[PYTHON] Combinatorial optimization-typical problem-combinatorial auction problem

Typical problem and execution method

Combination auction problem

$ n $ Candidates (set $ M = \ {1, \ dots, m \} $ subset $ S_j (\ subseteq M), j \ in N = \ {1, \ dots, n \ } $) Is given the amount $ c_j $. Select from the candidates so that the total amount of money is maximized. Do not select duplicate elements of the set $ M $ It can also be considered that the objective function is maximized and the constraint inequality sign is reversed in Set Cover Problem.

Execution method

usage

Signature: combinatorial_auction(n, cand, limit=-1)
Docstring:
Combination auction problem
Maximize the sale price so that the maximum number of candidates for each purchaser is not exceeded without duplicate selling of elements
input
    n:Element count
    cand: (Amount of money,Subset,Buyer ID)Candidate list. You do not have to have a purchaser ID
    limit:Maximum number of candidates for each purchaser.-1 is unlimited. A dictionary using the purchaser ID as a key is possible
output
Number list of selected candidate list

python

#sample
from ortoolpy import combinatorial_auction
cand = [
    ( 15, (0,2), 0),
    ( 10, (0,), 1),
    (  8, (1,), 1),
    ( 14, (1,2), 2),
]
combinatorial_auction(3, cand)

result

[1, 3]

python

# pandas.DataFrame
from ortoolpy.optimization import CombinatorialAuction
CombinatorialAuction('data/auction.csv')

python

# pandas.DataFrame
from ortoolpy.optimization import CombinatorialAuction
CombinatorialAuction('data/auction.csv',limit=1)

data

• data/auction.csv

Supplement

--By adding a small random number to the amount of money, it also functions as a lottery.