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Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization algorithms in preserving high diversity, this paper intends to extend ant colony optimization algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ant colony optimization algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima.
[1] K. Deb and A. Srinivasan, “Innovization: Innovating design principles through optimization,” in Proc. Conf. Genet. Evol. Comput., Seattle, WA, USA, 2006, pp. 1629-1636.
[2] T. Liao, D. Aydin, and T. Stützle, “Artificial bee colonies for continuous optimization: Experimental analysis and improvements,” Swarm Intell., vol. 7, no. 4, pp. 327-356, 2013.
[3] T. Liao, D. Molina, and T. Stützle, “Performance evaluation of automatically tuned continuous optimizers on different benchmark sets,” Appl. Soft Comput., vol. 27, pp. 490-503, Feb. 2015.
[4] N. Chen et al., “An evolutionary algorithm with double-level archives for multiobjective optimization,” IEEE Trans. Cybern., vol. 45, no. 9, pp. 1851-1863, Sep. 2015.
[5] Y.-C. Lin, M. Clauß, and M. Middendorf, “Simple probabilistic population-based optimization,” IEEE Trans. Evol. Comput., vol. 20, no. 2, pp. 245-262, Apr. 2016.
[7] M. A. Muñoz, M. Kirley, and S. K. Halgamuge, “Exploratory landscape analysis of continuous space optimization problems using information content,” IEEE Trans. Evol. Comput., vol. 19, no. 1, pp. 74-87, Feb. 2015.
[8] M. Campos, R. A. Krohling, and I. Enriquez, “Bare bones particle swarm optimization with scale matrix adaptation,” IEEE Trans. Cybern., vol. 44, no. 9, pp. 1567-1578, Sep. 2014.
[9] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proc. IEEE Int. Conf. Neural Netw., vol. 4. Perth, WA, Australia, 1995, pp. 1942-1948.
[10] W.-N. Chen et al., “A novel set-based particle swarm optimization method for discrete optimization problems,” IEEE Trans. Evol. Comput., vol. 14, no. 2, pp. 278-300, Apr. 2010.
[11] W.-N. Chen et al., “Particle swarm optimization with an aging leader and challengers,” IEEE Trans. Evol. Comput., vol. 17, no. 2, pp. 241-258, Apr. 2013.
[12] R. A. Sarker, S. M. Elsayed, and T. Ray, “Differential evolution with dynamic parameters selection for optimization problems,” IEEE Trans. Evol. Comput., vol. 18, no. 5, pp. 689-707, Oct. 2014.
[13] S. Das and P. N. Suganthan, “Differential evolution: A survey of the state-of-the-art,” IEEE Trans. Evol. Comput., vol. 15, no. 1, pp. 4-31, Feb. 2011.
[14] S.-Y. Park and J.-J. Lee, “Stochastic opposition-based learning using a beta distribution in differential evolution,” IEEE Trans. Cybern., in press, 2016.
[15] N. M. Hamza, D. L. Essam, and R. A. Sarker, “Constraint consensus mutation-based differential evolution for constrained optimization,” IEEE Trans. Evol. Comput., vol. 20, no. 3, pp. 447-459, Jun. 2016.
[16] S. Das, A. Mandal, and R. Mukherjee, “An adaptive differential evolution algorithm for global optimization in dynamic environments,” IEEE Trans. Cybern., vol. 44, no. 6, pp. 966-978, Jun. 2014.
[18] C.-F. Juang, C.-W. Hung, and C.-H. Hsu, “Rule-based cooperative continuous ant colony optimization to improve the accuracy of fuzzy system design,” IEEE Trans. Fuzzy Syst., vol. 22, no. 4, pp. 723-735, Aug. 2014.
[19] X.-M. Hu, J. Zhang, H. S.-H. Chung, Y. Li, and O. Liu, “SamACO: Variable sampling ant colony optimization algorithm for continuous optimization,” IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 40, no. 6, pp. 1555-1566, Dec. 2010.
[20] K. Socha, “ACO for continuous and mixed-variable optimization,” in Proc. ANTS 4th Int. Conf. Swarm Intell., Brussels, Belgium, 2004, pp. 25-36.
[21] T. Liao, T. Stützle, M. A. M. de Oca, and M. Dorigo, “A unified ant colony optimization algorithm for continuous optimization,” Eur. J. Oper. Res., vol. 234, no. 3, pp. 597-609, 2014.
[23] V. A. Shim, K. C. Tan, and C. Y. Cheong, “A hybrid estimation of distribution algorithm with decomposition for solving the multiobjective multiple traveling salesman problem,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 42, no. 5, pp. 682-691, Sep. 2012.
[24] C. W. Ahn, J. An, and J.-C. Yoo, “Estimation of particle swarm distribution algorithms: Combining the benefits of PSO and EDAs,” Inf. Sci., vol. 192, pp. 109-119, Jun. 2012.
[25] J. Ceberio, E. Irurozki, A. Mendiburu, and J. A. Lozano, “A distancebased ranking model estimation of distribution algorithm for the flowshop scheduling problem,” IEEE Trans. Evol. Comput., vol. 18, no. 2, pp. 286-300, Apr. 2014.
[26] H. Karshenas, R. Santana, C. Bielza, and P. Larrañaga, “Multiobjective estimation of distribution algorithm based on joint modeling of objectives and variables,” IEEE Trans. Evol. Comput., vol. 18, no. 4, pp. 519-542, Aug. 2014.
[27] K. Kim and R. I. McKay, “Stochastic diversity loss and scalability in estimation of distribution genetic programming,” IEEE Trans. Evol. Comput., vol. 17, no. 3, pp. 301-320, Jun. 2013.
[28] F. Rogai, C. Manfredi, and L. Bocchi, “Metaheuristics for specialization of a segmentation algorithm for ultrasound images,” IEEE Trans. Evol. Comput., in press, 2016.
[29] H. Q. Dinh et al., “An effective method for evolving reaction networks in synthetic biochemical systems,” IEEE Trans. Evol. Comput., vol. 19, no. 3, pp. 374-386, Jun. 2015.
[30] C.-H. Yeh and C.-Y. Yang, “Social networks and asset price dynamics,” IEEE Trans. Evol. Comput., vol. 19, no. 3, pp. 387-399, Jun. 2015.
[31] Z. Vasicek and L. Sekanina, “Evolutionary approach to approximate digital circuits design,” IEEE Trans. Evol. Comput., vol. 19, no. 3, pp. 432-444, Jun. 2015.
[32] C. W. Fong, H. Asmuni, and B. McCollum, “A hybrid swarm-based approach to university timetabling,” IEEE Trans. Evol. Comput., vol. 19, no. 6, pp. 870-884, Dec. 2015.
[33] D. Ashlock and A. McEachern, “Evolutionary nonlinear projection,” IEEE Trans. Evol. Comput., vol. 19, no. 6, pp. 857-869, Dec. 2015.
[34] S. Cussat-Blanc, K. Harrington, and J. Pollack, “Gene regulatory network evolution through augmenting topologies,” IEEE Trans. Evol. Comput., vol. 19, no. 6, pp. 823-837, Dec. 2015.
[36] W. Sheng, S. Swift, L. Zhang, and X. Liu, “A weighted sum validity function for clustering with a hybrid niching genetic algorithm,” IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 6, pp. 1156-1167, Dec. 2005.
[37] L. Qing, W. Gang, and W. Qiuping, “Restricted evolution based multimodal function optimization in holographic grating design,” in Proc. IEEE Congr. Evol. Comput., Edinburgh, U.K., 2005, pp. 789-794.
[38] X. Li, “Efficient differential evolution using speciation for multimodal function optimization,” in Proc. Genet. Evol. Comput. Conf., Washington, DC, USA, 2005, pp. 873-880.
[39] R. Thomsen, “Multimodal optimization using crowding-based differential evolution,” in Proc. IEEE Congr. Evol. Comput., vol. 2. Portland, OR, USA, 2004, pp. 1382-1389.
[40] J.-P. Li, M. E. Balazs, G. T. Parks, and P. J. Clarkson, “A species conserving genetic algorithm for multimodal function optimization,” Evol. Comput., vol. 10, no. 3, pp. 207-234, 2002.
[41] J. Gan and K. Warwick, “Dynamic niche clustering: A fuzzy variable radius niching technique for multimodal optimisation in GAs,” in Proc. IEEE Congr. Evol. Comput., Seoul, South Korea, 2001, pp. 215-222.
[42] A. Pétrowski, “A clearing procedure as a niching method for genetic algorithms,” in Proc. IEEE Congr. Evol. Comput., Nagoya, Japan, 1996, pp. 798-803.
[43] D. E. Goldberg and J. Richardson, “Genetic algorithms with sharing for multimodal function optimization,” in Proc. Int. Conf. Genet. Algorithms, 1987, pp. 41-49.
[44] W. Gao, G. G. Yen, and S. Liu, “A cluster-based differential evolution with self-adaptive strategy for multimodal optimization,” IEEE Trans. Cybern., vol. 44, no. 8, pp. 1314-1327, Aug. 2014.
[45] L. Li and K. Tang, “History-based topological speciation for multimodal optimization,” IEEE Trans. Evol. Comput., vol. 19, no. 1, pp. 136-150, Feb. 2015.
[46] B. Y. Qu, P. N. Suganthan, and J. J. Liang, “Differential evolution with neighborhood mutation for multimodal optimization,” IEEE Trans. Evol. Comput., vol. 16, no. 5, pp. 601-614, Oct. 2012.
[47] X. Li, “Niching without niching parameters: Particle swarm optimization using a ring topology,” IEEE Trans. Evol. Comput., vol. 14, no. 1, pp. 150-169, Feb. 2010.
[48] C. Stoean, M. Preuss, R. Stoean, and D. Dumitrescu, “Multimodal optimization by means of a topological species conservation algorithm,” IEEE Trans. Evol. Comput., vol. 14, no. 6, pp. 842-864, Dec. 2010.
[49] G. R. Harik, “Finding multimodal solutions using restricted tournament selection,” in Proc. Int. Conf. Genet. Algorithms, 1995, pp. 24-31.
[50] S. Hui and P. N. Suganthan, “Ensemble and arithmetic recombinationbased speciation differential evolution for multimodal optimization,” IEEE Trans. Cybern., vol. 46, no. 1, pp. 64-74, Jan. 2016.
[51] S. Biswas, S. Kundu, and S. Das, “An improved parent-centric mutation with normalized neighborhoods for inducing niching behavior in differential evolution,” IEEE Trans. Cybern., vol. 44, no. 10, pp. 1726-1737, Oct. 2014.
[52] S. Biswas, S. Kundu, and S. Das, “Inducing niching behavior in differential evolution through local information sharing,” IEEE Trans. Evol. Comput., vol. 19, no. 2, pp. 246-263, Apr. 2015.
[53] B. Y. Qu, P. N. Suganthan, and S. Das, “A distance-based locally informed particle swarm model for multimodal optimization,” IEEE Trans. Evol. Comput., vol. 17, no. 3, pp. 387-402, Jun. 2013.
[54] Y. Wang, H.-X. Li, G. G. Yen, and W. Song, “MOMMOP: Multiobjective optimization for locating multiple optimal solutions of multimodal optimization problems,” IEEE Trans. Cybern., vol. 45, no. 4, pp. 830-843, Apr. 2015.
[55] A. Basak, S. Das, and K. C. Tan, “Multimodal optimization using a biobjective differential evolution algorithm enhanced with mean distance-based selection,” IEEE Trans. Evol. Comput., vol. 17, no. 5, pp. 666-685, Oct. 2013.
[56] K. Deb and A. Saha, “Multimodal optimization using a bi-objective evolutionary algorithm,” Evol. Comput., vol. 20, no. 1, pp. 27-62, 2012.
[57] J. Yao, N. Kharma, and P. Grogono, “Bi-objective multipopulation genetic algorithm for multimodal function optimization,” IEEE Trans. Evol. Comput., vol. 14, no. 1, pp. 80-102, Feb. 2010.
[58] X. Li, “Adaptively choosing neighbourhood bests using species in a particle swarm optimizer for multimodal function optimization,” in Proc. Conf. Genet. Evol. Comput., Seattle, WA, USA, 2004, pp. 105-116.
[59] M. Dorigo, “Optimization, learning and natural algorithms,” Ph.D. dissertation, Dipartimento di Elettronica, Politecnico di Milano, Milan, Italy, 1992.
[60] M. Dorigo, V. Maniezzo, and A. Colorni, “Ant system: Optimization by a colony of cooperating agents,” IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 26, no. 1, pp. 29-41, Feb. 1996.
[61] M. Dorigo and L. M. Gambardella, “Ant colony system: A cooperative learning approach to the traveling salesman problem,” IEEE Trans. Evol. Comput., vol. 1, no. 1, pp. 53-66, Apr. 1997.
[62] M. Dorigo, M. Birattari, and T. Stützle, “Ant colony optimization,” IEEE Comput. Intell. Mag., vol. 1, no. 4, pp. 28-39, Nov. 2006.
[63] K. Socha and M. Dorigo, “Ant colony optimization for continuous domains,” Eur. J. Oper. Res., vol. 185, no. 3, pp. 1155-1173, 2008.
[64] R. K. Ursem, “Multinational evolutionary algorithms,” in Proc. IEEE Congr. Evol. Comput., Washington, DC, USA, 1999, pp. 1633-1640.
[65] R. K. Ursem, “Multinational GAs: Multimodal optimization techniques in dynamic environments,” in Proc. Conf. Genet. Evol. Comput., 2000, pp. 19-26.
[66] J. Yao, N. Kharma, and Y. Q. Zhu, “On clustering in evolutionary computation,” in Proc. IEEE Congr. Evol. Comput., Vancouver, BC, Canada, 2006, pp. 1752-1759.
[67] C. L. Stoean, M. Preuss, R. Stoean, and D. Dumitrescu, “Disburdening the species conservation evolutionary algorithm of arguing with radii,” in Proc. Conf. Genet. Evol. Comput., London, U.K., 2007, pp. 1420-1427.
[68] Q. Yang et al., “Multimodal estimation of distribution algorithms,” IEEE Trans. Cybern., in press, 2016.
[70] Y. Lin et al., “An ant colony optimization approach for maximizing the lifetime of heterogeneous wireless sensor networks,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 42, no. 3, pp. 408-420, May 2012.
[71] Y. Zhou, X. Lai, Y. Li, and W. Dong, “Ant colony optimization with combining Gaussian eliminations for matrix multiplication,” IEEE Trans. Cybern., vol. 43, no. 1, pp. 347-357, Feb. 2013.
[72] J.-W. Lee, B.-S. Choi, and J.-J. Lee, “Energy-efficient coverage of wireless sensor networks using ant colony optimization with three types of pheromones,” IEEE Trans. Ind. Informat., vol. 7, no. 3, pp. 419-427, Aug. 2011.
[73] W.-N. Chen and J. Zhang, “Ant colony optimization for software project scheduling and staffing with an event-based scheduler,” IEEE Trans. Softw. Eng., vol. 39, no. 1, pp. 1-17, Jan. 2013.
[74] W.-N. Chen and J. Zhang, “An ant colony optimization approach to a grid workflow scheduling problem with various QoS requirements,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 39, no. 1, pp. 29-43, Jan. 2009.
[75] W.-N. Chen, J. Zhang, H. S.-H. Chung, R.-Z. Huang, and O. Liu, “Optimizing discounted cash flows in project scheduling-An ant colony optimization approach,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 40, no. 1, pp. 64-77, Jan. 2010.
[76] M. Shen, W.-N. Chen, J. Zhang, H. S.-H. Chung, and O. Kaynak, “Optimal selection of parameters for nonuniform embedding of chaotic time series using ant colony optimization,” IEEE Trans. Cybern., vol. 43, no. 2, pp. 790-802, Apr. 2013.
[77] T. Liao, M. A. M. de Oca, D. Aydin, T. Stützle, and M. Dorigo, “An incremental ant colony algorithm with local search for continuous optimization,” in Proc. Genet. Evol. Comput. Conf., Dublin, Ireland, 2011, pp. 125-132.
[78] D. Martens et al., “Classification with ant colony optimization,” IEEE Trans. Evol. Comput., vol. 11, no. 5, pp. 651-665, Oct. 2007.
[79] C. Blum and M. Dorigo, “Search bias in ant colony optimization: On the role of competition-balanced systems,” IEEE Trans. Evol. Comput., vol. 9, no. 2, pp. 159-174, Apr. 2005.
[80] M. Birattari, P. Pellegrini, and M. Dorigo, “On the invariance of ant colony optimization,” IEEE Trans. Evol. Comput., vol. 11, no. 6, pp. 732-742, Dec. 2007.
[81] S. Das, A. Konar, and U. K. Chakraborty, “Two improved differential evolution schemes for faster global search,” in Proc. Genet. Evol. Comput. Conf., Washington, DC, USA, 2005, pp. 991-998.
[82] X. Li, A. Engelbrecht, and M. G. Epitropakis, “Benchmark functions for CEC'2013 special session and competition on niching methods for multimodal function optimization,” Evol. Comput. Mach. Learn. Group, RMIT Univ., Melbourne VIC, Australia, Tech. Rep., 2013.
[83] J. Kennedy, “Small worlds and mega-minds: Effects of neighborhood topology on particle swarm performance,” in Proc. IEEE Congr. Evol. Comput., Washington, DC, USA, 1999, pp. 1931-1938.
[84] P. N. Suganthan, “Particle swarm optimiser with neighbourhood operator,” in Proc. IEEE Congr. Evol. Comput., Washington, DC, USA, 1999, pp. 1958-1962.
[85] C. J. Wild, Chance Encounters: A First Course in Data Analysis and Inference. New York, NY, USA: Wiley, 2000.
[86] M. Preuss, “Niching the CMA-ES via nearest-better clustering,” in Proc. Genet. Evol. Comput. Conf., Portland, OR, USA, 2010, pp. 1711-1718.