8,016 research outputs found
Mathematical Programming formulations for the efficient solution of the -sum approval voting problem
In this paper we address the problem of electing a committee among a set of
candidates and on the basis of the preferences of a set of voters. We
consider the approval voting method in which each voter can approve as many
candidates as she/he likes by expressing a preference profile (boolean
-vector). In order to elect a committee, a voting rule must be established
to `transform' the voters' profiles into a winning committee. The problem
is widely studied in voting theory; for a variety of voting rules the problem
was shown to be computationally difficult and approximation algorithms and
heuristic techniques were proposed in the literature. In this paper we follow
an Ordered Weighted Averaging approach and study the -sum approval voting
(optimization) problem in the general case . For this problem we
provide different mathematical programming formulations that allow us to solve
it in an exact solution framework. We provide computational results showing
that our approach is efficient for medium-size test problems ( up to 200,
up to 60) since in all tested cases it was able to find the exact optimal
solution in very short computational times
Induced aggregation operators in decision making with the Dempster-Shafer belief structure
We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.aggregation operators, dempster-shafer belief structure, uncertainty, iowa operator, decision making
Optimal scaling of the ADMM algorithm for distributed quadratic programming
This paper presents optimal scaling of the alternating directions method of
multipliers (ADMM) algorithm for a class of distributed quadratic programming
problems. The scaling corresponds to the ADMM step-size and relaxation
parameter, as well as the edge-weights of the underlying communication graph.
We optimize these parameters to yield the smallest convergence factor of the
algorithm. Explicit expressions are derived for the step-size and relaxation
parameter, as well as for the corresponding convergence factor. Numerical
simulations justify our results and highlight the benefits of optimally scaling
the ADMM algorithm.Comment: Submitted to the IEEE Transactions on Signal Processing. Prior work
was presented at the 52nd IEEE Conference on Decision and Control, 201
Generalizing the Min-Max Regret Criterion using Ordered Weighted Averaging
In decision making under uncertainty, several criteria have been studied to
aggregate the performance of a solution over multiple possible scenarios,
including the ordered weighted averaging (OWA) criterion and min-max regret.
This paper introduces a novel generalization of min-max regret, leveraging the
modeling power of OWA to enable a more nuanced expression of preferences in
handling regret values. This new OWA regret approach is studied both
theoretically and numerically. We derive several properties, including
polynomially solvable and hard cases, and introduce an approximation algorithm.
Through computational experiments using artificial and real-world data, we
demonstrate the advantages of our OWAR method over the conventional min-max
regret approach, alongside the effectiveness of the proposed clustering
heuristics
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