j)) print(Result) T2 =time.time()print('程序運(yùn)行時(shí)間:%s毫秒' % ((T2 - T1)*1000))

for...else...運(yùn)行結(jié)果：

C:\Users\xzr\.conda\envs\py310gurobi\python.exe F:\PycharmProjects\workspace\untitled\jizulunban\caogao.py [('A', 'B'), ('A', 'C')] 程序運(yùn)行時(shí)間:0.0毫秒進(jìn)程已結(jié)束,退出代碼0

尷尬了，竟然是for...else...的運(yùn)行速度更快，原因是數(shù)據(jù)量太少了體現(xiàn)不出效果。

2.tupledict方法：

tupledict是Python Dictionary的擴(kuò)展對(duì)象，鍵值是tuple（元組），可以使用select、sum、prob函數(shù)。用于變量和約束。后面有詳細(xì)介紹。

3.multidict方法：

multidict()創(chuàng)建tuplelist和tupledict的便捷方法。代碼示例：

from gurobipy import * import time# T1 = time.time() cities,supply,demand = multidict({"A":[100,20],"B":[150,50],"C":[20,300],"D":[10,200]}) print(cities) print(supply) print(demand) # T2 =time.time()

運(yùn)行結(jié)果：

C:\Users\xzr\.conda\envs\py310gurobi\python.exe F:\PycharmProjects\workspace\untitled\jizulunban\caogao.py ['A', 'B', 'C', 'D'] {'A': 100, 'B': 150, 'C': 20, 'D': 10} {'A': 20, 'B': 50, 'C': 300, 'D': 200}進(jìn)程已結(jié)束,退出代碼0

運(yùn)行結(jié)果第一行是list，第二三行是dictionary。

4.創(chuàng)建list：

python有多種創(chuàng)建list的方法：

a=[] a.append("A") b=[i**2 for i in range(6)] #[0,1,4,9,16,25] c=[(i,j)for j in range(4) for i in range(j)] #[(0,1),(0,2),(1,2),(0,3),(1,3),(2,3)] d=[i for i in range(10) if i not in b] #[2,3,5,6,7,8] Pairs=[] for j in range(4):for i in range(j):Pairs.append((i,j))

對(duì)于求和，Python的Generator（生成器）：

SumSquares=sum(i**2 for i in range(6)) #55

Gurobi中采用quicksum，效率更高：

obj=quicksum(cost[i,j]*x[i,j] for i,j in arcs)

5.tupledict建模示例

tupledict（Gurobi變量一般都是tupledict類型）有sum函數(shù)

from gurobipy import * import time# T1 = time.time() m=Model() x=m.addVars(3,4,vtype=GRB.BINARY,name="x") m.addConstrs((x.sum(i,"*")<=1 for i in range(3)),name="con") m.update() m.write("test.lp") # T2 =time.time()# print('程序運(yùn)行時(shí)間:%s毫秒' % ((T2 - T1)*1000))

運(yùn)行后，打開(kāi)“test.lp”文件查看寫入的模型

\ LP format - for model browsing. Use MPS format to capture full model detail. MinimizeSubject Tocon[0]: x[0,0] + x[0,1] + x[0,2] + x[0,3] <= 1con[1]: x[1,0] + x[1,1] + x[1,2] + x[1,3] <= 1con[2]: x[2,0] + x[2,1] + x[2,2] + x[2,3] <= 1 Bounds Binariesx[0,0] x[0,1] x[0,2] x[0,3] x[1,0] x[1,1] x[1,2] x[1,3] x[2,0] x[2,1]x[2,2] x[2,3] End

太妙了太妙了

tupledict（Gurobi變量一般都是tupledict類型）還有prob函數(shù)，用于變量和系數(shù)相乘后累加

以下表達(dá)式等效

obj=quicksum(cost[i,j]*x[i,j] for i,j in arcs) obj=x.prod(cost)

建模建議，盡量采用稀疏方式，采用tuplelists篩選和指定合適的下標(biāo)組合關(guān)系，基于這些組合關(guān)系建立變量和數(shù)據(jù)字典，利用tuplelist.select()以及tupledict.select()，tupledict.sum()，tupledict.prob()來(lái)對(duì)下標(biāo)進(jìn)行組合處理。

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?Gurobi建模舉例1

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from gurobipy import *# T1 = time.time()try:#Create a new modelm=Model("mip1")#Create variablesx=m.addVar(vtype=GRB.BINARY,name="x")y=m.addVar(vtype=GRB.BINARY,name="y")z=m.addVar(vtype=GRB.BINARY,name="z")#Set objectivem.setObjective(x+y+2*z,GRB.MAXIMIZE)#Add constraint:x+2y+3z<=4m.addConstr(x+2*y+3*z<=4,"c0")#Add constraint:x+y>=1m.addConstr(x+y>=1,"c1")m.optimize()for v in m.getVars(): #getVars獲取所有變量print("%s %g" % (v.varName,v.x)) #(v.varName,v.x)是（變量名字，優(yōu)化結(jié)果）print("Obj: %g" % m.objVal)except GurobiError as e:print("Error code" + str(e.errno)+":"+str(e))except AttributeError:print("Encountered an attribute error")# T2 =time.time() # print('程序運(yùn)行時(shí)間:%s毫秒' % ((T2 - T1)*1000))

?運(yùn)行結(jié)果

C:\Users\xzr\.conda\envs\py310gurobi\python.exe F:\PycharmProjects\workspace\untitled\jizulunban\caogao.py Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (win64)CPU model: Intel(R) Core(TM) i7-7500U CPU @ 2.70GHz, instruction set [SSE2|AVX|AVX2] Thread count: 2 physical cores, 4 logical processors, using up to 4 threadsOptimize a model with 2 rows, 3 columns and 5 nonzeros Model fingerprint: 0x98886187 Variable types: 0 continuous, 3 integer (3 binary) Coefficient statistics:Matrix range [1e+00, 3e+00]Objective range [1e+00, 2e+00]Bounds range [1e+00, 1e+00]RHS range [1e+00, 4e+00] Found heuristic solution: objective 2.0000000 Presolve removed 2 rows and 3 columns Presolve time: 0.02s Presolve: All rows and columns removedExplored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors)Solution count 2: 3 2 Optimal solution found (tolerance 1.00e-04) Best objective 3.000000000000e+00, best bound 3.000000000000e+00, gap 0.0000% x 1 y 0 z 1 Obj: 3進(jìn)程已結(jié)束,退出代碼0

Gurobi建模舉例2

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from gurobipy import *categories,minNutrition,maxNutrition=multidict({"calories":[1800,2200],"protein":[91,GRB.INFINITY],"fat":[0,65],"sodium":[0,1779] })foods,cost=multidict({"hamburger":2.49,"chicken":2.89,"hot dog":1.50,"fries":1.89,"macaroni":2.09,"pizza":1.99,"salad":2.49,"milk":0.89,"ice cream":1.59 })#Nutrition values for the foods nutritionValues={("hamburger","calories"):410,("hamburger","protein"):24,("hamburger","fat"):26,("hamburger","sodium"):730,("chicken","calories"):420,("chicken", "protein"):32,("chicken", "fat"):10,("chicken", "sodium"):1190,("hot dog","calories"):560,("hot dog", "protein"):20,("hot dog", "fat"):32,("hot dog", "sodium"):1800,("fries","calories"):380,("fries", "protein"):4,("fries", "fat"):19,("fries", "sodium"):720,("macaroni", "calories"): 320,("macaroni", "protein"): 12,("macaroni", "fat"): 10,("macaroni", "sodium"): 930,("pizza", "calories"): 320,("pizza", "protein"): 15,("pizza", "fat"): 12,("pizza", "sodium"): 820,("salad", "calories"): 320,("salad", "protein"): 31,("salad", "fat"): 12,("salad", "sodium"): 1230,("milk", "calories"): 100,("milk", "protein"): 8,("milk", "fat"): 2.5,("milk", "sodium"): 125,("ice cream", "calories"): 330,("ice cream", "protein"): 8,("ice cream", "fat"): 10,("ice cream", "sodium"): 180 }#Model m=Model("diet")#Create decision variables for the foods to buy buy=m.addVars(foods,name="buy") #也可以是： # buy=[] # for f in foods: # buy[f]=m.addVar(name=f)#目標(biāo)函數(shù)是最小化cost m.setObjective(buy.prod(cost),GRB.MINIMIZE) #如果使用循環(huán)結(jié)構(gòu)，應(yīng)該是： # m.setObjective(sum(buy[f]*cost[f] for f in foods),GRB.MINIMIZE)#Nutrition constraints m.addConstrs((quicksum(nutritionValues[f,c]*buy[f] for f in foods)== [minNutrition[c],maxNutrition[c]]for c in categories),"_") #如果使用循環(huán)結(jié)構(gòu)，應(yīng)該是： # for c in categories: # m.addRange( # sum(nutritionValues[f,c] * buy[f] for f in foods),minNutrition[c],maxNutrition[c],c) # )def printSolution():if m.status == GRB.Status.OPTIMAL:print("\nCost:%g" % m.objval)print("\nBuy:")buyx=m.getAttr("x",buy)for f in foods:if buy[f].x>0.0001:print("%s %g" % (f,buyx[f]))else:print("No solution")#solve m.optimize() printSolution()# T1 = time.time()# T2 =time.time() # print('程序運(yùn)行時(shí)間:%s毫秒' % ((T2 - T1)*1000))

?運(yùn)行結(jié)果

C:\Users\xzr\.conda\envs\py310gurobi\python.exe F:\PycharmProjects\workspace\untitled\jizulunban\caogao.py Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (win64)CPU model: Intel(R) Core(TM) i7-7500U CPU @ 2.70GHz, instruction set [SSE2|AVX|AVX2] Thread count: 2 physical cores, 4 logical processors, using up to 4 threadsOptimize a model with 4 rows, 12 columns and 39 nonzeros Model fingerprint: 0xed649f3c Coefficient statistics:Matrix range [1e+00, 2e+03]Objective range [9e-01, 3e+00]Bounds range [7e+01, 2e+03]RHS range [7e+01, 2e+03] Presolve removed 0 rows and 2 columns Presolve time: 0.01s Presolved: 4 rows, 10 columns, 37 nonzerosIteration Objective Primal Inf. Dual Inf. Time0 0.0000000e+00 1.472500e+02 0.000000e+00 0s4 1.1828861e+01 0.000000e+00 0.000000e+00 0sSolved in 4 iterations and 0.03 seconds (0.00 work units) Optimal objective 1.182886111e+01

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注意：

若出現(xiàn)眾多warning，刪去warning給的路徑下的帶“~”的文件

若出現(xiàn)ERROR: Could not find a version that satisfies the requirement time (from versions: none)，是找不到適應(yīng)現(xiàn)有python版本的包

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