A Dual Heuristic for Set Partitioning

Dual heuristics have been successfully used to generate bounds in the context of branch and bound algorithms. In the current work, we present a new dual heuristic for the set partitioning problem. Our approach provides a lower bound at each node of the branch and bound tree by calculating approximate solutions to the dual of the linear relaxation of the set partitioning problem. The calculation of the lower bound is carried out incrementally as we optimise over reduced costs instead of the original ones. This feature increases efficiency and reduces memory requirements. Key-Words: Integer programming, Set partitioning, Branch and Bound, Dual heuristic