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Empirical analysis of a modified Artificial Bee Colony for constrained numerical optimization. (English) Zbl 1284.90079
Summary: A modified artificial bee colony algorithm to solve constrained numerical optimization problems is presented. Four modifications related with the selection mechanism, the scout bee operator, and the equality and boundary constraints are made to the algorithm with the aim to modify its behavior in a constrained search space. Six performance measures found in the specialized literature are employed to analyze different capabilities in the proposed algorithm such as the ability and cost to generate feasible solutions, the capacity and cost to locate the feasible global optimum solution and the competency to improve feasible solutions. Three experiments, including a comparison with state-of-the-art algorithms, are considered in the test design where twenty four well-known benchmark problems with different features are utilized. The overall results show that the proposed algorithm differs in its behavior with respect to the original artificial bee colony algorithm but its performance is improved, mostly in problems with small feasible regions due to the presence of equality constraints.

##### MSC:
 90C30 Nonlinear programming 90C59 Approximation methods and heuristics in mathematical programming 65K10 Numerical optimization and variational techniques
CEC 05; ABC
Full Text:
##### References:
 [1] Engelbrecht, A.P., Fundamentals of computational swarm intelligence, (2005), Wiley [2] Eiben, A.; Smith, J.E., Introduction to evolutionary computing, Natural computing series, (2003), Springer-Verlag · Zbl 1028.68022 [3] () [4] Michalewicz, Z.; Schoenauer, M., Evolutionary algorithms for constrained parameter optimization problems, Evolutionary computation, 4, 1, 1-32, (1996) [5] Coello, C.A.C., Theoretical and numerical constraint handling techniques used with evolutionary algorithms: a survey of the state of the art, Computer methods in applied mechanics and engineering, 191, 11-12, 1245-1287, (2002) · Zbl 1026.74056 [6] Monson, C.K.; Seppi, K.D., Linear equality constraints homomorphous mappings in PSO, (), 73-80 [7] Cagnina, L.; Esquivel, S.; Coello-Coello, C., A bi-population PSO with a shake-mechanism for solving constrained numerical optimization, (), 670-676 [8] E. Mezura-Montes, J.I. Flores-Mendoza, Multiobjective problems solving from nature: From concepts to applications, in: R. Chiong (Ed.), Nature-Inspired Algorithms for Optimization, Studies in Computational Intelligence Series, Ch. Improved Particle Swarm Optimization in Constrained Numerical Search Spaces, , ISBN: 978-3-540-72963-1, 2009, Springer-Verlag, vol. 193, (2009), pp. 299-332. [9] Muñoz-Zavala, Angel E.; Hernández-Aguirre, A.; Villa-Diharce, E.R.; Botello-Rionda, S., PESO+for constrained optimization, (), 935 [10] Muñoz Zavala, A.E.; Hernández Aguirre, A.; Villa Diharce, E.R.; Botello Rionda, S., Constrained optimization with an improved particle swarm optimization algorithm, International journal of intelligent computing and cybernetics, 1, 3, 425-453, (2008) · Zbl 1151.90597 [11] Abbass, H.A., Marriage in honey bees optimization (mbo): a haplometrosis polygynous swarming approach, (), 207-214 [12] Haddad, O.B.; Marino, M.A., Dynamic penalty function as a strategy in solving water resources combinatorial optimization problems with honey-bee mating operation (hbmo) algorithm, Journal of hydroinformatics, 9, 3, 233-250, (2007) [13] Baykasoglu, A.; Ozbakir, L.; Tapkan, P., Artificial bee colony algorithm and its application to generalized assignment problem, (), 113-144 [14] Pham, D.; Ghanbarzadeh, A.; Ko, S.O.E.; Rahim, S.; Zaidi, M., The bees algorithm: a novel tool for complex optimisation problems, (), 454-461 [15] D. Karaboga, B. Akay, Artificial bee colony (abc), harmony search and bees algorithms on numerical optimization, in: Innovative Production Machines and Systems Virtual Conference (IPROMS 2009), 2009. . [16] Yang, X.-S., Engineering optimizations via nature-inspired virtual bee algorithms, (), 317-323 [17] Karaboga, D.; Basturk, B., A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm, Journal of global optimization, 39, 3, 459-471, (2007) · Zbl 1149.90186 [18] D. Karaboga, B. Basturk, Artificial bee colony(abc) optimization algorithm for solving constrained optimization problems, in: P. Melin, O. Castillo, L.T. Aguilar, J. Kacptrzyk, W. Pedrycz (Eds.), Foundations of Fuzzy Logic and Soft Computing, 12th International Fuzzy Systems Association, World Congress, IFSA 2007, Lecture Notes in Artificial Intelligence, Springer, Cancun, Mexico, vol. 4529, 2007, pp. 789-798. · Zbl 1149.90186 [19] Mezura-Montes, E.; Cetina-Domínguez, O., Exploring promising regions of the search space with the scout bee in the artificial bee colony for constrained optimization, (), 253-260 [20] Karaboga, D., An idea based on honey bee swarm for numerical optimization, (2005), Erciyes University, Engineering Faculty, Turkey Tech. rep. [21] P.-W. TSai, J.-S. Pan, B.-Y. Liao, S.-C. Chu, Enhanced artificial bee colony optimization, International Journal of Innovative Computing, Information and Control 5 (12). [22] Haddad, O.B.; Afshar, A.; Mario, M.A., Honey-bees mating optimization (hbmo) algorithm: a new heuristic approach for water resources optimization, Water resources management, 20, 661-680, (2006) [23] Goldberg, D.E., Genetic algorithms in search, optimization and machine learning, (1989), Addison-Wesley Publishing Co., Reading, Massachusetts · Zbl 0721.68056 [24] Karaboga, D.; Basturk, B., On the performance of artificial bee colony (abc) algorithm, Applied soft computing, 8, 1, 687-697, (2008) [25] Deb, K., An efficient constraint handling method for genetic algorithms, Computer methods in applied mechanics and engineering, 186, 2/4, 311-338, (2000) · Zbl 1028.90533 [26] Zielinski, K.; Vudathu, S.P.; Laur, R.; Krasnogor, N., Influence of different deviations allowed for equality constraints on particle swarm optimization and differential evolution, () [27] J.J. Liang, T. Runarsson, E. Mezura-Montes, M. Clerc, P. Suganthan, C.A. Coello Coello, K. Deb, Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization, Technical report, Nanyang Technological University, Singapore, (December, 2005). . [28] Eiben, G.; Schut, M., New ways to calibrate evolutionary algorithms, (), 153-177 · Zbl 1211.90303 [29] Hamida, S.B.; Schoenauer, M., ASCHEA: new results using adaptive segregational constraint handling, (), 884-889 [30] Mezura-Montes, E.; Coello, C.A.C., Identifying on-line behavior some sources of difficulty in two competitive approaches for constrained optimization, (), 1477-1484 [31] Lu, H.; Chen, W., Self-adaptive velocity particle swarm optimization for solving constrained optimization problems, Journal of global optimization, 41, 3, 427-445, (2008) · Zbl 1152.90670 [32] () [33] Price, K.; Storn, R.; Lampinen, J., Differential evolution: a practical approach to global optimization, () [34] Kennedy, J.; Eberhart, R.C., Swarm intelligence, (2001), Morgan Kaufmann UK [35] Kukkonen, S.; Lampinen, J., Constrained real-parameter optimization with generalized differential evolution, (), 911-918 [36] Price, K.V.; Rönkkönen, J.I., Comparing the uni-modal scaling performance of global and local selection in a mutation-only differential evolution algorithm, (), 7387-7394 [37] Lampinen, J., A constraint handling approach for the differential evolution algorithm, (), 1468-1473 [38] Mallipeddi, R.; Suganthan, P., Ensemble of constraint handling techniques, IEEE transactions on evolutionary computation, 14, 4, 561-579, (2010) [39] Wang, Y.; Cai, Z.; Guo, G.; Zhou, Y., Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems, IEEE transactions on systems, man and cybernetics part B - cybernetics, 37, 3, 560-575, (2007) [40] Wang, Y.; Cai, Z.; Zhou, Y.; Zeng, W., An adaptive tradeoff model for constrained evolutionary optimization, IEEE transactions on evolutionary computation, 12, 1, 80-92, (2008) [41] Zhang, M.; Luo, W.; Wang, X., Differential evolution with dynamic stochastic selection for constrained optimization, Information sciences, 178, 15, 3043-3074, (2008) [42] Wolpert, D.H.; Macready, W.G., No free lunch theorems for optimization, IEEE transactions on evolutionary computation, 1, 1, 67-82, (1997) [43] Takahama, T.; Sakai, S., Constrained optimization by the $$\operatorname{\&z.epsi;}$$ constrained differential evolution with gradient-based mutation and feasible elites, (), 308-315 [44] Huang, V.L.; Qin, A.K.; Suganthan, P.N., Self-adaptative differential evolution algorithm for constrained real-parameter optimization, (), 324-331
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