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python - 如何将 max 函数从 CPLEX OPL 切换到 Docplex？

问题描述

我在 CPLEX OPL 上实施了以下限制。

forall (i in N)
        forall (j in M)
            forall (k in 1..i)
                sum(z in 1 ..i)(p[z]*(x[z][j][k]+y[z][j][k])) + (t[k]*max(z in 1 ..i)(x[z][j][k]+y[z][j][k]))<= d[i];

而且我已经尝试在 Docplex (python) 中实现它，但我不知道它是否真的有效，有谁知道如何将 max 函数从 CPLEX OPL 切换到 Docplex，或者我所做的是否可以？

for i in N:
    for j in M:
        for k in range(i):
            mdl.sum((x[(i,j,k)]+y[(i,j,k)])*p[z] for z in range(i))+(t[k]*mdl.max(x[(z,j,k)]+y[(z,j,k)] for z in range(i)) <= d[i]

标签： pythonmodelingcplexopldocplex

解决方案

mdl.max 就是这样。

在 OPL https://github.com/AlexFleischerParis/zooopl/blob/master/zoomax.mod

int nbKids=300;

{int} buses={30,40,50};


dvar int+ nbBus[buses];
dvar int maxNbOfBusesGivenSize;

    
minimize maxNbOfBusesGivenSize;
     
subject to
{
 // logical constraint
 // maxNbOfBusesGivenSize is the max of all nbBus
 maxNbOfBusesGivenSize==max(i in buses) nbBus[i];
 sum(i in buses) i*nbBus[i]>=nbKids;
}

execute DISPLAY_After_SOLVE
{
  writeln("The max number of buses is ",maxNbOfBusesGivenSize);
  writeln("nbBus = ",nbBus);
}

而在 python https://github.com/AlexFleischerParis/zoodocplex/blob/master/zoomax.py

from docplex.mp.model import Model

mdl = Model(name='buses')

nbKids=300;
buses=[30,40,50]

#decision variables
mdl.nbBus = {b: mdl.integer_var(name="nbBus"+str(b)) for b in buses}

# Constraint
mdl.add_constraint(sum(mdl.nbBus[b]*b for b in buses) >= nbKids, 'kids')

# Objective
# logical constraint is the max of all nbBus
mdl.minimize(mdl.max(mdl.nbBus[b] for b in buses)) 

mdl.solve(log_output=True,)

mdl.export("c:\\temp\\buses.lp")

for v in mdl.iter_integer_vars():
    print(v," = ",v.solution_value)

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