A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem
Computational Optimization and Applications
Efficient Production-Distribution System Design
Management Science
Selected Topics in Column Generation
Operations Research
Computational Optimization and Applications
An interior point cutting plane heuristic for mixed integer programming
Computers and Operations Research
On Interior-Point Warmstarts for Linear and Combinatorial Optimization
SIAM Journal on Optimization
Chebyshev center based column generation
Discrete Applied Mathematics
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
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This paper presents a novel integration of interior point cutting plane methods within branch-and-price algorithms. Unlike the classical method, columns are generated at a ‘‘central’’ dual solution by applying the analytic centre cutting plane method (ACCPM) on the dual of the full master problem. First, we introduce some modifications to ACCPM. We propose a new procedure to recover primal feasibility after adding cuts and use, for the first time, a dual Newton’s method to calculate the new analytic centre after branching. Second, we discuss the integration of ACCPM within the branch-and-price algorithm. We detail the use of ACCPM as the search goes deep in the branch and bound tree, making full utilization of past information as a warm start. We exploit dual information from ACCPM to generate incumbent feasible solutions and to guide branching. Finally, the overall approach is implemented and tested for the bin-packing problem and the capacitated facility location problem with single sourcing. We compare against Cplex-MIP 7.5 as well as a classical branch-and-price algorithm.