Abstract
In the Max FS problem, given an infeasible linear system A x ≥ b, one wishes to find a feasible subsystem containing a maximum number of inequalities. This NP-hard problem has interesting applications in a variety of fields. In some challenging applications in telecommunications and computational biology one faces very large Max FS instances with up to millions of inequalities in thousands of variables. We propose to tackle large-scale instances of Max FS using randomized and thermal variants of the classical relaxation method for solving systems of linear inequalities. We present a theoretical analysis of one particular version of such a method in which we derive a lower bound on the probability that it identifies an optimal solution within a given number of iterations. This bound, which is expressed as a function of a condition number of the input data, implies that with probability 1 the randomized method identifies an optimal solution after finitely many iterations. We also present computational results obtained for medium- to large-scale instances arising in the planning of digital video broadcasts and in the modelling of the energy functions driving protein folding. Our experiments indicate that these methods perform very well in practice.
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Amaldi, E., Belotti, P., Hauser, R. (2005). Randomized Relaxation Methods for the Maximum Feasible Subsystem Problem. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_19
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DOI: https://doi.org/10.1007/11496915_19
Publisher Name: Springer, Berlin, Heidelberg
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