●  How to use · Scheduling

Flight crew scheduling

Staff every seat on every flight with crew who hold the right qualification, without overlaps and with feasible connections.

What it decides

For every crew seat on every flight, the solver picks a crew member.

Minimal example

from datetime import datetime, timedelta

from optimaru import flight_crew_scheduling as fc
from optimaru.flight_crew_scheduling.models import (
    AirportModel, EmployeeModel, FlightAssignmentModel, FlightCrewScheduleModel, FlightModel,
)

out = datetime(2026, 1, 5, 8)
flights = [
    FlightModel(flight_number="OUT", departure_airport="ICN", departure_utc_date_time=out,
                arrival_airport="NRT", arrival_utc_date_time=out + timedelta(hours=2)),
    FlightModel(flight_number="BACK", departure_airport="NRT",
                departure_utc_date_time=out + timedelta(hours=5),
                arrival_airport="ICN", arrival_utc_date_time=out + timedelta(hours=7)),
]
problem = FlightCrewScheduleModel(
    airports=[AirportModel(code="ICN"), AirportModel(code="NRT")],
    employees=[EmployeeModel(id="P1", home_airport="ICN", skills=["Pilot"])],
    flights=flights,
    flight_assignments=[
        FlightAssignmentModel(id=f"A{i}", flight=f.flight_number, required_skill="Pilot")
        for i, f in enumerate(flights)
    ],
)

result = fc.solve(problem, time_limit_seconds=2.0, random_seed=42)
print(result.score_hard, result.score_soft)
print({a.id: a.employee for a in result.flight_assignments})

The same use case as a Jupyter notebook, with charts and saved outputs: examples/flight-crew-scheduling.ipynb ↗

Input parameters

AirportModel

Field Meaning
code required Airport code. Flights and crew refer to it.

EmployeeModel

Field Meaning
id required Crew member id. home_airport required Code of the home airport. skills Qualifications the person holds. unavailable_days Dates the person cannot fly.

FlightModel

Field Meaning
flight_number required Flight id. departure_airport required Code of the departure airport. departure_utc_date_time required Departure in UTC. A naive datetime is read as UTC. arrival_airport required Code of the arrival airport. arrival_utc_date_time required Arrival in UTC.

FlightAssignmentModel

Field Meaning
id required Seat id. flight required flight_number of the flight. required_skill Qualification the seat needs. pinned Keep the seat's employee: it counts in the score but never moves.

FlightCrewScheduleModel

Field Meaning
airports required Airports. employees required Crew. flights required Flights. flight_assignments required One entry per crew seat.

Solve parameters

What you pass to the solve call. Time limit, seed and parallel count are here.

Parameter Default Meaning
time_limit_seconds None Search budget in seconds, from 0 to 1e9. Left unset, it is the config's spent_limit_seconds, 30 by default.
random_seed None Seed for the search. Left unset, it is the config's value, 0 by default.
parallel_solver_count None Independent parallel starts. Each gets its own seed and the full budget, and the best result wins. Left unset, it is the config's value, 1 by default.
stop_at_first_feasible False Stop as soon as hard 0 is reached.
on_new_best None Callback run on each new best solution. If it raises, the solve stops and raises the same exception.
config None A SolverConfig as the base configuration. Keyword arguments here override it for this solve only; the object you pass is not changed.
constraints None Which constraints to score, and how. Left unset, the defaults apply.
All search options (20)

Set these on a SolverConfig and pass it as config=.

Parameter Default Meaning
best_score_limit — Stop early once the best score reaches this value. By default it never fires.
change_move_weight 0.75 Relative share of change moves. 0 disables them.
full_assert False Check every incremental score against a full recompute. Slow; for debugging.
late_acceptance_size 0 Late-acceptance history length. 0 picks it from the instance size.
on_new_best None Callback run on each new best solution. If it raises, the solve stops and raises the same exception.
parallel_solver_count 1 Independent parallel starts, each with its own seed and the full budget. The best one wins.
random_seed 0 Seed for the search.
ruin_recreate True Run adaptive ruin-and-recreate kicks when the search stagnates.
ruin_recreate_max_ruin_count 60 Absolute cap on entities removed per kick.
ruin_recreate_max_ruin_fraction 0.3 Largest share of the solution one kick removes.
ruin_recreate_min_ruin_fraction 0.1 Smallest share of the solution one kick removes.
ruin_recreate_operator_decay 0.8 How fast operator weights adapt.
ruin_recreate_polish_steps 5000 Hill-climbing moves that polish each kick. Not counted against step_count_limit.
ruin_recreate_rewards [33.0, 9.0, 3.0, 0.0] Operator rewards for a new best, a better, an accepted and a rejected result.
ruin_recreate_unimproved_step_trigger 5000 Steps without a new best before a kick.
spent_limit_seconds 30.0 Time budget in seconds, from 0 to 1e9.
step_count_limit 0 Stop after this many steps. 0 means no limit.
swap_move_weight 0.25 Relative share of swap moves. 0 disables them.
unimproved_spent_limit_seconds 0.0 Stop after this many seconds without a new best. 0 means no limit.
unimproved_step_count_limit 0 Stop after this many steps without a new best. 0 means no limit.

What comes back

solve takes the model, or a dict of the same shape, and returns the solved model.

FlightAssignmentModel

Field Meaning
employee Id of the crew member on this seat. None means unassigned.

FlightCrewScheduleModel

Field Meaning
score_hard Hard score. 0 means feasible. score_soft Soft score.

Constraints

Pick them by calling their classes from optimaru.flight_crew_scheduling.constraints, such as RequiredSkillCost(). Only what you pass is scored; pass nothing to keep the defaults. A list may name a constraint more than once, and each pick is scored on its own. Each one takes these parameters:

Parameter Default Meaning
weight None Multiplier on the constraint's cost, in units of the level in effect. Left unset, the default weight below applies. A constraint whose default weight is 0 is off until you give it a weight.
level None "hard" makes the constraint a must and "soft" a preference, as do Level.HARD and Level.SOFT. Left unset, it keeps the level below. This use case has no medium level, so "medium" raises ValueError. A reward refuses "hard", and a fixed level refuses any change; both raise ValueError.
exponent 1.0 Sign-preserving power on the cost, above 0, taken after offset. 2.0 squares it, so concentrated violations cost much more. It applies per unit, such as a vehicle or a day, or to the total of a constraint scored as one sum.
offset 0.0 Subtracted from the cost x before the exponent, per unit or total like the exponent. It is in the cost's own measure: seconds, minutes, a count and so on. Any finite number of either sign, keyword only. clip decides what happens below it.
clip True True makes offset a threshold: only the part beyond it counts, max(0, x - offset) ** exponent, so a cost at or below it adds nothing. False takes the literal (x - offset) ** exponent, sign kept: a unit below the offset counts negative, as a reward, even one whose cost is 0. On a level that counts toward hard, clip=False with a non-zero offset raises ValueError, since hard 0 must mean no violation. Keyword only.

This continues the minimal example above.

from optimaru.flight_crew_scheduling.constraints import (
    EmployeeUnavailabilityCost, FlightConflictCost, RequiredSkillCost, get_constraints,
)

picked = get_constraints([
    RequiredSkillCost(), FlightConflictCost(), EmployeeUnavailabilityCost(level="soft"),
])
custom = fc.solve(problem, time_limit_seconds=2.0, random_seed=42, constraints=picked)
print(custom.score_hard, custom.score_soft)
Name Level Default weight What it does
required_skill_cost Hard 100 A crew member on a seat without the skill it requires.
flight_conflict_cost Hard 10 Pairs of one person's assignments that overlap in time.
transfer_between_two_flights_cost Hard 1 An arrival airport that differs from the person's next departure airport.
employee_unavailability_cost Hard 10 An assignment touching an unavailable date, from departure date to arrival date.
first_assignment_not_departing_from_home_cost Soft 1000 A person's first assignment not leaving from home_airport.
last_assignment_not_arriving_at_home_cost Soft 1000 A person's last assignment not ending at home_airport.

How constraints work →

Starting from an existing solution

This needs the latest release: pip install -U optimaru.

with_initial_solution(problem, solution) returns a copy of problem whose search starts from solution, the model a solve returned or that model as a JSON dict.

This continues the minimal example above.

seeded = fc.with_initial_solution(problem, result.model_dump(mode="json"))
again = fc.solve(seeded, time_limit_seconds=2.0, random_seed=43)
print(again.score_hard, again.score_soft)
  • Assignments are matched by id.
  • A complete solution skips construction: the search starts exactly from it. A partial one keeps what it gives, and only the assignments it leaves out are constructed.
  • With time_limit_seconds=0 the solve stops at once, so a complete solution comes back as it went in. Use the time limit for this: step_count_limit = 0 means no limit.
  • Pinned assignments keep their employee on problem, whatever the solution says.
  • Unknown ids raise ValueError.

Exceptions and limits

  • There is no rest-time or duty-hour rule. The hard rules are skills, overlaps, connections and unavailable dates.