Effcient storage of Pareto solutions in biobjective mixed integer programming

Many of the techniques for solving biobjective mixed integer linear programs
(BOMILP) are iterative processes which utilize solutions discovered during early iterations to aid in the discovery of improved solutions during later iterations. Thus, it is highly desirable to efficiently store the nondominated subset of a given set of solutions. To this end, we present a new data structure in the form of a modified binary tree. The structure takes points and line segments as input and stores the nondominated subset of the input. We perform two computational experiments. The results of the first show that this structure processes inserted data faster than alternative structures currently implemented in the literature. Results of the second experiment show that when our structure is utilized inside fathoming procedures for biobjective branch-and-bound (BB), the running times for BB are reduced in most cases.