A heuristic ceiling point algorithm for general integer linear programming
Management Science
Solving combinatorial optimization problems using Karmakar's algorithm
Mathematical Programming: Series A and B
On the computation of weighted analytic centers and dual ellipsoids with the projective algorithm
Mathematical Programming: Series A and B
Solving nonlinear multicommodity flow problems by the analytic center cutting plane method
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
Warm start of the primal-dual method applied in the cutting-plane scheme
Mathematical Programming: Series A and B
Computational Experience with an Interior Point Cutting Plane Algorithm
SIAM Journal on Optimization
General Purpose Heuristics for Integer Programming—Part II
Journal of Heuristics
IEEE Computational Science & Engineering
Octane: A New Heuristic for Pure 0-1 Programs
Operations Research
The integration of an interior-point cutting plane method within a branch-and-price algorithm
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
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
Recursive central rounding for mixed integer programs
Computers and Operations Research
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We explore the use of interior point methods in finding feasible solutions to mixed integer programming. As integer solutions are typically in the interior, we use the analytic center cutting plane method to search for integer feasible points within the interior of the feasible set. The algorithm searches along two line segments that connect the weighted analytic center and two extreme points of the linear programming relaxation. Candidate points are rounded and tested for feasibility. Cuts aimed to improve the objective function and restore feasibility are then added to displace the weighted analytic center until a feasible integer solution is found. The algorithm is composed of three phases. In the first, points along the two line segments are rounded gradually to find integer feasible solutions. Then in an attempt to improve the quality of the solutions, the cut related to the bound constraint is updated and a new weighted analytic center is found. Upon failing to find a feasible integer solution, a second phase is started where cuts related to the violated feasibility constraints are added. As a last resort, the algorithm solves a minimum distance problem in a third phase. The heuristic is tested on a set of problems from MIPLIB and CORAL. The algorithm finds good quality feasible solutions in the first two phases and never requires the third phase.