# 数理最適化モジュール mypulp


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## インポート

## GRB（定数）クラス

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L37"
target="_blank" style="float:right; font-size:smaller">source</a>

### GRB

``` python

def GRB(
    args:VAR_POSITIONAL, kwargs:VAR_KEYWORD
):

```

*Initialize self. See help(type(self)) for accurate signature.*

## 区分的線形関数

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L60"
target="_blank" style="float:right; font-size:smaller">source</a>

### gray

``` python

def gray(
    i
):

```

*Call self as a function.*

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L64"
target="_blank" style="float:right; font-size:smaller">source</a>

### convex_comb_agg_log

``` python

def convex_comb_agg_log(
    model, var_list:list=[]
):

```

*add piecewise relation with a logarithmic number of binary variables*

using the convex combination formulation – non-disaggregated.
Parameters: - model: a model where to include the SOS type 2 - vars :
list of variables that declare the SOS type 2

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L96"
target="_blank" style="float:right; font-size:smaller">source</a>

### mult_selection

``` python

def mult_selection(
    model, x, a, b
):

```

*mult_selection – add piecewise relation with multiple selection
formulation* Parameters: - model: a model where to include the piecewise
linear relation - a\[k\]: x-coordinate of the k-th point in the
piecewise linear relation - b\[k\]: y-coordinate of the k-th point in
the piecewise linear relation Returns the model with the piecewise
linear relation on added variables x, f, and z.

## multidict関数

multidict関数は，辞書を引数として入力すると，
第1の返値としてキーのリスト，2番目以降の返値として辞書を返す．

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L131"
target="_blank" style="float:right; font-size:smaller">source</a>

### multidict

``` python

def multidict(
    dic
):

```

*Call self as a function.*

``` python
I,d = multidict({1:80, 2:270, 3:250 , 4:160, 5:180})
J,M,N = multidict({1:[500,600], 2:[800,500], 3:[500,100]})
print(I,d)
print(J,M,N)
```

    [1, 2, 3, 4, 5] {1: 80, 2: 270, 3: 250, 4: 160, 5: 180}
    [1, 2, 3] {1: 500, 2: 800, 3: 500} {1: 600, 2: 500, 3: 100}

## tuplelistクラス

tuplelistは，名前の通りタプル（組）を要素としたリストである．

tuplelistには，引数によって指定した条件を満たす要素を取り出すselectメソッドが
準備されている．

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L150"
target="_blank" style="float:right; font-size:smaller">source</a>

### tuplelist

``` python

def tuplelist(
    args:VAR_POSITIONAL, kwargs:VAR_KEYWORD
):

```

*Tuplelist class for mypulp.py* It works like Gurobi’s tuplelist

``` python
cost = {(1,1):4,  (1,2):6, (1,3):9,
        (2,1):5,  (2,2):4, (2,3):7,
        (3,1):6,  (3,2):3, (3,3):4,
        (4,1):8,  (4,2):5, (4,3):3,
        (5,1):10, (5,2):8, (5,3):4
        } 
arcs = tuplelist([(i,j) for (i,j) in cost])
print( arcs.select(2,"*") )
```

    [(2, 1), (2, 2), (2, 3)]

## 線形表現クラス

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L172"
target="_blank" style="float:right; font-size:smaller">source</a>

### LinExpr

``` python

def LinExpr(
    coeff:list=[], var:list=[]
):

```

*Linear Expresstion Class*

## 変数クラス

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L192"
target="_blank" style="float:right; font-size:smaller">source</a>

### Variable

``` python

def Variable(
    name:str='', lowBound:float=0.0, upBound:float=1e+100, cat:str='Continuous'
):

```

*Variable Class*

## CBC options

Coin Branch and
Cutを用いて最適化する際に，以下のオプションを付加することができる．

    class pulp.apis.PULP_CBC_CMD(mip=True, msg=True, timeLimit=None, fracGap=None, maxSeconds=None, gapRel=None, gapAbs=None, presolve=None, cuts=None, strong=None, options=None, warmStart=False, keepFiles=False, path=None, threads=None, logPath=None, mip_start=False)
    Bases: pulp.apis.coin_api.COIN_CMD

This solver uses a precompiled version of cbc provided with the package

Parameters

- mip (bool) – if False, assume LP even if integer variables

- msg (bool) – if False, no log is shown

- timeLimit (float) – maximum time for solver (in seconds)

- gapRel (float) – relative gap tolerance for the solver to stop (in
  fraction)

- gapAbs (float) – absolute gap tolerance for the solver to stop

- threads (int) – sets the maximum number of threads

- options (list) – list of additional options to pass to solver

- warmStart (bool) – if True, the solver will use the current value of
  variables as a start

- keepFiles (bool) – if True, files are saved in the current directory
  and not deleted after solving

- path (str) – path to the solver binary

- logPath (str) – path to the log file

- presolve (bool) – if True, adds presolve on

- cuts (bool) – if True, adds gomory on knapsack on probing on

- strong (bool) – if True, adds strong

モデルクラスの最適化メソッド optimize の引数 solverで，
PULP_CBC_CMDのインスタンスを渡す．

``` python
 optimize(self, solver=PULP_CBC_CMD(timeLimit=max_cpu, presolve=True)) 
```

## モデルクラス

------------------------------------------------------------------------

<a
href="https://github.com/scmopt/manual/tree/master/blob/master/scmopt/mypulp.py#L221"
target="_blank" style="float:right; font-size:smaller">source</a>

### Model

``` python

def Model(
    name:str=''
):

```

*Model Class*

## 例題

``` python
TEST=True
if TEST:
    model = Model("lo1")

    J, v = multidict({1: 16, 2: 19, 3: 23, 4: 28})

    # x1 = model.addVar(vtype="C", name="x1")
    # x2 = model.addVar(vtype="I", name="x2")
    # x3 = model.addVar(lb=0, ub=30, vtype="B", name="x3")

    x1 = model.addVar(vtype=GRB.CONTINUOUS, name="x1")
    # x1 = model.addVar(vtype="N", lb=10.5, ub=50,name="x1")
    x2 = model.addVar(vtype="C", name="x2")
    x3 = model.addVar(lb=0, ub=30, vtype="C", name="x3")

    model.update()
    #model.addSOS(2, [x1, x2, x3])
    #L1 = LinExpr([2, 1, 1], [x1, x2, x3])
    # L1=LinExpr()
    # L1.addTerms(2,x1)
    # L1.addTerms(1,x2)
    # L1.addTerms(1,x3)

    #model.addConstr(lhs=L1,sense="<=",rhs=60,name="C0")
    model.addConstr(x1 + 2*x2 + x3 <= 60, name="C1")

    #c1 = model.addConstr(lhs=L1, sense="<=", rhs=60)
    model.addConstr(x1 + 2 * x2 + x3 <= 60)

    model.setObjective(15 * x1 + 18 * x2 + 30 * x3, GRB.MAXIMIZE)

    #model.write("mypulp1.mps")
    #model.write("mypulp1.lp")
    
    #SCIPを使用する場合
    solver = pulp.SCIP(timeLimit=1)
    model.optimize(solver=solver)
    
    #model.optimize()

    if model.Status == GRB.Status.OPTIMAL:
        model.write("answer.sol")
        print("Opt. Value=", model.ObjVal)
        # for v in model.getVars():
        #    print(v.VarName,v.X,v.RC)
        for v in model.getVars():
            print(v.VarName, v.X)
        for c in model.getConstrs():
            print(c.ConstrName, c.Pi)
    # m=Model()
    # x=m.addVar( name="x", vtype="I" , lb=1)
    # y=m.addVar( name="y", vtype="I" , lb=1)
    # z=m.addVar( name="z", vtype="I" , lb=1)
    # m.update()
    # m.addConstr(2*x+ y ==11)
    # m.addConstr(y+ 3*z ==14)
    # # m.setObjective(0,GRB.MINIMIZE)
    # m.optimize()
    # print(x.X,y.X,z.X)
```

    Opt. Value= 1350.0
    x1 30.0
    x2 0.0
    x3 30.0
    C1 None
    c_1 None

``` python
if TEST:
    m=Model()

    x = [0,2,3,1]
    y = [1,0,3,3]

    n=len(x)

    X=m.addVar(ub=3.0, name="X")
    Y=m.addVar(ub=3.0, name ="Y")

    Z=m.addVar(name ="Z")

    a,b={},{}
    for i in range(n):
        a[i] =m.addVar(name="a({0})".format(i))
        b[i] =m.addVar(name="b({0})".format(i))
        m.update()

    for i in range(n):
        m.addConstr( a[i] >= x[i] -X )
        m.addConstr( a[i] >= X-x[i] )
        m.addConstr( b[i] >= y[i] -Y )
        m.addConstr( b[i] >= Y-y[i] )

        m.addConstr(Z>=a[i]+b[i])

    m.setObjective(Z, GRB.MINIMIZE)
    # m.setObjective( quicksum( 1*a[i] for i in range(n))
    #                + quicksum( 1*b[i] for i in range(n)), GRB.MINIMIZE )


    m.optimize()

    print(X.X,Y.X)
    print(m.ObjVal)
    for i in range(n):
        print(a[i].X,b[i].X)
```

    Welcome to the CBC MILP Solver 
    Version: 2.10.3 
    Build Date: Dec 15 2019 

    command line - /Users/mikiokubo/Library/Caches/pypoetry/virtualenvs/scmopt-KVX_UVCf-py3.8/lib/python3.8/site-packages/pulp/apis/../solverdir/cbc/osx/64/cbc /var/folders/69/5y96sdc94jxf6khgc8mlmxrr0000gn/T/a9600581b8304017ab19ab021b6e0065-pulp.mps branch printingOptions all solution /var/folders/69/5y96sdc94jxf6khgc8mlmxrr0000gn/T/a9600581b8304017ab19ab021b6e0065-pulp.sol (default strategy 1)
    At line 2 NAME          MODEL
    At line 3 ROWS
    At line 25 COLUMNS
    At line 71 RHS
    At line 92 BOUNDS
    At line 104 ENDATA
    Problem MODEL has 20 rows, 11 columns and 44 elements
    Coin0008I MODEL read with 0 errors
    Presolve 10 (-10) rows, 6 (-5) columns and 26 (-18) elements
    0  Obj 0 Primal inf 12.999995 (5)
    6  Obj 2.5
    Optimal - objective value 2.5
    After Postsolve, objective 2.5, infeasibilities - dual 0 (0), primal 0 (0)
    Optimal objective 2.5 - 6 iterations time 0.002, Presolve 0.00
    Option for printingOptions changed from normal to all
    Total time (CPU seconds):       0.00   (Wallclock seconds):       0.01

    1.5 2.0
    2.5
    1.5 1.0
    0.5 2.0
    1.5 1.0
    1.5 1.0

``` python
if TEST:
    model = Model("lo1")

    x = model.addVar(name='tonkoke')
    y = model.addVar(name='kokenton')
    z = model.addVar(name='mix')

    model.setObjective(15*x + 18*y + 30*z, GRB.MAXIMIZE)
    model.addConstr(2*x +   y + z <= 60, name='pork')
    model.addConstr(  x + 2*y + z <= 60, name='chicken')
    model.addConstr(            z <= 30, name='beef')

    model.optimize()
    print( model.ObjVal )
    for i in model.getVars():
        print(i.VarName, i.X)
```

    Welcome to the CBC MILP Solver 
    Version: 2.10.3 
    Build Date: Dec 15 2019 

    command line - /Users/mikiokubo/Library/Caches/pypoetry/virtualenvs/scmopt-KVX_UVCf-py3.8/lib/python3.8/site-packages/pulp/apis/../solverdir/cbc/osx/64/cbc /var/folders/69/5y96sdc94jxf6khgc8mlmxrr0000gn/T/3175126010324092b3a9adfcf59ef2f7-pulp.mps max branch printingOptions all solution /var/folders/69/5y96sdc94jxf6khgc8mlmxrr0000gn/T/3175126010324092b3a9adfcf59ef2f7-pulp.sol (default strategy 1)
    At line 2 NAME          MODEL
    At line 3 ROWS
    At line 8 COLUMNS
    At line 19 RHS
    At line 23 BOUNDS
    At line 27 ENDATA
    Problem MODEL has 3 rows, 3 columns and 7 elements
    Coin0008I MODEL read with 0 errors
    Presolve 2 (-1) rows, 3 (0) columns and 6 (-1) elements
    0  Obj -0 Dual inf 62.999997 (3)
    2  Obj 1230
    Optimal - objective value 1230
    After Postsolve, objective 1230, infeasibilities - dual 0 (0), primal 0 (0)
    Optimal objective 1230 - 2 iterations time 0.002, Presolve 0.00
    Option for printingOptions changed from normal to all
    Total time (CPU seconds):       0.00   (Wallclock seconds):       0.00

    1230.0
    kokenton 10.0
    mix 30.0
    tonkoke 10.0