A matching problem generator and solver.

## Project description

# matchingproblems

This python package can generate and solve single or multiple matching problem instances using the PuLP Linear Program (LP) Solver.

It can be used both for individual real-world runs (for example to assign students to projects at your university), and for experimental work including correctness testing of the LP using a brute force approach (smaller instances only).

- Installation
- Generator
- Solver
- Testing details

## 1) Installation

The simplest way to install this package is via Pip.

```
pip install matchingproblems
```

Alternatively the package may be downloaded from this git repository and installed manually.

## 2) Generator

Instances of the following types can be generated:

- HA - House Allocation Problem (and variants)
- SM - Stable Marriage Problem (and variants)
- HR - Hospital/Residents Problem (and variants)
- SPA - Student-Project Allocation Problem (and variants)

For a definition of each of these problems, please see Chapter 2 of this thesis.

Example run_generator.py script to run the generator:

```
from matchingproblems import generator
import sys
if __name__ == "__main__":
generator = generator.Generator(sys.argv[1:])
```

This program may then be called as follows:

```
python run_generator.py [-h] -numinst NUMBERINSTANCES -o OUTPUTDIRECTORY -mp {ha,sm,hr,spa}
[-twopl] [-skew SKEW] [-n1 N1] [-n2 N2] [-n3 N3]
[-pmin MINPREFLISTLENGTH] [-pmax MAXPREFLISTLENGTH] [-t1 TIES1] [-t2 TIES2]
[-lq LOWERQUOTAS] [-uq UPPERQUOTAS] [-llq LECTURERLOWERQUOTAS] [-luq LECTURERUPPERQUOTAS] [-lt LECTURERTARGETS]
```

Alternatively, arguments may be defined in the python script itself.

Arguments have the following meanings:

Argument | Meaning |
---|---|

`-h, --help` |
Show help message and exit. |

`-numinst x, --numberinstances x` |
Total number of instances to generate. |

`-o x, --outputdirectory x` |
Output directory path. |

`-mp {ha,sm,hr,spa}, --matchingproblem {ha,sm,hr,spa}` |
Matching problem type, as specified above. |

`-twopl, --preferencelists2` |
Preference lists on both sides of the matching problem. |

`-skew x, --linearskew x` |
Linear skew for preference lists, a value of x indicates that the most popular agent is x times more popular than the least. |

`-n1 x, --numberofagents1 x` |
Number of applicants (HA) / men (SM) / residents (HR) / students (SPA). |

`-n2 x, --numberofagents2 x` |
Number of houses (HA) / hospitals (HR) / projects (SPA). |

`-n3 x, --numberofagents3 x` |
Number of lecturers (SPA). |

`-pmin x, --minpreflistlength x` |
Minimum size of preference lists for applicants (HA) / men (SM) / residents (HR) / students (SPA). |

`-pmax x, --maxpreflistlength x` |
Maximum size of preference lists for applicants (HA) / men (SM) / residents (HR) / students (SPA). |

`-t1 x, --ties1 x` |
Probability of ties for applicants (HA) / men (SM) / residents (HR) / students (SPA) [0.0, 1.0]. |

`-t2 x, --ties2 x` |
Probability of ties for women (SM) / hospitals (HR) / lecturers (SPA) [0.0, 1.0]. |

`-lq x, --lowerquotas x` |
Sum of lower quotas for houses (HA) / hospitals (HR) / projects (SPA). |

`-uq x, --upperquotas x` |
Sum of upper quotas for houses (HA) / hospitals (HR) / projects (SPA). |

`-llq x, --lecturerlowerquotas x` |
Sum of lower quotas for lecturers (SPA). |

`-lt x, --lecturertargets x` |
Sum of targets for lecturers (SPA). |

`-luq x, --lecturerupperquotas x` |
Sum of upper quotas for lecturers (SPA). |

HA instances require the following arguments to be specified: `-n1 -n2 -pmin -pmax -uq`

SM instances require the following arguments to be specified: `-n1 -pmin -pmax -twopl`

HR instances require the following arguments to be specified: `-n1 -n2 -pmin -pmax -uq -twopl`

SPA instances require the following arguments to be specified: `-n1 -n2 -n3 -pmin -pmax -uq -luq`

Two examples of calls to run_generator.py are as follows:

```
# Generates 5 HR instances
python run_generator.py -numinst 5 -o ./hr/instances -mp hr -n1 6 -n2 4 -pmin 2 -pmax 4 -t1 0.2 -t2 0.2 -skew 5 -lq 4 -uq 6 -twopl
```

```
# Generates 5 SPA instances with one-sided preference lists
python run_generator.py -numinst $NUMINSTANCES -o ./spa/instances -mp spa -n1 6 -n2 8 -n3 4 -pmin 3 -pmax 5 -t1 0.2 -t2 0.2 -skew 5 -lq 4 -uq 10 -llq 1 -lt 4 -luq 10 -twopl
```

## 3) Solver

Each input instance of HA, SM, HR or SPA is converted into an instance of SPA-STL (the Student-Project Allocation Problem with lecturer preferences over Students including Ties and Lecturer targets) and solved using the PuLP LP Solver.

Example run_solver.py script to run the solver:

```
from matchingproblems import solver
import sys
if __name__ == "__main__":
solver = solver.Solver(sys.argv[1:])
solver.solve(msg=False, timeLimit=None, threads=None, write=False)
# print(solver.get_debug())
# print(solver.get_results())
# print(solver.get_results_short())
print(solver.get_results_long())
```

This program may then be called as follows:

```
python run_solver.py [-h] -f FILENAME -na NUMAGENTS
[-twopl] [-pc] [-stab] [-maxsize MAXSIZE] [-minsize MINSIZE] [-gen GEN]
[-gre GRE] [-mincost MINCOST] [-minsqcost MINSQCOST] [-lmb LMB] [-lsb LSB] [-bf]
```

As with the generator, an alternative is to specify arguments in the python script.

Arguments have the following meanings:

Argument | Meaning |
---|---|

`-h, --help` |
Show help message and exit. |

`-f x, -filename x` |
Input file name. |

`-na x, -numagents x` |
Number of agents in the instance (2 for HA, SM and HR, 3 for SPA). |

`-twopl, -twosidedpreferencelists` |
Men (SM), Hospital (HR) or lecturer (SPA) preference lists present. |

`-pc, -projectclosures` |
Project closures allowed. |

`-stab, -stability` |
Add stability constraints |

`-maxsize x, -maximisesize x` |
Maximise size at the given optimisation position. |

`-minsize x, -minimisesize x` |
Minimise size at the given optimisation position. |

`-gen x, -generous x` |
Performs generous optimisation at the given optimisation position. |

`-gre x, -greedy x` |
Performs greedy optimisation at the given optimisation position. |

`-mincost x, -minimisecost x` |
Minimise cost at the given optimisation position. |

`-minsqcost x, -minimisesquaredcost x` |
Minimises sum of squares of costs at the given optimisation position. |

`-lmb x, -loadmaxbalanced x` |
Minimises the maximum absolute difference between lecturer occupancy and target at the given optimisation position. |

`-lsb x, -loadsumbalanced x` |
Minimises the sum of absolute differences between lecturer occupancies and targets at the given optimisation position. |

`-bf, -bruteforce` |
Solve using the brute force method. |

Two examples of calls to run_solver.py are as follows:

```
# Find a generous maximum matching in an HA, SM or HR instance.
python run_solver.py -f ./path/to/instance.txt genmax -na 2 -maxsize 1 -gen 2 -twopl
```

```
# Find optimal assignments for an SPA instance with one sided preference lists using a brute force approach.
python run_solver.py -f ./path/to/instance.txt -na 3 -bf
```

## 4) Testing details

Unit tests may be run by executing the `test.sh`

script in this git repository.

Correctness testing which compared output from the LP Solver and brute force programs was conducted on some optimisations. Results for this testing can be seen at this zenodo repository.

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