Abstract
This paper introduces DEVIATION, a soft global constraint to obtain balanced solutions. A violation measure of the perfect balance can be defined as the L p norm of the vector variables minus their mean. SPREAD constraints the sum of square deviations to the mean [5,7] i.e. the L 2 norm. The L 1 norm is considered here. Neither criterion subsumes the other but the design of a propagator for L 1 is simpler. We also show that a propagator for DEVIATION runs in \(\mathcal{O}(n)\) (with respect to the number of variables) against \(\mathcal{O}(n^2)\) for SPREAD.
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Schaus, P., Deville, Y., Dupont, P., Régin, JC. (2007). The Deviation Constraint. In: Van Hentenryck, P., Wolsey, L. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2007. Lecture Notes in Computer Science, vol 4510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72397-4_19
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DOI: https://doi.org/10.1007/978-3-540-72397-4_19
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