Algorithms for the generalized independent set problem based on a quadratic optimization approach
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This paper presents two algorithms—a construction heuristic and an exact solution method—for the generalized independent set problem. Both methods take advantage of a nonlinear formulation of this problem and are based on optimization of a quadratic function over a hypersphere. Heuristic solutions are constructed by exploring stationary points of a surrogate problem of this form. The exact method is a combinatorial branch-and-bound algorithm that uses a spherical relaxation of the original feasible region in its pruning subroutine. We show competence of the proposed methods through computational experiments on benchmark instances.
KeywordsGeneralized independent set problem Quadratic optimization Combinatorial branch-and-bound Construction heuristic
We would like to thank Dr. Renata Mansini for providing the test instances, and the anonymous referees, whose feedback helped us to improve the paper.
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