Feasibility Pump Heuristics for Column Generation Approaches

Primal heuristics have become an essential component in mixed integer programming (MIP). Generic heuristic paradigms of the literature remain to be extended to the context of a column generation so- lution approach. As the Dantzig-Wolfe reformulation is typically tighter than the original compact formulation, techniques based on rounding its linear programming solution have better chance to yield good primal so- lutions. However, the dynamic generation of variables requires specific adaptation of heuristic paradigms. We focus here on "feasibility pump" approaches. We show how such methods can be implemented in a context of dynamically defined variables, and we report on numerically testing "feasibility pump" for cutting stock and generalized assignment prob- lems