MoL-2007-17:
Ottens, Brammert
(2007)
*Comparing Winner Determination Algorithms for Mixed Multi-Unit Combinatorial Auctions.*
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## Abstract

In this thesis three different approaches to the Winner Determination

Problem (WDP) for Mixed Multi-Unit Combinatorial Auctions (MMUCA) are

explored. The first, due to [Cerquides et al., 2007] is based on a

traditional integer programming approach. The second, due to [Uckelman

and Endriss, 2007] is based on constraint programing and the third is

based on a division of the original problem in two subproblems.

These two subproblems are the problem of finding an allocation that

produces enough goods, and the problem of finding a sequence of the

transformations in this allocation. It is shown that both problems are

NP-complete. However, in the case of an acyclic goods graph the

problem of finding a sequence becomes trivial. This is also the case

when any cycles present limit themselves to just one good, i.e. the

good occurs both in the input and in the output of a transformations.

All three algorithms are tested using two different datasets. The

first is created using the generator described in [Vinyals et al.,

2007] and discerns three different types of transformations, input,

output and input-output transformations. The second is created using

a generator that discerns four different types of transformations,

namely input, output, structured and unstructured transformations.

In terms of performance the results are not conclusive. Although the

constraint programming approach does not perform very well, the

performance of both the integer programming approach and the division

approach vary. In several situations the latter is better and in other

situations the former is better. Furthermore, the influence of the

number of transformations on the complexity of the auction varies for

the different datasets.

However, the results do show that structured auctions are easier to

solve than unstructured and hybrid auctions and that the division

approach performs much better on structured auctions.

Item Type: | Report |
---|---|

Report Nr: | MoL-2007-17 |

Series Name: | Master of Logic Thesis (MoL) Series |

Year: | 2007 |

Date Deposited: | 12 Oct 2016 14:38 |

Last Modified: | 12 Oct 2016 14:38 |

URI: | https://eprints.illc.uva.nl/id/eprint/789 |

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