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Leo Liberti(leolibertigmail.com) Abstract: If a mathematical program (be it linear or nonlinear) has many symmetric optima, solving it via BranchandBound techniques often yields search trees of disproportionate sizes; thus, finding and exploiting symmetries is an important task. We propose a method for automatically finding the formulation group of any given MixedInteger Nonlinear Program, and reformulating the problem so that some symmetric solutions become infeasible. The reformulated problem can then be solved via standard BranchandBound codes such as CPLEX (for linear programs) and {\sc Couenne} (for nonlinear programs). Our computational results include formulation group tables for the MIPLib3, MIPLib2003, GlobalLib and MINLPLib instance libraries, solution tables for some instances in the aforementioned libraries, and a theoretical and computational study of the symmetries of the Kissing Number Problem. Keywords: symmetry, mixed integer nonlinear programming, branch and bound, kissing number problem Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming ) Category 2: Global Optimization (Theory ) Category 3: Integer Programming ((Mixed) Integer Linear Programming ) Citation: Download: [PDF] Entry Submitted: 12/03/2008 Modify/Update this entry  
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