HLPL / VerTeX Modelling Language Documentation

← lessons

Binary variables

Yes or no, on or off.

Chapter: IV — Discrete decisions · lesson id binary-variables · practice lesson

---

bin x declares a 0/1 variable — you either pick it or you don't. This is the cornerstone of discrete decision-making.

Three binary variables compete under a sum cap. The objective tells the solver which to prefer.

Predict before running

For max 5*a + 3*b + 4*c with a + b + c <= 2, which two binaries flip on?

• a and b (objective 8)
• a and c (objective 9)
• b and c (objective 7)

Starter code

model binary_pick
bin a
bin b
bin c
constr a + b + c <= 2
max 5*a + 3*b + 4*c
end

import elytica
def main():
  elytica.init_model("binary_pick")
  elytica.run_model("binary_pick")
  print("a =", elytica.get_variable_value("binary_pick", "a"))
  print("b =", elytica.get_variable_value("binary_pick", "b"))
  print("c =", elytica.get_variable_value("binary_pick", "c"))
  print("obj =", elytica.get_best_primal_bound("binary_pick"))
  return 0

Hint

The constraint allows at most two of the three. Pick the two with the largest weights.

What counts as correct

• no-error — Model solves
• numeric-match — Optimal value is 9 (a + c)
• numeric-match — Picks a
• numeric-match — Picks c
• numeric-match — Skips b
• code-contains — Reads the objective from the solver (no hardcoding)
• code-contains — Reads variable values from the solver (no hardcoding)

Mastery variant

Four binaries this time. Pick at most three. Which one gets dropped?

model binary_pick_v
bin p
bin q
bin r
bin s
constr p + q + r + s <= 3
max 7*p + 4*q + 6*r + 5*s
end

import elytica
def main():
  elytica.init_model("binary_pick_v")
  elytica.run_model("binary_pick_v")
  print("p =", elytica.get_variable_value("binary_pick_v", "p"))
  print("q =", elytica.get_variable_value("binary_pick_v", "q"))
  print("r =", elytica.get_variable_value("binary_pick_v", "r"))
  print("s =", elytica.get_variable_value("binary_pick_v", "s"))
  print("obj =", elytica.get_best_primal_bound("binary_pick_v"))
  return 0

Read this through MCP: read with path: "lessons/binary-variables", or resource hlpl://lessons/binary-variables.