Differential-evolution-based coevolution ant colony optimization algorithm for Bayesian network structure learning. (English) Zbl 1461.90202

Summary: Learning the Bayesian networks (BNs) structure from data has received increasing attention. Many heuristic algorithms have been introduced to search for the optimal network that best matches the given training data set. To further improve the performance of ant colony optimization (ACO) in learning the BNs structure, this paper proposes a new improved coevolution ACO (coACO) algorithm, which uses the pheromone information as the cooperative factor and the differential evolution (DE) as the cooperative strategy. Different from the basic ACO, the coACO divides the entire ant colony into various sub-colonies (groups), among which DE operators are adopted to implement the cooperative evolutionary process. Experimental results demonstrate that the proposed coACO outperforms the basic ACO in learning the BN structure in terms of convergence and accuracy.


90C59 Approximation methods and heuristics in mathematical programming
90B15 Stochastic network models in operations research
68T05 Learning and adaptive systems in artificial intelligence
90C35 Programming involving graphs or networks


Full Text: DOI


[1] Pinto, P.C.; Nägele, A.; Dejori, M.; Runkler, T.A.; Sousa, J.M.C.; Using a local discovery ant algorithm for Bayesian network structure learning; IEEE Trans. Evol. Comput.: 2009; Volume 13 ,767-779.
[2] Campos, L.M.; Fernández-Luna, J.M.; Gámez, J.A.; Puerta, J.M.; Ant colony optimization for learning Bayesian networks; Int. J. Approx. Reason.: 2002; Volume 31 ,291-311. · Zbl 1033.68091
[3] Larrañaga, P.; Karshenas, H.; Bielza, C.; Santana, R.; A review on evolutionary algorithms in Bayesian network learning and inference tasks; Inf. Sci.: 2013; Volume 233 ,109-125. · Zbl 1284.68501
[4] Gheisari, S.; Meybodi, M.R.; Dehghan, M.; Ebadzadeh, M.M.; Bayesian network structure training based on a game of learning automata; Int. J. Mach. Learn. Cybern.: 2017; Volume 8 ,1093-1105.
[5] Martínez-Rodríguez, A.M.; May, J.H.; Vargas, L.G.; An optimization-based approach for the design of Bayesian networks; Math. Comput. Model.: 2008; Volume 48 ,1265-1278. · Zbl 1187.90086
[6] Cano, A.; Masegosa, A.R.; Moral, S.A.; A method for integrating expert knowledge when learning Bayesian networks from data; IEEE Trans. Syst. Man Cybern. Part B Cybern.: 2011; Volume 41 ,1382-1394.
[7] Campos, L.M.; Castellano, J.G.; Bayesian network learning algorithms using structural restrictions; Int. J. Approx. Reason.: 2007; Volume 45 ,233-254. · Zbl 1122.68104
[8] Zhang, X.Y.; Jia, S.M.; Li, X.Z.; Guo, G.; Learning the Bayesian networks structure based on ant colony optimization and differential evolution; Proceedings of the 2018 4th International Conference on Control, Automation and Robotics (ICCAR): ; ,354-358.
[9] Arefi, M.; Taheri, S.M.; Possibilistic Bayesian inference based on fuzzy data; Int. J. Mach. Learn. Cybern.: 2016; Volume 7 ,753-763.
[10] Yan, L.J.; Cercone, N.; Bayesian network modeling for evolutionary genetic structures; Comput. Math. Appl.: 2010; Volume 59 ,2541-2551. · Zbl 1193.92078
[11] Khanteymoori, A.R.; Olyaee, M.-H.; Abbaszadeh, O.; Valian, M.; A novel method for Bayesian networks structure learning based on Breeding Swarm algorithm; Soft Comput.: 2017; Volume 21 ,6713-6738.
[12] Wong, M.L.; Leung, K.S.; An efficient data mining method for learning Bayesian networks using an evolutionary algorithm-based hybrid approach; IEEE Trans. Evol. Comput.: 2004; Volume 8 ,378-404.
[13] Wang, T.; Yang, J.; A heuristic method for learning Bayesian networks using discrete particle swarm optimization; Knowl. Inf. Syst.: 2010; Volume 24 ,269-281.
[14] Ji, J.Z.; Zhang, H.X.; Hu, R.B.; A Bayesian network learning algorithm based on independence test and ant colony optimization; Acta Autom. Sin.: 2009; Volume 35 ,281-288. · Zbl 1212.68129
[15] Ji, J.Z.; Zhang, H.X.; Hu, R.B.; A hybrid method for learning Bayesian networks based on ant colony optimization; Appl. Soft Comput.: 2011; Volume 11 ,3373-3384.
[16] Yang, J.; Li, L.; Wang, A.G.; A partial correlation-based Bayesian network structure learning algorithm under linear SEM; Knowl. Based Syst.: 2011; Volume 24 ,963-976.
[17] Baumgartner, K.; Ferrari, S.; Palermo, G.; Constructing Bayesian networks for criminal profiling from limited data; Knowl. Based Syst.: 2008; Volume 21 ,563-572.
[18] Garey, M.R.; Johnson, D.S.; ; Computers and Intractability: A Guide to the Theory of NP-Completeness: New York, NY, USA 1979; . · Zbl 0411.68039
[19] Colorni, A.; Dorigo, M.; Maniezzo, V.; Distributed optimization by ant colonies; Proceedings of the First European Conference on Artificial Life: ; ,134-142.
[20] Dorigo, M.; Maniezzo, V.; Colorni, A.; The ant system: Optimization by a colony of cooperating agents; IEEE Trans. Syst. Man Cybern. Part B Cybern.: 1996; Volume 26 ,29-41.
[21] Storn, R.; Price, K.; Differential evolution: A simple and efficient heuristic for global optimization over continuous spaces; J. Glob. Optim.: 1997; Volume 11 ,341-359. · Zbl 0888.90135
[22] Das, S.; Suganthan, P.N.; Differential evolution: A survey of the state-of-the-art; IEEE Trans. Evol. Comput.: 2011; Volume 9 ,4-31.
[23] Derrac, J.; García, S.; Molina, D.; Herrera, F.; A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms; Swarm Evol. Comput.: 2011; Volume 1 ,3-18.
[24] Duan, H.B.; Yu, Y.X.; Zhang, X.Y.; Three-dimension path planning for UCAV using hybrid meta-heuristic ACO-DE algorithm; Simul. Model. Pract. Theory: 2010; Volume 18 ,1104-1115.
[25] Serani, A.; Leotardi, C.; Iemma, U.; Campana, E.F.; Fasano, G.; Diez, M.; Parameter selection in synchronous and asynchronous deterministic particle swarm optimization for ship hydrodynamics problems; Appl. Soft Comput.: 2016; Volume 49 ,313-334.
[26] Zhang, X.Y.; Duan, H.B.; Yu, Y.X.; Receding horizon control for multi-UAVs close formation control based on differential evolution; Sci. China Inf. Sci.: 2010; Volume 53 ,223-235.
[27] Zhang, X.Y.; Duan, H.B.; An improved constrained differential evolution algorithm for unmanned aerial vehicle global route planning; Appl. Soft Comput.: 2015; Volume 26 ,270-284.
[28] Murphy, K.; The Bayes Net Toolbox for Matlab; Comput. Sci. Stat.: 2001; Volume 33 ,1024-1034.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.