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Getting Started with Jia

Jia is a unified modelling language for constraint programming (CP) and linear programming (LP). You describe a problem as variables, their domains, and the constraints that must hold — then the solver finds a solution.

Model structure​

Every Jia model follows an X, D, C pattern:

model <name>

variables { ... }   // X — declare decision variables and their types

domains   { ... }   // D — bound variable attributes, assign set membership

constraints { ... } // C — relationships that must hold in any valid solution

minimize <expr>     // optional objective

Sections can appear in any order. Comments start with //.

Your first LP model​

Linear programming operates on continuous Real variables. Declare the model type with @model lp at the top of the file.

@model lp
model simple_lp

variables {
  Real: x, y
}

domains {
  x in 0..inf
  y in 0..inf
}

constraints {
  x + y >= 10
}

minimize x + y

The solver will find the values of x and y that minimise x + y while satisfying x + y >= 10 and both variables being non-negative. The optimal solution is x = 0, y = 10 (or any split summing to 10).

Your first CP model​

Constraint programming operates on Interval variables — tasks with a start time, end time, and duration. CP models do not require an @model tag.

model two_tasks

variables {
  Interval: task_a, task_b
}

domains {
  duration(task_a) = 3
  duration(task_b) = 2
}

constraints {
  end_of(task_a) <= start_of(task_b)
}

minimize end_of(task_b)

This model schedules two tasks where task_a must finish before task_b starts, and minimises when task_b finishes. The optimal schedule starts task_a at 0 (ends at 3) and task_b at 3 (ends at 5).

Running a model​

Use the jia-cp CLI for CP models and jia-lp for LP models:

# CP
jia-cp path/to/model.jia

# LP
jia-lp path/to/model.jia

Both print the objective value and the variable assignments found by the solver.

Next steps​