Who is this for

This particular package is most likely to be useful for people either developing algorithms for techniques for KEPs, or setting kep_solver for use within an organisation with specific requirements. A sample web interface is viewable at, and the code for said interface is at


This package is available via pip, and requires Python 3.9 at least. To install it, I recommend using a Python virtual environment (see virtualenvwrapper for an easy-to-use introduction) and then running pip install kep_solver

Reading and inspecting instances

File IO functionality is available in the kep_solver.fileio module module. The following code should read in any supported file format.

from kep_solver.fileio import read_file
instance = read_file("instance.json")

Instances can be analysed for a number of properties, as can the Donor and Recipient entities they contain. These are documented in kep_solver.entities module.

print(f"This instance has {len(instance.recipients())} recipients")

Analysing the compatibility graph

The underlying compatibility graph can be accessed by creating a Compatibility Graph object as follows. Specifics are documented in kep_solver.graph module.

graph = CompatibilityGraph(instance)
cycles = graph.findCycles(maxCycleLength)
chains = graph.findChains(maxChainLength)
print(f"There are {len(cycles)} cycles and {len(chains)} chains")

Using different models

Different IP models can be used for solving KEP instances, and kep_solver currently supports two such models: the kep_solver.models.CycleAndChainFormulation [Abraham07] [Roth07] and kep_solver.models.PICEF [Dickerson16]. PICEF is currently significantly faster for longer chain lengths, but not all objectives are able to be used with PICEF. As such, the cycle and chain formulation is still the default. An example using PICEF is given below.

from kep_solver.model import PICEF
model = PICEF(
solution, model_times, numSols = model.solve()

You can also create a kep_solver.pool.Pool that uses kep_solver.models.PICEF by default.

from kep_solver.pool import Pool
from kep_solver.model import TransplantCount, PICEF
pool = Pool(
            description="My PICEF Pool",
solution, model = pool.solve_single(instance)

As mentioned above, not all objectives are compatible with PICEF. If you see an exception stating that “Edge value is not defined for this objective”, then this indicates that the objective cannot be used with PICEF as the model.

Creating new objectives

New objectives can be created by inheriting from the kep_solver.model.Objective and implementing kep_solver.model.Objective.value() (as well as a constructor). Note that if you wish to use kep_solver.model.PICEF you will also need to implement kep_solver.model.Objective.edgeValue() which takes as input the compatibility graph, the edge of the compatibility, and also the position of said edge in the chain. An example objective that maximises the number of 4-chains using either PICEF or the cycle formulation is given below. Note that for PICEF, this functions by counting each edge used in 4th position in a chain positively, but subtracting each edge used in 5th position in a chain.

from typing import Optional
from kep_solver.graph import CompatibilityGraph, Edge, Exchange
from kep_solver.model import Objective, Sense

class FourChain(Objective):

    def __init__(self):

    def edgeValue(
        self, graph: CompatibilityGraph, edge: Edge, position: Optional[int] = None
    ) -> float:
        """What value should the given transplant in the given graph be given,
        if it is at the given position (i.e., position = 1 means this is the
        first edge in a chain)?

        :param graph: The graph containing the exchange
        :param edge: The edge, representing a transplant
        :param position: The position of this edge in an exchange
        :return: The value of this edge in this position
        if position == 4:
            return 1
        if position == 5:
            return -1
        return 0

    def value(self, graph: CompatibilityGraph, exchange: Exchange) -> float:
        """Is the given exchange a 4-chain.

        :param graph: The graph containing the exchange
        :param exchange: A cycle or chain.
        :return: the number of transplants
        if exchange.chain and len(exchange) == 4:
                return 1
        return 0

    def describe(self) -> str:
        """Describes what this objective optimises.

        :return: the description
        return "Number of 4-chains"

    def sense(self) -> Sense:
        """This is a maximisation objective."""
        return Sense.MAX