Methods and systems are provided for solving an optimization problem using a model expressed in a mixed integer programming (MIP) language. The problem is constrained within a space of valid solutions by a plurality of MIP variables. A skeleton set of the variables are designated as eligible for fixed value assignments. An initial solution for the problem is obtained, which forms the basis for refinement. New versions of the problem are prepared and solved iteratively by fixing a proportion of the skeleton set to their best known values, as found in a previous problem-solving iteration.