First International Conference on MOLDAVIAN RISKS – FROM ...

<strong>First</strong> <strong>International</strong> <strong>Conference</strong> on MOLDAVIAN RISKS - FROM GLOBAL TO LOCAL SCALE
16-19 May 2012, Bacau, Romania
DATA INCOHERENCE FOR COMBINATORIAL
OPTIMIZATION PROBLEMS
Gloria Cerasela Crisan 1 , Camelia-M. Pintea 2 , Camelia Chira 3
1 “Vasile Alecsandri” University of Bacau, Department of Mathematics, Informatics and Education
Sciences
2 Tech Univ Cluj-Napoca, North Univ Center Baia-Mare, Faculty of Science
3 “Babeş-Bolyai” University of Cluj-Napoca, Department of Computer Science
Corresponding author: Gloria Cerasela Crisan, ceraselacrisan@ub.ro
Abstract: Data collections are fundamental in taking correct and on time decisions. In risk
management, the coherence and the integrity of the problem’s data have great impact on
the quality of the decision. If the data are biased, the applications that assist the manager
can provide poor advices. The real-life problems reflect the complexity and heterogeneity
of our modern society. The applications designed for solving them are therefore expensive,
sophisticated and complex; inherently their results are hard to predict. This is why the
influence of the data incoherence over the results is an extremely important issue to
consider. The a-priori knowledge and its efficient handling are compulsory for modern,
proactive strategy in problem solving. Knowing how a specific algorithm would behave
when input data might be incoherent may help choosing between several algorithms athand
to better deal with real-world problems. We here approach the influence of
incoherent input data when solving Combinatorial Optimization Problems (COPs). Several
new COP variants are defined and the stability of the corresponding solving methods under
imperfect input data is investigated. Some parameters are defined and a parameterized
complexity study is performed. Numerical experiments engage the well-known COP
Travelling Salesman Problem in its standard form and a dynamic variant (with and without
errors in the input data for both problem variants). All the problems are solved using Ant
Colony Optimization algorithms, a biologically-inspired metaheuristic approach. The
adaptation and the resilience of natural systems (Darwinian evolution, ant colony
behaviour) suggest the same behaviour. We use a natural incoherence measure and we
compare the applications results on correct and incoherent data. We modify the algorithms
in order to store both the correct and the incoherent data. We extend our numerical
experiments by coupling a new imperfection dimension: the uncertainty. The algorithms’
behaviour does not have a pattern: we observe stable, unstable, even catastrophic effects of
input data incoherence. The paper generalizes a metaheuristic approach to a classical
optimization problem when the data entry has some degree of incoherence.
Key words: combinatorial optimization problems, parameterized complexity, data incoherence,
heuristics, ant colony optimization.
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