A Metaheuristic Algorithm for Large Maximum Weight Independent Set Problems. (arXiv:2203.15805v1 [cs.AI])

Motivated by a real-world vehicle routing application, we consider the
maximum-weight independent set problem: Given a node-weighted graph, find a set
of independent (mutually nonadjacent) nodes whose node-weight sum is maximum.
Some of the graphs airsing in this application are large, having hundreds of
thousands of nodes and hundreds of millions of edges. To solve instances of
this size, we develop a new local search algorithm, which is a metaheuristic in
the greedy randomized adaptive search (GRASP) framework. This algorithm, which
we call METAMIS, uses a wider range of simple local search operations than
previously described in the literature. We introduce data structures that make
these operations efficient. A new variant of path-relinking is introduced to
escape local optima and so is a new alternating augmenting-path local search
move that improves algorithm performance. We compare an implementation of our
algorithm with a state-of-the-art openly available code on public benchmark
sets, including some large instances with hundreds of millions of vertices. Our
algorithm is, in general, competitive and outperforms this openly available
code on large vehicle routing instances. We hope that our results will lead to
even better MWIS algorithms.

Source: https://arxiv.org/abs/2203.15805

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