Efficient storage of Pareto points in biobjective mixed integer
programming
release_cbnwbjxkozavboyzjjvccz7f7q
by
Nathan Adelgren, Pietro Belotti, Akshay Gupte
2017
Abstract
In biobjective mixed integer linear programs (BOMILPs), two linear objectives
are minimized over a polyhedron while restricting some of the variables to be
integer. Since many of the techniques for finding or approximating the Pareto
set of a BOMILP use and update a subset of nondominated solutions, it is highly
desirable to efficiently store this subset. We present a new data structure, a
variant of a binary tree that takes as input points and line segments in ^2
and stores the nondominated subset of this input. When used within an exact
solution procedure, such as branch-and-bound (BB), at termination this
structure contains the set of Pareto optimal solutions.
We compare the efficiency of our structure in storing solutions to that of a
dynamic list which updates via pairwise comparison. Then we use our data
structure in two biobjective BB techniques available in the literature and
solve three classes of instances of BOMILP, one of which is generated by us.
The first experiment shows that our data structure handles up to 10^7 points
or segments much more efficiently than a dynamic list. The second experiment
shows that our data structure handles points and segments much more efficiently
than a list when used in a BB.
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