A hybrid constraint programming and semidefinite programming approach for the stable set problem

This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxation. Using this ranking, we generate the most promising subproblems first, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure. Computational results show that the semidefinite relaxation is very informative, since solutions of good quality are found in the first subproblems, or optimality is proven immediately.Comment: 14 page

Engineering Branch-and-Cut Algorithms for the Equicut Problem

A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such hat the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefnite relaxations for the equicut problem, and and that linear bounds are competitive with the corresponding semidefnite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-andcut algorithm has a better performance than the algorithm of Brunetta et al.. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application

Cost Optimization for the Slitting of Core Laminations for Power Transformers

The successful realization of a project for slitting core laminations for power transformers under minimizing costs is presented. The production of the core of power transformers requires great amounts of grain oriented silicon steel (up to 200 tons for a single transformer). The shape of the cross section of the core is approximated to a circle by stacking sheets of different widths. To supply these sheets, coils of given lengths and widths are to be slitted following a cutting plan that minimizes the costs. We describe an efficient solution method which is based on the solution of various knapsack problems

Engineering Branch-and-Cut Algorithms for the Equicut Problem

A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such hat the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefnite relaxations for the equicut problem, and and that linear bounds are competitive with the corresponding semidefnite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-andcut algorithm has a better performance than the algorithm of Brunetta et al.. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application

Multicommodity Flow Approximation used for Exact Graph Partitioning

We present a fully polynomial-time approximation scheme for a multicommodity flow problem that yields lower bounds of the graph bisection problem. We compar