Adaptive Improvements of Multi-Objective Branch and Bound
CoRR(2023)
摘要
Branch and bound methods which are based on the principle "divide and
conquer" are a well established solution approach in single-objective integer
programming. In multi-objective optimization branch and bound algorithms are
increasingly attracting interest. However, the larger number of objectives
raises additional difficulties for implicit enumeration approaches like branch
and bound. Since bounding and pruning is considerably weaker in multiple
objectives, many branches have to be (partially) searched and may not be pruned
directly. The adaptive use of objective space information can guide the search
in promising directions to determine a good approximation of the Pareto front
already in early stages of the algorithm. In particular we focus in this
article on improving the branching and queuing of subproblems and the handling
of lower bound sets.
In our numerical test we evaluate the impact of the proposed methods in
comparison to a standard implementation of multiobjective branch and bound on
knapsack problems, generalized assignment problems and (un)capacitated facility
location problems.
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