Branch-and-bound for biobjective mixed integer programming
Nathan Adelgren, Akshay Gupte · arXiv (Cornell University) · 2017
We present a generic branch-and-bound method for finding all the Pareto solutions of a biobjective mixed integer program. Our main contribution is new algorithms for obtaining dual bounds at a node, for checking node fathoming, presolve and duality gap measurement. Our various procedures are implemented and empirically validated on instances from literature and a new set of hard instances. We also perform comparisons against the triangle splitting method of Boland et al. [\emph{INFORMS Journal on Computing}, \textbf{27} (4), 2015], which is a objective space search algorithm as opposed to our variable space search algorithm. On each of the literature instances, our branch-and-bound is able to compute the entire Pareto set in significantly lesser time. Most of the instances of the harder problem set were not solved by either algorithm in a reasonable time limit, but our algorithm performs better on average on the instances that were solved.