Syntax comparison

In order to compare the syntax between different API’s, let’s initialize the following problem in the different API’s:

\[\begin{split}& \min \;\; \sum_{i,j} 2 x_{i,j} \; y_{i,j} \\ s.t. & \\ & x_{i,j} - y_{i,j} \; \ge \; i \qquad \forall \; i,j \in \{1,...,N\} \\ & x_{i,j} + y_{i,j} \; \ge \; 0 \qquad \forall \; i,j \in \{1,...,N\}\end{split}\]

In JuMP the formulation translates to the following code:

using JuMP

function create_model(N)
    m = Model()
    @variable(m, x[1:N, 1:N])
    @variable(m, y[1:N, 1:N])
    @constraint(m, [i=1:N, j=1:N], x[i, j] - y[i, j] >= i)
    @constraint(m, [i=1:N, j=1:N], x[i, j] + y[i, j] >= 0)
    @objective(m, Min, sum(2 * x[i, j] + y[i, j] for i in 1:N, j in 1:N))
    return m
end

The same model in linopy is initialized by

from linopy import Model
from numpy import arange


def create_model(N):
    m = Model()
    x = m.add_variables(coords=[arange(N), arange(N)])
    y = m.add_variables(coords=[arange(N), arange(N)])
    m.add_constraints(x - y >= arange(N))
    m.add_constraints(x + y >= 0)
    m.add_objective((2 * x).sum() + y.sum())
    return m

Note that the syntax is quiet similar. An important difference lays in the fact that linopy operates all arithmetic operations on variable arrays, while the JuMP syntax uses control variables i and j.

In Pyomo the code would look like

from numpy import arange
from pyomo.environ import ConcreteModel, Constraint, Objective, Set, Var


def create_model(N):
    m = ConcreteModel()
    m.N = Set(initialize=arange(N))

    m.x = Var(m.N, m.N, bounds=(None, None))
    m.y = Var(m.N, m.N, bounds=(None, None))

    def bound1(m, i, j):
        return m.x[(i, j)] - m.y[(i, j)] >= i

    def bound2(m, i, j):
        return m.x[(i, j)] + m.y[(i, j)] >= 0

    def objective(m):
        return sum(2 * m.x[(i, j)] + m.y[(i, j)] for i in m.N for j in m.N)

    m.con1 = Constraint(m.N, m.N, rule=bound1)
    m.con2 = Constraint(m.N, m.N, rule=bound2)
    m.obj = Objective(rule=objective)
    return m

which is heavily based on the internal call of functions in order to define the constraints.