Branch-and-Bound for Biobjective Mixed-Integer Linear Programming

We present a generic branch-and-bound algorithm for finding all the Pareto solutions of biobjective mixed-integer linear program. The main contributions are new algorithms obtaining dual bounds at node, checking node fathoming, presolve, and duality gap measurement. Our is predominantly decision space search method because branching performed on variables, akin to single objective problems, although we also sometimes split gaps branch in space. various implemented using data structure storing sets. Computational experiments carried out literature instances set that generate benchmark library (MIPLIB2017) problems. perform comparisons against triangle splitting from literature, which an algorithm. Summary Contribution: Biobjective optimization problems have two objectives feasible region. Such many applications operations research, real-world naturally comprise conflicting optimize or can be approximated such manner even harder than programs. Solving them exactly requires computation nondominated space, whereas some may require least one solution corresponding each solution. This paper provides exact solving these method, works Of ingredients this algorithm, parts direct extensions single-objective version, but newly designed handle distinct challenges optimizing over objectives. goal study improve quality speed show decision-space comparably to, better than, work mainly objective-space.