A Constraints-Aware Reweighted Feasibility Pump Approach

We extend the Reweighted Feasibility Pump (RFP) approach of [De Santis, Lucidi, Rinaldi, SIOPT, 2013], which is based on the interpretation of the (main step of the) Feasibility Pump as the Frank-Wolfe method applied to an appropriate penalty function that drives the search towards integer solutions. We modify the function that is minimized by incorporating barrier terms that provide information about how much changing a variable is possible due to it being involved in (almost) active constraints. The corresponding Constraints-Aware RWP is experimentally tested on two sets of hard pure binary feasibility problems, and the results show that, all other things being equal, the modification leads to a more effective and robust method w.r.t. the original RFP one.