Abstract: Symmetry plays an important role in optimization. The usual approach to cope with symmetry in discrete optimization is to try to eliminate it by introducing artificial symmetry-breaking conditions into the problem, and/or by using an ad-hoc search strategy. In this paper we argue that symmetry is instead a beneficial feature that we should preserve and exploit as much as possible, breaking it only as a last resort. To this end, we outline a new approach, that we call orbital shrinking, where additional integer variables expressing variable sums within each symmetry orbit are introduces and used to ``encapsulate'' model symmetry. This leads to a discrete relaxation of the original problem, whose solution yields a bound on its optimal value. Encouraging preliminary computational experiments on the tightness and solution speed of this relaxation are presented.
Keywords: Mathematical programming, discrete optimization, algebra, symmetry, relaxation, MILP, convex MINLP.
Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )
Entry Submitted: 09/26/2011
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