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Quantum Solver for Vehicle Routing Problems

This packages offers utilities to model and solve Vehicle Routing Problems (VRP) using quantum algorithms, such as QAOA and Quantum Annealing.

This project was part of a Master's Thesis named "Quantum Algorithms for Optimizing Urban Transportation" developed by Bruno Rosendo. The thesis can be found at Repositório Aberto.

Feel free to use this code as a reference for your projects and experiments, but please keep the licence intact.

How to Use

To use the solvers, you must choose your preferred model (CVRP or RPP) and solver (D-Wave, Qiskit or Classic) and set the parameters for the routing problem and platform. You can then solve and visualize or save the results.

An example of a simple CVRP problem with the D-Wave solver is shown below:

from vrp_quantum_solver.model.dispatcher import CVRP
from vrp_quantum_solver.solver.qubo.DWaveSolver import DWaveSolver

# Define the problem parameters
model = CVRP(1, [(46, 32), (20, 32), (71, 32), (46, 60), (46, 4)], 5, [1] * 5)

# Define the solver
solver = DWaveSolver(model)

# Solve the problem
solution = solver.solve()

# Display the solution
solution.display()

Choosing the Model

Currently, the project supports four routing problem variations: Vehicle Routing Problem (VRP), Capacitated VRP (CVRP), Multi-Capacitated VRP (MCVRP) and Ride Pooling Problem (RPP). You can find details about each problem in the thesis document.

The model be chosen by using one of two dispatcher functions: CVRP or RPP, depending on which problem you're trying to solve. The functions reside in model/dispatcher.py. The right variation will be used depending on the parameters you set.

These functions use a set of parameters that will define the routing problem at hand. These parameters are in the table:

Parameter Type Description Default
num_vehicles int Number of vehicles in the problem. -
capacities int | list[int] | None Capacity for the vehicles. You can also specify for each or use None for infinite capacity. -
locations list[tuple[float, float]] List of coordinates representing the locations in the problem. -
demands list[int] List of demands for each location. Must be specified if capacities is not None. The minimum demand is 1 for each location. Used only for CVRP. None
trips list[tuple[int, int, int]] List of trips in the format (src, dest, demand). Used only for RPP. -
cost_function Callable Cost function used to generate a distance matrix. See below for details. Manhattan Distance
distance_matrix list[list[float]] Optional parameter to set the distance matrix directly. None
location_names list[str] Optional list of location names used for display. None
distance_unit DistanceUnit Unit used for distance/cost. Used for proper visualization. Meters

Choosing the Solver

D-Wave Solver (Leap)

The DWaveSolver interacts with D-Wave's Leap cloud provider and is this project's most recommended quantum solver.

To set it up, you need to authenticate yourself in one of three ways:

  • Copy your API token from the platform and create a .env file in the project's root with the line DWAVE_API_TOKEN=<token>.
  • Create a DWAVE_API_TOKEN environment variable under your Python (virtual) environment with your API token.
  • Install the dwave-ocean-sdk package and authenticate there.

This solver has the following parameters that can be configured:

Parameter Type Description Default
track_progress bool Whether to track progress by printing logs every iteration of the algorithm. True
sampler Sampler The sampler for the annealing. It can be a classical or quantum sampler. ExactCQMSolver
embedding Embedding Embedding class used to embed the problem into the quantum hardware. EmbeddingComposite
embed_bqm bool If using a BQM sampler, locally embed the problem before sampling. True
num_reads int If using a BQM sampler, sets a fixed number of reads. None
time_limit int Optionally sets a time limit for the annealing process in seconds. If not specified, the sampler usually has its default value. None
embedding_timeout int Optionally sets a time limit for the embedding process in seconds. If not specified, the sampler usually has the default value of 1000 seconds. None

Qiskit Solver (IBM)

The QiskitSolver interacts with the IBM Quantum cloud platform.

To set it up, you need to authenticate yourself in one of two ways:

  • Copy your API token from the platform and create a .env file in the project's root with the line IBM_TOKEN=<token>.
  • Create an IBM_TOKEN environment variable under your Python (virtual) environment with your API token.
  • To solve it in a quantum computer, you can use the get_backend_sampler() function to get the right sampler.

This solver has the following parameters that can be configured:

Parameter Type Description Default
track_progress bool Whether to track progress by printing logs every iteration of the algorithm. True
classical_solver bool Whether to use a classical optimizer (CPLEX) instead of a quantum optimizer. False
sampler Sampler The sampler used in the quantum optimizer. It can either be a simulator or a real quantum computer. Sampler
classical_optimizer Optimizer Classical optimizer used to decide new parameters in between QAOA iterations. COBYLA
warm_start bool Whether to run QAOA with a warm start. False
pre_solver OptimizationAlgorithm Classical optimizer used to pre-solve the problem if warm start is used. CplexOptimizer

Classic Solver (OR-Tools)

The ClassicSolver uses the Google OR-Tools library to solve the routing problem classically. This is a great way to test your inputs or compare the quantum solvers with a well-known classical solver.

This solver does not require any authentication, as it is a local solver. It has the following parameters that can be configured:

Parameter Type Description Default
track_progress bool Whether to track progress by printing logs every iteration of the algorithm. True
solution_strategy FirstSolution (enum) First solution strategy. The method used to find an initial solution. Automatic
local_search_metaheuristic LocalSearch (enum) Local search strategy (metaheuristic) used by the solver. Automatic
distance_global_span_cost_coefficient int The coefficient is multiplied by each vehicle’s travelled distance and is helpful to distribute distance between routes. 1
time_limit_seconds int Maximum execution time in seconds. 10
max_distance_capacity int Maximum capacity for the distance dimension within OR-Tools. This doesn't need to be changed unless some overflow error happens. 90000

Cost functions

A cost function generates a distance matrix from the locations list. The default cost function is the Manhattan distance, but you can define your own cost function by creating a function that takes a list of coordinates and returns the matrix. For example:

from vrp_quantum_solver.model.VRP import DistanceUnit

def manhattan_distance(
    locations: list[tuple[int, int]], unit: DistanceUnit = DistanceUnit.METERS
) -> list[list[float]]:
    """
    Compute the Manhattan distance between all locations.
    """

    return [
        [
            abs(from_location[0] - to_location[0])
            + abs(from_location[1] - to_location[1])
            for to_location in locations
        ]
        for from_location in locations
    ]

The project currently supports the following distance units: manhattan_distance, euclidean_distance, haversine_distance and distance_api.

The last one, distance_api, is a particular cost function that uses Google's Distance Matrix API to calculate the distance between locations. This is useful for real-world problems where the distance matrix is unknown beforehand. To use it, you must set the GOOGLE_API_KEY environment variable with your API key by adding it to the .env file or setting it in your (virtual) environment.

Running the Solver

After defining the problem and choosing the solver, you can run the solver with the solve() method. This will return a VRPSolution object. You can then visualize the solution in the browser with the display() method, print it to the console using the print() method, or save it to a file with the save_json() method.

Loading a solution from a JSON file using the VRPSolution from_json() static method is also possible. This is useful for comparing solutions or visualizing them later.

Development setup

If you want to contribute to this project, follow the instructions below to set up your development environment. Feel free to open issues or pull requests with questions or suggestions.

Prerequisites

  • Python 3.10+
  • pip3
  • All the dependencies listed in the requirements.txt file, installed via pip

Code Formatting

We use the Black formatter for all Python code. There is no specific linter, as Black is an opinionated formatter that enforces a consistent style.

Project Structure

  • model/ - All classes and functions related to the VRP models and adapters.
  • qiskit_algorithms/ - Modified version of the qiskit-algorithms used in the project.
  • solvers/ - Quantum and classical solvers for the VRP.