https://github.com/beacon-biosignals/multiwaynumberpartitioning.jl

Solving a partitioning problem exactly
https://github.com/beacon-biosignals/multiwaynumberpartitioning.jl

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Solving a partitioning problem exactly

• Host: GitHub
• URL: https://github.com/beacon-biosignals/multiwaynumberpartitioning.jl
• Owner: beacon-biosignals
• License: mit
• Created: 2021-08-17T12:45:56.000Z (about 3 years ago)
• Default Branch: main
• Last Pushed: 2022-03-31T14:48:14.000Z (over 2 years ago)
• Last Synced: 2024-07-09T19:12:30.780Z (4 months ago)
• Language: Julia
• Homepage:
• Size: 24.4 KB
• Stars: 2
• Watchers: 21
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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# MultiwayNumberPartitioning

A simple Julia package to optimally solve the [multiway number partitioning](https://en.wikipedia.org/wiki/Multiway_number_partitioning) problem

using a JuMP model with mixed-integer programming.

There is one main function `partition` which tries to accomplish the following task:

given a collection of numbers `S` and a number `k`, try to partition `S` into `k` subsets of roughly equal sum.

For example:

```julia

julia> using MultiwayNumberPartitioning, HiGHS

julia> S =  [1, 1, 1, 3, 2, 1];

julia> inds = partition(S, 3; optimizer = HiGHS.Optimizer)

6-element Vector{Int64}:

 2

 2

 3

 1

 3

 2

julia> S[inds .== 1] # group 1

1-element Vector{Int64}:

 3

julia> S[inds .== 2] # group 2

3-element Vector{Int64}:

 1

 1

 1

julia> S[inds .== 3] # group 3

2-element Vector{Int64}:

 1

 2

```

We can see all three groups here have equal sum.

See the [example](./example/example.jl) for a more detailed usage example.

## Choice of objective function

We can choose various objective functions for the algorithm to use during the optimization procedure when finding a partitioning configuration.

MultiwayNumberPartitioning.jl provides three objective functions:

* `partition_min_largest!`: minimize sum of the largest subset

* `partition_max_smallest!`: maximize the sum of the smallest subset

* `partition_min_range!`: minimize the difference between the sum of the largest subset and the smallest

(where here "largest" and "smallest" refer to the sums of the subsets).