Solving symmetric indefinite systems in an interior-point method for linear programming
Mathematical Programming: Series A and B
Multiple centrality corrections in a primal-dual method for linear programming
Computational Optimization and Applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
Octane: A New Heuristic for Pure 0-1 Programs
Operations Research
Solving convex programs by random walks
Journal of the ACM (JACM)
Exploring relaxation induced neighborhoods to improve MIP solutions
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
SIAM Journal on Computing
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
An Evolutionary Algorithm for Polishing Mixed Integer Programming Solutions
INFORMS Journal on Computing
Random walks on polytopes and an affine interior point method for linear programming
Proceedings of the forty-first annual ACM symposium on Theory of computing
A feasibility pump heuristic for general mixed-integer problems
Discrete Optimization
Improving the feasibility pump
Discrete Optimization
Pivot and shift-a mixed integer programming heuristic
Discrete Optimization
Computational experience with a modified potential reduction algorithm for linear programming
Optimization Methods & Software - Special issue in honour of Professor Florian A. Potra's 60th birthday
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Feasibility pump is a general purpose technique for finding feasible solutions of mixed integer programs. In this paper we report our computational experience on using geometric random walks and a random ray approach to provide good points for the feasibility pump. Computational results on MIPLIB2003 and COR@L test libraries show that the walk-and-round approach improves the upper bounds of a large number of test problems when compared to running the feasibility pump either at the optimal solution or the analytic center of the continuous relaxation. In our experiments the hit-and-run walk (a specific type of random walk strategy) started from near the analytic center is generally better than other random search approaches, when short walks are used. The performance may be improved by expanding the feasible region before walking. Although the upper bound produced in the geometric random walk approach are generally inferior than the best available upper bounds for the test problems, we managed to prove optimality of three test problems which were considered unsolved in the COR@L benchmark library (though the COR@L bounds available to us seem to be out of date).