An ant colony optimisation algorithm for the triple matching problem

Krzysztof Schiff


In this article, ant colony optimisation algorithms for the triple matching problem are described. This is the
first elaborated ant algorithm for this problem. The problem is modeled by means of a 3-dimensional array. The ant algorithm was compared with the Apx3Dmatchnig-F algorithm and tested for different values of ant algorithm parameters. The results of these tests were presented and discussed.

Słowa kluczowe: triple maximum matching problem, ant colony optimization algorithm, non weighted version

[1] Karp R.M., Reducibility among combinatorial problems, [in:] R. Miller, J. Thatcher, Complexity of Computer Computations, Plenum, 1972, 85–103.
[2] Knuth, D., Stable marriage and its relation to other combinatorial problems, An introduction to the mathematical analysis of algorithms, Amer. Math. Soc., Providence, RI, 1997.
[3] Biro P., McDermid, E., Three-sided stable matching with cyclic p, Algorithmica 58(1), 2010, 5–18.
[4] Eriksson, K., Sjostrand, J., Strimling, P., Three-dimensional stable matching with cyclic p, Math. Soc. Sci. 52(1), 2006, 77–87.
[5] Dorigo M., Stützle T., Ant colony optimization, Cambridge MIT Press. Proceedings of EvoWorkshops 2002, Berlin, Heidelberg, Springer-Verlag, 2002, 61–71.
[6] Chen J., Iterative Expansion and Color Coding, an Improved Algorithm for 3D-Matching, ACM Transactions on Algorithms, 2012, 6.1–6.22.
[7] Cao J., Chang W-L, Guo M., Using sticker to solve the 3-dimensional matching problem in molecular supercomputers, Int. J. High Performance Computing and Networking, Vol. 1, 2004, Nos. 1/2/3.
[8] Epifiano F.S., Ogasawara E., Soares J., Amorim M., Souza U., O Problema de Alocacao deTutores em Aplicacoes de Provas, XLVI Simposio Brasileiro de Pesquisa Operacional, Salvador, 16–19.09.2014 Brasil, 2014, 3007–3018.