optimizationlinear-programmingcplexpiecewisedocplex

Using the piecewise function of the IBM CPLEX python API, but the problem cannot be solved

I try to use MILP (Mixed Integer Linear Programming) to calculate the unit commitment problem. (unit commitment: An optimization problem trying to find the best scheduling of generator) Because the relationship between generator power and cost is a quadratic function, so I use piecewise function to convert power to cost.

enter image description here

I modify the answer on this page: unit commitment problem using piecewise-linear approximation become MIQP

The simple program structure is like this:

from docplex.mp.model import Model

mdl = Model(name='buses')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')
mdl.add_constraint(nbbus40*40 + nbbus30*30 >= 300, 'kids')

#after 4 buses, additional buses of a given size are cheaper
f1=mdl.piecewise(0, [(0,0),(4,2000),(10,4400)], 0.8) 
f2=mdl.piecewise(0, [(0,0),(4,1600),(10,3520)], 0.8) 
cost1= f1(nbbus40)
cost2 = f2(nbbus30)

mdl.minimize(cost1+ cost1)
mdl.solve()
mdl.report()

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

which gives

* model buses solved with 
objective = 3520.000
nbBus40  =  0
nbBus30  =  10.0

The answer is perfect but there is no way to apply my example. I used a piecewise function to formulate a piecewise linear relationship between power and cost, and got a new object (cost1), and then calculated the minimum value of this object. The following is my actual code(simply):

enter image description here

(min1,miny1), (pw1_1,pw1_1y),(pw1_2,pw1_2y), (max1,maxy1) are the breakpoints on the power-cost curve.

pwl_func_1phase = ucpm.piecewise(
    0,
    [(0,0),(min1,miny1),
     (pw1_1,pw1_1y),
     (pw1_2,pw1_2y),
     (max1,maxy1)
    ],
    0
)

#df_decision_vars_spinning is a dataframe store Optimization variables
df_decision_vars_spinning.at[
    (units,period),
    'variable_cost'
] = pwl_func_1phase(
    df_decision_vars_spinning.at[
        (units,period),
        'production'
    ]
)

total_variable_cost = ucpm.sum(
       (df_decision_vars_spinning.variable_cost))
ucpm.minimize(total_variable_cost )

I don’t know what causes this optimization problem can't be solve. Here is my complete code :

https://colab.research.google.com/drive/1JSKfOf0Vzo3E3FywsxcDdOz4sAwCgOHd?usp=sharing

Solution

  • With an unlimited edition of CPLEX, your model solves (though very slowly). Here are two ideas to better control what happens in solve()

    1. use solve(log_output=True) to print the log: you'll see the gap going down

    2. set a mip gap: setting mip gap to 5% stops the solve at 36s

      ucpm.parameters.mip.tolerances.mipgap = 0.05

      ucpm.solve(log_output=True)