The document proposes a memetic firefly algorithm (MFFA) for solving combinatorial optimization problems, specifically graph 3-coloring problems. The MFFA represents solutions as real-valued vectors whose elements determine the order vertices are colored. A local search heuristic is also incorporated. The results of the MFFA were compared to other algorithms on random graphs, showing it performs comparably or better at finding solutions. The structure of the paper outlines the graph 3-coloring problem, describes the MFFA approach, and presents experimental results.

1. Memetic

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y algorithm for
combinatorial optimization
Iztok Fister Jr., Xin-She Yang,y Iztok Fister,z and Janez Brestx
Abstract
Fire
y algorithms belong to modern meta-heuristic algorithms inspired by nature that can be
successfully applied to continuous optimization problems. In this paper, we have been applied the

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y algorithm, hybridized with local search heuristic, to combinatorial optimization problems,
where we use graph 3-coloring problems as test benchmarks. The results of the proposed memetic

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y algorithm (MFFA) were compared with the results of the Hybrid Evolutionary Algorithm
(HEA), Tabucol, and the evolutionary algorithm with SAWmethod (EA-SAW) by coloring the suite
of medium-scaled random graphs (graphs with 500 vertices) generated using the Culberson random
graph generator. The results of

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y algorithm were very promising and showed a potential that
this algorithm could successfully be applied in near future to the other combinatorial optimization
problems as well.
To cite paper as follows: I. Fister Jr., X.-S. Yang, I. Fister, J. Brest, Memetic

6. re
y algo-
rithm for combinatorial optimization, in Bioinspired Optimization Methods and their Applications
(BIOMA 2012), B. Filipic and J.Silc, Eds. Jozef Stefan Institute, Ljubljana, Slovenia, 2012
1 arXiv:1204.5165v2 [math.OC] 10 May 2012
University of Maribor, Faculty of electrical engineering and computer science Smetanova 17, 2000 Maribor;
Electronic address: iztok.

7. ster@guest.arnes.si
yUniversity of Cambridge, Department of Engineering Trumpington Street, Cambridge CB2 1PZ, UK; Elec-tronic
address: xy227@cam.ac.uk
zUniversity of Maribor, Faculty of electrical engineering and computer science Smetanova 17, 2000 Maribor;
Electronic address: iztok.

8. ster@uni-mb.si
xUniversity of Maribor, Faculty of electrical engineering and computer science Smetanova 17, 2000 Maribor;
Electronic address: janez.brest@uni-mb.si

9. I. INTRODUCTION
Nature, especially biological systems, has always been an inspiration for those scientists
who would like to transform some successful features of a biological system into computer
algorithms for ecient problem solving. Birds, insects, ants, and

10. sh may display some
so-called, collective or swarm intelligence in foraging, defending, path

11. nding, etc. This
collective intelligence of self-organizing systems or agents has served as a basis for many
good and ecient algorithms developed in the past, e.g.: ant-colony optimization [7], particle
swarm optimization[22], arti

12. cial bee colony [11, 12, 21], bacterial foraging [23]. Today, all
these algorithms are referred to as swarm intelligence.
The

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y algorithm (FFA) belongs to swarm intelligence as well. It was developed by
X. S. Yang [28]. This algorithm is based on the behavior of

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ies. Each