Branching with hyperplanes in the criterion space: the frontier partitioner algorithm for biobjective integer programming

We present an algorithm for finding the complete Pareto frontier of biobjective integer programming problems. The method is based on the solution of a finite number of integer programs, each of them returning a Pareto optimal point. The feasible sets of the integer programs are built from the original feasible set, by adding cuts that separate efficient solutions. providing the existence of an oracle to solve suitably defined single objective integer subproblems, the algorithm can handle biobjective nonlinear integer problems, in particular biobjective convex quadratic integer optimization problems. Our numerical experience on a benchmark of biobjective integer linear programming instances shows the efficiency of the approach in comparison with existing state-of-the-art methods. Further experiments on biobjective integer quadratic programming instances are reported.