Branch-and-bound for biobjective mixed integer programming
release_hx6e4dcupvbynhtro3qmfsh55a
by
Nathan Adelgren, Akshay Gupte
2017
Abstract
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. [INFORMS Journal on Computing, 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.
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