915 research outputs found
RIGA: A Regret-Based Interactive Genetic Algorithm
In this paper, we propose an interactive genetic algorithm for solving
multi-objective combinatorial optimization problems under preference
imprecision. More precisely, we consider problems where the decision maker's
preferences over solutions can be represented by a parameterized aggregation
function (e.g., a weighted sum, an OWA operator, a Choquet integral), and we
assume that the parameters are initially not known by the recommendation
system. In order to quickly make a good recommendation, we combine elicitation
and search in the following way: 1) we use regret-based elicitation techniques
to reduce the parameter space in a efficient way, 2) genetic operators are
applied on parameter instances (instead of solutions) to better explore the
parameter space, and 3) we generate promising solutions (population) using
existing solving methods designed for the problem with known preferences. Our
algorithm, called RIGA, can be applied to any multi-objective combinatorial
optimization problem provided that the aggregation function is linear in its
parameters and that a (near-)optimal solution can be efficiently determined for
the problem with known preferences. We also study its theoretical performances:
RIGA can be implemented in such way that it runs in polynomial time while
asking no more than a polynomial number of queries. The method is tested on the
multi-objective knapsack and traveling salesman problems. For several
performance indicators (computation times, gap to optimality and number of
queries), RIGA obtains better results than state-of-the-art algorithms
Online Ranking: Discrete Choice, Spearman Correlation and Other Feedback
Given a set of objects, an online ranking system outputs at each time
step a full ranking of the set, observes a feedback of some form and suffers a
loss. We study the setting in which the (adversarial) feedback is an element in
, and the loss is the position (0th, 1st, 2nd...) of the item in the
outputted ranking. More generally, we study a setting in which the feedback is
a subset of at most elements in , and the loss is the sum of the
positions of those elements.
We present an algorithm of expected regret over a time
horizon of steps with respect to the best single ranking in hindsight. This
improves previous algorithms and analyses either by a factor of either
, a factor of or by improving running
time from quadratic to per round. We also prove a matching lower
bound. Our techniques also imply an improved regret bound for online rank
aggregation over the Spearman correlation measure, and to other more complex
ranking loss functions
Finding Favourite Tuples on Data Streams with Provably Few Comparisons
One of the most fundamental tasks in data science is to assist a user with
unknown preferences in finding high-utility tuples within a large database. To
accurately elicit the unknown user preferences, a widely-adopted way is by
asking the user to compare pairs of tuples. In this paper, we study the problem
of identifying one or more high-utility tuples by adaptively receiving user
input on a minimum number of pairwise comparisons. We devise a single-pass
streaming algorithm, which processes each tuple in the stream at most once,
while ensuring that the memory size and the number of requested comparisons are
in the worst case logarithmic in , where is the number of all tuples. An
important variant of the problem, which can help to reduce human error in
comparisons, is to allow users to declare ties when confronted with pairs of
tuples of nearly equal utility. We show that the theoretical guarantees of our
method can be maintained for this important problem variant. In addition, we
show how to enhance existing pruning techniques in the literature by leveraging
powerful tools from mathematical programming. Finally, we systematically
evaluate all proposed algorithms over both synthetic and real-life datasets,
examine their scalability, and demonstrate their superior performance over
existing methods.Comment: To appear in KDD 202
Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability
The purpose of this thesis is twofold. The first and major part is devoted to
sensitivity analysis of various discrete optimization problems while the second
part addresses methods applied for calculating measures of solution stability
and solving multicriteria discrete optimization problems.
Despite numerous approaches to stability analysis of discrete optimization
problems two major directions can be single out: quantitative and qualitative.
Qualitative sensitivity analysis is conducted for multicriteria discrete optimization
problems with minisum, minimax and minimin partial criteria. The main
results obtained here are necessary and sufficient conditions for different stability
types of optimal solutions (or a set of optimal solutions) of the considered
problems.
Within the framework of quantitative direction various measures of solution
stability are investigated. A formula for a quantitative characteristic called
stability radius is obtained for the generalized equilibrium situation invariant
to changes of game parameters in the case of the H¨older metric. Quality of the
problem solution can also be described in terms of robustness analysis. In this
work the concepts of accuracy and robustness tolerances are presented for a
strategic game with a finite number of players where initial coefficients (costs)
of linear payoff functions are subject to perturbations.
Investigation of stability radius also aims to devise methods for its calculation.
A new metaheuristic approach is derived for calculation of stability
radius of an optimal solution to the shortest path problem. The main advantage
of the developed method is that it can be potentially applicable for
calculating stability radii of NP-hard problems.
The last chapter of the thesis focuses on deriving innovative methods based
on interactive optimization approach for solving multicriteria combinatorial
optimization problems. The key idea of the proposed approach is to utilize
a parameterized achievement scalarizing function for solution calculation and
to direct interactive procedure by changing weighting coefficients of this function.
In order to illustrate the introduced ideas a decision making process is
simulated for three objective median location problem.
The concepts, models, and ideas collected and analyzed in this thesis create
a good and relevant grounds for developing more complicated and integrated
models of postoptimal analysis and solving the most computationally challenging
problems related to it.Siirretty Doriast
Preference Learning
This report documents the program and the outcomes of Dagstuhl Seminar 14101 “Preference Learning”. Preferences have recently received considerable attention in disciplines such as machine learning, knowledge discovery, information retrieval, statistics, social choice theory, multiple criteria decision making, decision under risk and uncertainty, operations research, and others. The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies
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