Weighted iterated local branching for mathematical programming problems with binary variables

Abstract

Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search procedure is by using a mixed-integer programming solver to explore a neighborhood defined through a constraint that limits the number of binary variables whose values are allowed to change in a given iteration. Recognizing that not all variables are equally promising to change when searching for better neighboring solutions, we propose a weighted iterated local branching heuristic. This new procedure differs from similar existing methods since it considers groups of binary variables and associates with each group a limit on the number of variables that can change. The groups of variables are defined using weights that indicate the expected contribution of flipping the variables when trying to identify improving solutions in the current neighborhood. When the mixed-integer programming solver fails to identify an improving solution in a given iteration, the proposed heuristic may force the search into new regions of the search space by utilizing the group of variables that are least promising to flip. The weighted iterated local branching heuristic is tested on benchmark instances of the optimum satisfiability problem, and computational results show that the weighted method is superior to an alternative method without weights.