02-modeling-primitives.md

RAMS: Modeling Primitives

The first class you need to instantiate is RAMS::Model. Everything else is created by interacting with instances of the Model class.

require 'rams'

m = RAMS::Model.new

Variables

Variables can be continuous (the default), integer, or binary. They are associated with an individual model.

x1 = m.variable
x2 = m.variable type: :integer
x3 = m.variable type: :binary

By default, a continuous variable has a lower bound of 0 and an upper bound of nil, representing positive infinity.

puts "#{m.variables.values.map { |x| [x.low, x.high ]}}"

[[0.0, nil], [0.0, nil], [0.0, nil]]

To set a variable's lower bound to negative infinity, pass a low: inf keyword argument to the Model.variable method. Similarly, upper bounds can be passed in to Model.variable using the high keyword argument.

x4 = m.variable(type: :integer, low: nil, high: 10)

The binary variables may appear to have an upper bound of positive infinity, but that becomes 1 when it is written to the solver. To see a model the way it is passed to a solver, use the to_lp method. This returns the model in LP format. Note that the variable names are different in the to_lp output.

puts m.to_lp

max
  obj: 0 v1
st

bounds
  0.0 <= v1 <= +inf
  0.0 <= v2 <= +inf
  0.0 <= v3 <= 1.0
  -inf <= v4 <= 10
general
  v2
  v4
binary
  v3
end

Constraints

Now we're ready to add some constraints. These can be done using linear inequalities and the Model.constrain method.

c1 = m.constrain(2*x1 + x2/2 <= 5)
c2 = m.constrain(x2 + x3 >= 2 - x4)
c3 = m.constrain(x2 == 2*x3)

When an inequality is instantiated, all the variables are moved into its lhs attribute, and the constant is stored in its rhs attribute. The sense of the inequality is also available.

puts <<-HERE
#{c1.lhs[x1]} * x1 + #{c1.lhs[x2]} * x2 #{c1.sense} #{c1.rhs}
#{c2.lhs[x2]} * x2 + #{c2.lhs[x3]} * x3 + #{c2.lhs[x4]} * x4 #{c2.sense} #{c2.rhs}
#{c3.lhs[x2]} * x2 + #{c3.lhs[x3]} #{c3.sense} #{c3.rhs}
HERE

2.0 * x1 + 0.5 * x2 <= 5.0
1.0 * x2 + 1.0 * x3 + 1.0 * x4 >= 2.0
1.0 * x2 + -2.0 == 0.0

Objective Functions

The objective sense is available through the sense attribute. :max is the default. To minimize, set the sense to :min. Similarly, assign to the objective attribute to set the objective function. RAMS defaults to no objective function, or feasibility models. Explicitly setting the sense is always a good idea.

m.objective = x1 + 2*x2 + 3*x3 - x4
m.sense = :max

Solutions

To get a model solution, simply call solve. The objective, primal variable values, and dual prices can be accessed directly off of this object, along with the solution status.

puts <<-HERE
z = #{solution.objective}
x = #{[x1, x2, x3, x4].map { |x| solution[x] }}
y = #{[c1, c2, c3].map { |c| solution.dual[c] }}
HERE

z = 10.0
x = [2.0, 2.0, 1.0, -1.0]
y = [5.0, 0.0, 0.0]