smart-cruise 0.1.1

Find Pareto-optimal cruise trajectories to optimize energy consumption and travel time for any vehicle with state-dependent costs.

Smart Cruise

Find Pareto-optimal cruise trajectories to optimize energy consumption and travel time.

• Free software: MIT
• Documentation: https://balouf.github.io/smart-cruise/.
• Github: https://github.com/balouf/smart-cruise

Features

• Find Pareto-optimal cruise trajectories balancing energy consumption and travel time.
• Dynamic programming with multi-objective Pareto optimization.
• JIT-compiled core engine for fast computation.
• Customizable cost models for different scenarios.
• Trajectory visualization tools.

Theoretical Foundations

This package implements the multi-objective dynamic programming framework described in:

Bui-Xuan, Mathieu, Tighilt (2026). La croisière s'amuse. submitted to Algotel 2026.

Main model assumptions:

• Dominance preservation (H1): Any resource advantage at step d can be maintained through transitions
• Lipschitz continuity (H2): Small perturbations lead to bounded output changes

Complexity: O(n² log n) for 2 objectives with constant precision, vs. exponential for exact Pareto front

The pareto_max parameter (denoted S in the paper) controls the trade-off between computation time and approximation quality.

Model Applicability

This package implements a state-dependent multi-objective optimization model using dynamic programming to find Pareto-optimal trajectories. While the default parameters are tuned for ship / aircraft cruise optimization, the underlying model applies to any vehicle where:

1. Cruise mode exists: A fixed trajectory is studied, which can be split in segments.
2. A set of values (e.g. time, energy) must be optimized.
3. The rest of the state description (e.g., height, speed, ...) has finite values.
4. H1 and H2 apply.

The name Smart Cruise refers to optimizing any steady-state operation mode ("cruise") and is not restricted to, for instance, just aircraft flights.

Example Applications

Domain	"Height" dimension	"Energy" dimension	State dependency
Aircraft	Flight level/altitude	Fuel remaining	Lighter aircraft = more efficient
UAV	Altitude	Battery charge	Altitude affects efficiency
AUV	Depth	Battery charge	Depth affects drag/buoyancy
Ground vehicle	Terrain elevation	Fuel/battery	Elevation changes cost energy
Ship	Sails	Fuel remaining	Weight affects hull resistance

Scientific References

The model draws on established principles from various domains:

• Aircraft: The Breguet range equation captures state-dependent fuel consumption
• UAV optimization: Fuel-weight trajectory optimization demonstrates 25% fuel reduction through weight tracking
• Multi-rotor UAV: Energy-aware path planning shows power varies with flight state
• Fuel cell vehicles: Multi-dimensional DP for global energy optimization
• AUV trajectory: Energy-optimal MPC for underwater vehicle path planning

Quickstart

Install Smart Cruise:

$ pip install smart-cruise

Use Smart Cruise in a Python project:

>>> from smart_cruise import CostRandom, Cruise
>>> model = CostRandom(n_d=100, seed=42)
>>> cruise = Cruise(model)
>>> cruise.parameters.pareto_max = 5
>>> cruise.compute()
>>> w, t = cruise.trajectories.get_front()
>>> f"Weight optimal: {w[0]:.2f}, Time optimal: {t[-1]:.2f}"
'Weight optimal: 22979.35, Time optimal: 22734.91'

Credits

This package was created with Cookiecutter and the Package Helper 3 project template.