Abstract
Numerous metaheuristic-based dynamic optimization algorithms have emerged recently. While these algorithms excel in locating a single global optimum, they fall short in identifying multiple optimal solutions. The primary objective of dynamic multimodal optimization is to identify several optimal solutions for a problem where the objective function changes over time. The discovery of multiple optimal solutions, both global and local, holds significant importance for numerous applications. The best implementable alternative may not always be the optimal solution due to practical limitations. Surprisingly, the literature has paid scant attention to the problem of dynamic multimodal optimization using evolutionary principles. Conversely, mean shift, a nonparametric iterative process, is capable of detecting local maxima in a density function represented by a sample set. Mean shift exhibits adaptive qualities that enable it to identify local maxima in dynamic environments. In this chapter, we present a mean shift approach to detect global and local optima in dynamic optimization problems. The presented method modifies the search strategy of mean shift by considering both density and fitness values of candidate solutions. To expedite the convergence process, a competitive memory and dynamic strategy are incorporated to leverage valuable information from previous environments. Consequently, the present approach effectively identifies a significant number of global and local optima in dynamic environments. To showcase its performance, we compare the present algorithm with well-known dynamic optimization methods using the CEC competition benchmark generator. Experimental results demonstrate the present scheme's high accuracy and robustness, positioning it as a highly competitive solution.
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References
Halder, U., Das, S., Maity, D.: A cluster-based differential evolution algorithm with external archive for optimization in dynamic environments. IEEE Trans. Cybern. 43(3), 881–897 (2013)
Das, S., Mandal, A., Mukherjee, R.: An adaptive differential evolution algorithm for global optimization in dynamic environments. IEEE Trans. Cybern. 44(6), 966–978 (2014)
Mavrovouniotis, M., Müller, F.M., Yang, S.: Ant colony optimization with local search for dynamic traveling salesman problems. IEEE Trans. Cybern. 47(7), 1743–1756 (2017)
Sadollah, A., Sayyaadi, H., Yadav, A.: A dynamic metaheuristic optimization model inspired by biological nervous systems: neural network algorithm. Appl. Soft Comput. 71, 747–782 (2018)
Baykasoğlu, A., Ozsoydan, F.B.: Evolutionary and population-based methods versus constructive search strategies in dynamic combinatorial optimization. Inf. Sci. 420, 159–183 (2017)
Nguyen, T.T., Yang, S., Branke, J.: Evolutionary dynamic optimization: a survey of the state of the art. Swarm Evolut. Comput. 6, 1–24 (2012)
Tinós, R., Yang, S.: Analysis of fitness landscape modifications in evolutionary dynamic optimization. Inf. Sci. 282, 214–236 (2014)
Mavrovouniotis, M., Li, C., Yang, S.: A survey of swarm intelligence for dynamic optimization: algorithms and applications. Swarm Evol. Comput. 33, 1–17 (2017)
Topcuoglu, L.A.R.: Impact of sensor-based change detection schemes on the performance of evolutionary dynamic optimization techniques. Soft. Comput. 22(14), 4741–4762 (2018)
Kazemi, J., Hossein, K., Firouzjaee, A., Meybodi, M.R.: An adaptive bi-flight cuckoo search with variable nests for continuous dynamic optimization problems. Appl. Intell. 48(1), 97–117 (2018)
Lissovoi, A., Witt, C.: A runtime analysis of parallel evolutionary algorithms in dynamic optimization. Algorithmica 78(2), 641–659 (2017)
Kazemi, J., Alireza, K., Mohammad, R., Meybodi, R.: New measures for comparing optimization algorithms on dynamic optimization problems. Nat. Comput. (2019) (in press)
Au, C.-K., Leung, H.-F.: Cooperative coevolutionary algorithms for dynamic optimization: an experimental study. Evol. Intell. 7(4), 201–218 (2014)
Zuo, X., **ao, L.: A DE and PSO based hybrid algorithm for dynamic optimization problems. Soft. Comput. 18(7), 1405–1424 (2014)
Cao, L., Xu, L., Goodman, E.D.: A collaboration-based particle swarm optimizer with history-guided estimation for optimization in dynamic environments. Expert Syst. Appl. 120, 1–13 (2019)
Liu, L., Yang, S., Wang, D.: Particle swarm optimization with composite particles in dynamic environments. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 40(6), 1634–1648 (2010)
Blackwell, T., Branke, J.: Multiswarms, exclusion, and anti-convergence in dynamic environments. IEEE Trans. Evol. Comput. 10(4), 459–472 (2006)
Mendes, R., Mohais, A.S.: DynDE: a differential evolution for dynamic optimization problems. In: Proceeding of the IEEE Congress on Evolutionary Computation, vol. 3, pp. 2808–2815 (2005)
Li, C., Yang, S.: A general framework of multipopulation methods with clustering in undetectable dynamic environments. IEEE Trans. Evol. Comput. 16(4), 556–577 (2012)
Brest, J., Zamuda, A., Boskovic, B., Maucec, M.S., Zumer, V.: Dynamic optimization using self-adaptive differential evolution. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 415–422 (2009)
Mukherjee, R., Debchoudhury, S., Das, S.: Modified differential evolution with locality induced genetic operators for dynamic optimization. Eur. J. Oper. Res. 253(2), 337–355 (2016)
Bravo, Y., Luque, G., Alba, E.: Global memory schemes for dynamic optimization. Nat. Comput. 15(2), 319–333 (2016)
Li, C., Yang, S.: A clustering particle swarm optimizer for dynamic optimization. In: Proceedings of the 2009 IEEE Congress on Evolutionary Computation, pp. 439–446 (2009)
Wong, K.-C., Chun-Ho, W., Mok, R.K.P., Peng, C.: Evolutionary multimodal optimization using the principle of locality. Inf. Sci. 194, 138–170 (2012)
Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of 2nd International Conference Genetic Algorithms, pp. 41–49 (1987)
De Jong, K.A.: An Analysis of the Behavior of a Class of Genetic Adaptive Systems. Ph.D. dissertation, University of Michigan, Ann Arbor (1975)
Li, J.-P., Balazs, M.E., Parks, G.T., Clarkson, P.J.: A species conserving genetic algorithm for multimodal function optimization. Evol. Comput. 10(3), 207–234 (2002)
Ramírez-Ortegón, M.A., Tapia, E., Ramírez-Ramírez, L.L., Rojas, R., Cuevas, E.: Transition pixel: a concept for binarization based on edge detection and gray-intensity histograms. Pattern Recogn. 43(4), 1233–1243 (2010)
Liang, J.J., Qu, B.Y., Mao, X.B., Niu, B., Wang, D.Y.: Differential evolution based on fitness Euclidean distance ratio for multimodal optimization. Neurocomputing 137, 252–260 (2014)
Miller, B.L., Shaw, M.J.: Genetic algorithms with dynamic niche sharing for multimodal function optimization. In: Proceedings of the 3rd IEEE Conference on Evolutionary Computation, pp. 786–791 (1996)
Thomsen, R.: Multimodal optimization using crowding-based differential evolution. In: Evolutionary Computation, CEC2004. Congress (2004)
Biswas, S., Das, S., Kundu, S., Patra, G.R.: Utilizing time-linkage property in DOPs: an information sharing based articial bee colony algorithm for tracking multiple optima in uncertain environments. Soft. Comput. 18, 1199–1212 (2014)
Das, S., Maity, S., Qu, B.Y., Suganthan, P.N.: Real-parameter evolutionary multimodal optimization—a survey of the state-of-the-art. Swarm Evol. Comput. 1(2), 71–88 (2011)
Mengshoel, O.J., Galán, S.F., De Dios, A.: Adaptive generalized crowding for genetic algorithms. Inf. Sci. 258, 140–159 (2014)
Yazdani, S., Nezamabadi-pour, H., Kamyab, S.: A gravitational search algorithm for multimodal optimization. Swarm Evol. Comput. 14, 1–14 (2014)
Chen, C.-H., Liu, T.-K., Chou, J.-H.: A novel crowding genetic algorithm and its applications to manufacturing robots. IEEE Trans. Ind. Inf. 10(3), 1705–1716 (2014)
Chang, W.-D.: A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems. Appl. Soft Comput. 33, 170–182 (2015)
Lianga, Y., Kwong-Sak, L.: Genetic algorithm with adaptive elitist-population strategies for multimodal function optimization. Appl. Soft Comput. 11, 2017–2034 (2011)
Qu, B.Y., Suganthan, P.N., Das, S.: A distance-based locally informed particle swarm model for multimodal optimization. IEEE Trans. Evol. Comput. 17(3), 387–402 (2013)
Sacco, W.F., Henderson, N., Rios-Coelho, A.C.: Topographical clearing differential evolution: a new method to solve multimodal. Prog. Nucl. Energy 71, 269–278 (2014)
Cheng, S., Lu, H., Guo, Y., Lei, X., Liang, J., Chen, J., Shi, Y.: Dynamic multimodal optimization: a preliminary study. In: 2019 IEEE Congress on Evolutionary Computation (CEC), Wellington, New Zealand (2019)
Kaiwartya, O., Kumar, S., Lobiyal, D.K., Tiwari, P.K., Abdullah, A.H., Hassan, A.N.: Multiobjective dynamic vehicle routing problem and time seed based solution using particle swarm optimization. J. Sensors 2015 (2015)
Okulewicz, M., Mańdziuk, J.: A metaheuristic approach to solve dynamic vehicle routing problem in continuous search space. Swarm Evol. Comput. 48(March), 44–61 (2019)
Lei, Y., Jasin, S., Sinha, A.: Joint dynamic pricing and order fulfillment for E−commerce retailers. Manuf. Serv. Oper. Manag. 20(2), 269–284 (2018)
Saharan, S., Bawa, S., Kumar, N.: Dynamic pricing techniques for intelligent transportation system in smart cities: a systematic review. Comput. Commun. 150, 603–625 (2020)
Manjunath, A., Raychoudhury, V., Saha, S.: Ant-taxi to pie-passenger: optimizing routes and time for distributed taxi ride sharing. In: 2020 International Conference on COMmunication System & NETworkS, COMSNETS 2020, pp. 736–743 (2020)
Wu, H., Qian, S., Liu, Y., Wang, D., Guo, B.: An immune-based response particle swarm optimizer for knapsack problems in dynamic environments. Soft. Comput. 24(20), 15409–15425 (2020)
Hao, X. et al.: Dynamic Knapsack Optimization Towards Efficient Multi-channel Sequential Advertising (2020)
Nguyen, V.Q., Johnson, R.T., Sup, F.C., Umberger, B.R.: Bilevel optimization for cost function determination in dynamic simulation of human gait. IEEE Trans. Neural Syst. Rehabil. Eng. 27(7), 1426–1435 (2019)
Luo, W., Lin, X., Zhu, T., Xu, P.: A clonal selection algorithm for dynamic multimodal function optimization. Swarm Evol. Comput. (2018) (in press)
Li, C., Yang, S.: A clustering particle swarm optimizer for dynamic optimization. In: 2009 IEEE Congress on Evolutionary Computation, Trondheim, Norway, pp. 439–446 (2009)
Fukunaga, K., Hostetler, L.D.: The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Trans. Inf. Theory 21, 32–40 (1975)
Tao, W., **, H., Zhang, Y.: Color image segmentation based on mean shift and normalized cuts. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 37(5), 1382–1389 (2007)
Comaniciu, D., Meer, P.: Mean shift: a robust approach towards feature space analysis. IEEE Trans. Pattern Anal. Mach. Intell. 24, 603–619 (2002)
Comaniciu, D.: An algorithm for data-driven bandwidth selection. IEEE Trans. Pattern Anal. Mach. Intell. 25, 281–288 (2003)
Anand, S., Mittal, S., Tuzel, O., Meer, P.: Semi-supervised kernel mean shift clustering. EEE Trans. Pattern Anal. Mach. Intell. 36(6), 1201–1215 (2014)
DeMenthon, D., Doermann, D.: Video retrieval using spatio-temporal descriptors pages. In: Proceedings of the Eleventh ACM International Conference on Multimedia, pp. 508–517 (2003)
Zivkovic, Z., Krose, B.: An EM-like algorithm for color-histogram-based object tracking. In: Proceedings of the International Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 798–803 (2004)
Cheng, Y.: Mean shift, mode seeking, and clustering. IEEE Trans. Pattern Anal. Mach. Intell. 17(8), 790–799 (1995)
Fashing, M., Tomasi, C.: Mean shift is a bound optimization. IEEE Trans. Pattern Anal. Mach. Intell. 27(3), 471–474 (2005)
Horová, I., Koláček, J., Zelinka, J.: Kernel Smoothing in Matlab. World Scientific (2012)
Gramacki, A.: Nonparametric Kernel Density Estimation and Its Computational Aspects. Springer (2018)
Scott, D.W.: Scott’s rule. Wires Comput. Statist. 2(4), 497–502 (2010)
Li, S., Yang S., Nguyen T., Yu E., Yao X., ** Y., Beyer H.G., Suganthan P.N.: Benchmark generator for CEC 2009 competition on dynamic optimization. Technical Report 2008, Department of Computer Science, University of Leicester, U.K., October 2009. http://hdl.handle.net/2086/11893
Brest, J., Zamuda, A., Bǒskovíc, B., Maǔcec, M.S., Žumer, V.: Dynamic optimization using self-adaptive differential evolution. In: 2009 IEEE Congress on Evolutionary Computation, CEC 2009, pp. 415–422 (2009)
Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics 80–83 (1945)
Cuevas, E., González, A., Fausto, F., Zaldívar, D., Pérez-Cisneros, M.: Multithreshold segmentation by using an algorithm based on the behavior of locust swarms. Math. Probl. Eng. (2015)
Zaldivar, D., Morales, B., Rodríguez, A., Valdivia-G, A., Cuevas, E., Pérez-Cisneros, M.: A novel bio-inspired optimization model based on Yellow Saddle Goatfish behavior. Biosystems 174, 1–21 (2018)
Cuevas, E., Gálvez, J., Hinojosa, S., Avalos, O., Zaldívar, D., Pérez-Cisneros, M.: A comparison of evolutionary computation techniques for IIR model identification. J. Appl. Math. (2014)
Bandyopadhyay, R., Basu, A., Cuevas, E., Sarkar, R.: Harris Hawks optimisation with simulated annealing as a deep feature selection method for screening of COVID-19 CT-scans. Appl. Soft Comput. 111, 107698 (2021)
Cuevas, E., Wario, F., Osuna-Enciso, V., Zaldivar, D., Pérez-Cisneros, M.: Fast algorithm for multiple-circle detection on images using learning automata. IET Image Proc. 6(8), 1124–1135 (2012)
Hinojosa, S., Dhal, K.G., Abd Elaziz, M., Oliva, D., Cuevas, E.: Entropy-based imagery segmentation for breast histology using the stochastic fractal search. Neurocomputing 321, 201–215 (2018)
Cuevas, E., Zaldivar, D., Pérez-Cisneros, M.: Seeking multi-thresholds for image segmentation with learning automata. Mach. Vis. Appl. 22, 805–818 (2011)
Ibrahim, R.A., Elaziz, M.A., Oliva, D., Cuevas, E., Lu, S.: An opposition-based social spider optimization for feature selection. Soft. Comput. 23, 13547–13567 (2019)
Xu, Q., Lei, W., Si, J.: Predication based immune network for multimodal function optimization. Eng. Appl. Artif. Intell. 23, 495–504 (2010)
Cuevas, E., González, M., Zaldivar, D., Pérez-Cisneros, M., García, G.: An Algorithm for Global Optimization Inspired by Collective Animal Behavior. Discrete Dynamics in Nature and Society, vol 2012, Article ID 638275
Cuevas, E., Gonzalez, M.: An optimization algorithm for multimodal functions inspired by collective animal behavior. Soft. Comput. 17, 489–502 (2013)
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Cuevas, E., Zaldívar, D., Pérez-Cisneros, M. (2024). Dynamic Multimodal Function Optimization: An Evolutionary-Mean Shift Approach. In: New Metaheuristic Schemes: Mechanisms and Applications. Intelligent Systems Reference Library, vol 246. Springer, Cham. https://doi.org/10.1007/978-3-031-45561-2_3
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