Welcome to kep_solver’s documentation!


This Python package is devoted to various algorithms, procedures and mechanisms that are useful when studying kidney exchange programmes in general. It is written and maintained by William Pettersson.


kep_solver runs on Python 3.9 or higher. As long as you install via pip, all other requirements will be handled by pip

Quick start with notebooks


This package provides two sample notebooks in the notebooks folder. You can access either of these using MyBinder.

Please note that MyBinder, as a free service, does have limits on its use. For more intensive use, or where the privacy of the data you use is important, you can self-install using the following instructions.

Quick start self-install

Create a virtual environment for kep_solver

mkvirtualenv kep_solver

Install kep_solver

pip install kep_solver

Download a sample JSON file from https://kep-web.optimalmatching.com/static/jsons/sample-1.json

Run the following Python commands

# Import the required functions
from kep_solver.fileio import read_json
from kep_solver.pool import Pool
from kep_solver.model import TransplantCount

# Read some input
instance = read_json("sample-1.json")

# Create a transplant pool with one objective.
# We will allow cycles to have at most 3 donor/recipient pairs and allow chains
# to have have at most 2 donors (i.e., one non-directed donor and one
# donor/recipient pair).
pool = Pool([TransplantCount()],
            description="My first KEP Pool",

# Solve our instance
solution, model = pool.solve_single(instance)

# Print the solution
for selected in solution.selected:
    print(f"Selected {selected}")

Current features

  • Reading instance files (json and XML formats)

  • Creation of compatibility graphs

  • Solving for the following objectives (single, or hierarchical)

    • Maximise the number of transplants

    • Maximise the number of backarcs

    • Maximise the number of effective 2-way exchanges

    • Minimise the number of three-cycles

    • Maximise the score using the UK scoring mechanisms

While the above objectives are exactly those in use by NHSBT when running the UKLKSS (the UK national KEP), I do intend to add further objectives

Expected users

I see two classes of users of this software:

  • Researchers - Depending on what questions you want answered, you can either test policy changes to determine how they affect the running of a KEP, or you can implement new models or objectives to see how they perform

  • Health care institutes - I have tried to make this software as robust as possible, but for now I cannot guarantee any particular level of performance or any exact optimality of a solution. If you do want to use this software for real-world impact, feel free to get in touch and I may be able to help.


Full documentation for kep_solver can be found at https://kep-solver.readthedocs.io/en/latest/.


This is just a Python module for now, a web-interface that demonstrates a basic use case is viewable at https://kep-web.optimalmatching.com, and the source code for said website is online at https://gitlab.com/wpettersson/kep_web

Future plans

  • More objective functions

  • Random instance generation

  • Simulating the development of a KEP over time

  • Supporting transnational pools

  • Implementation of faster models and modelling techniques


I welcome input from others, whether you have ideas for improvements or want to submit code. Details on contributing can be found in CONTRIBUTING.md. You can also get in touch directly, or raise an issue


This software has been supported by the Engineering and Physical Sciences Research Council (EPSRC) grants EP/T004878/1 (Multilayer Algorithmics to Leverage Graph Structure) and EP/X013618/1 (KidneyAlgo: New Algorithms for UK and International Kidney Exchange).

Indices and tables