Examples - Working with Pyomo model

Pyomo is an open source software package for modeling and solving mathematical programs in Python [Hart2011]. This section gives an example of how to optimize Pyomo models using Nevergrad.

Concrete Model

Let us create a ConcreteModel instance using Pyomo. In a ConcreteModel, each component is fully initialized.

import pyomo.environ as pyomo

def square(m):
    return pyomo.quicksum((m.x[i] - 0.5) ** 2 for i in m.x)

model = pyomo.ConcreteModel()
model.x = pyomo.Var([0, 1], domain=pyomo.Reals)
model.obj = pyomo.Objective(rule=square)
model.Constraint1 = pyomo.Constraint(rule=lambda m: m.x[0] >= 1)
model.Constraint2 = pyomo.Constraint(rule=lambda m: m.x[1] >= 0.8)

In the above model, it is clear that the parameter in the objective function is x, which is an indexed variable subjected to two constraints. Nevergrad has provided an utility to parse the Pyomo model to enable you to create ExperimentFunction automatically. Such ExperimentFunction contains the parameters, constraints, and an objective function to be optimized. Note that only single objective model is supported by the utility. To do this, you should first import new module.

import nevergrad as ng
import nevergrad.functions.pyomo as ng_pyomo

In our example as shown below, OnePlusOne optimizer is used to minimize the objective function:

func = ng_pyomo.Pyomo(model)
optimizer = ng.optimizers.OnePlusOne(parametrization=func.parametrization, budget=100)
recommendation = optimizer.minimize(func.function)

Finally, the result can be read using

print(recommendation.kwargs["x[0]"])
print(recommendation.kwargs["x[1]"])

Abstract Model

Pyomo model has to be fully constructed before you solve the model. When you define an AbstractModel, construction occurs in two phases. First of all, you declare and attach components to the model, those components are empty containers and not fully constructed. Next, you will fill in the containers using the create_instance() method. The create_instance() method allows you to take the abstract model and optional data and returns a new ConcreteModel instance. You are recommended to use DataPortal in Pyomo to load data in various format. You may refer to the Pyomo documentation for the details.

data = pyomo.DataPortal()
data.load(filename=data_path, model=abstract_model)
model = abstract_model.create_instance(data)

Hart2011

Hart, William E., Jean-Paul Watson, and David L. Woodruff. “Pyomo: modeling and solving mathematical programs in Python.” Mathematical Programming Computation 3, no. 3 (2011): 219-260.