Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A matheuristic approach for the $b$-coloring problem using integer
  programming and a multi-start multi-greedy randomized metaheuristic   Given a graph $G=(V,E)$, the $b$-coloring problem consists in attributing a
color to every vertex in $V$ such that adjacent vertices receive different
colors, every color has a $b$-vertex, and the number of colors is maximized. A
$b$-vertex is a vertex adjacent to vertices colored with all used colors but
its own. The $b$-coloring problem is known to be NP-Hard and its optimal
solution determines the $b$-chromatic number of $G$, denoted $\chi_b(G)$. This
paper presents an integer programming formulation and a very effective
multi-greedy randomized heuristic which can be used in a multi-start
metaheuristic. In addition, a matheuristic approach is proposed combining the
multi-start multi-greedy randomized metaheuristic with a MIP (mixed integer
programming) based local search procedure using the integer programming
formulation. Computational experiments establish the proposed multi-start
metaheuristic as very effective in generating high quality solutions, along
with the matheuristic approach successfully improving several of those results.
Moreover, the computational results show that the multi-start metaheuristic
outperforms a state-of-the-art hybrid evolutionary metaheuristic for a subset
of the large instances which were previously considered in the literature. An
additional contribution of this work is the proposal of a benchmark instance
set, which consists of newly generated instances as well as others available in
the literature for classical graph problems, with the aim of standardizing
computational comparisons of approaches for the $b$-coloring problem in future
works.

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The categories of this paper are: nlin
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat