Contributed Session Tue.1.H 1029

Tuesday, 10:30 - 12:00 h, Room: H 1029

Cluster 15: Multi-objective optimization [...]

Multiobjective optimization II

 

Chair: Nasrabadi Nasim

 

 

Tuesday, 10:30 - 10:55 h, Room: H 1029, Talk 1

Thomas Jacob Riis Stidsen
A branch & cut algorithm for bi-objective TSP

Coauthor: Christopher Ryther

 

Abstract:
Branch & cut algorithms were invented to solve TSP and have since become the standard approach to solve MIP's. In this presentation we will present a branch & cut algorithm for TSP's with two cost matrices. The solution to the TSP with two objective functions is not one optimal tour, but the set of all Pareto optimal tours. A Pareto optimal tour is a tour that no other tour exist which is better on one of the objectives and better or equal on the other objective. We will briefly review why the bi-objective TSP is a very hard optimization problem. Then we will present our branch & cut algorithm, which can find the Pareto optimal set of tours. Using cuts from The Concorde code in our branch & cut algorithm we are able to solve bi-objective TSP problems with up to 120 cities. This has to the best of our knowledge never been done before.

 

 

Tuesday, 11:00 - 11:25 h, Room: H 1029, Talk 2

Gulsah Karakaya
Decision support for multi-attribute multi-item reverse auctions

Coauthor: Murat Koksalan

 

Abstract:
In this study, we address multi-item auction problems in a multi-attribute, multi-round reverse auction setting. In each round, we provide the buyer with a set of efficient bid combinations, who then chooses the provisional winners whose bids collectively provide all the required items. We estimate preference information from the buyer's choices and provide this to the bidders. The bidders update/improve their bids in order to become/stay competitive. The process continues several rounds. The developed interactive approach tries to have the more competitive bidders eventually end up winning the auction.

 

 

Tuesday, 11:30 - 11:55 h, Room: H 1029, Talk 3

Nasrabadi Nasim
Non-radial models to define the preference measure for convex cone-based strict partial order

Coauthors: Akram Dehnokhalaji, Nasim Nasrabadi

 

Abstract:
Multiple Criteria Decision Making (MCDM) is an important field in applied mathematics. The main goal
in MCDM is finding the most preferred solution among a
set of alternatives or to rank order them. We consider the
problem of finding a strict partial order for a finite set of
multi-criteria alternatives. We assume an unknown quasi-concave value
function and the DM's
preferences are available in the form of pair-wise comparisons.
Then, a polyhedron and a convex cone are constructed such that
the vertex of the cone is an inferior alternative. To produce a
rank order, we determine the status of an arbitrary alternative
w.r.t. the vertex of the cone by solving two Linear programming
(LP) problems. A similar study has been done by Dehnokhalaji et
al. The main difference is that they built the two LPs
based on a radial distance. However, the
radial measure has some drawbacks, especially in the case that
the data are large, the results would not be much informative.
Also, the radial measure is unstable when small changes occur in
the data set of the problem. Therefore, the new non-radial models
solves the drawbacks and concludes more reliable results.

 

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