Abstract
Cooperative coevolution (CC) is an efficient framework for solving large-scale global optimization (LSGO) problems. It uses a decomposition method to divide the LSGO problems into several low-dimensional subcomponents; then, subcomponents are optimized. Since CC algorithms do not consider any imbalance feature, their performance degrades during solving imbalanced LSGO problems. In this paper, we propose an incremental CC (ICC) algorithm in which the algorithm optimizes an integrated subcomponent which subcomponents are dynamically added to it. Therefore, the search space of the optimizer is grown incrementally toward the original problem search space. Various search spaces are built according to three approaches, namely random-based, sensitivity analysis-based, and random sensitivity analysis-based methods; then, ICC explores these search spaces effectively. Random-based selects a subcomponent randomly for adding it to the current search space and the sensitivity analysis-based method uses a sensitivity analysis strategy to select a subcomponent. The random sensitivity analysis-based strategy is a hybrid of the random and sensitivity analysis-based methods. Theoretical analysis is provided to demonstrate that the proposed ICC-based algorithms are effective for solving imbalanced LSGO problems. Finally, the efficiency of these algorithms is benchmarked on the complex imbalanced LSGO problems. Simulation results confirm that ICC obtains a better performance overall.
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Arora J (2004) Introduction to optimum design. Academic Press, London
Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. In: 2005 IEEE congress on evolutionary computation, vol. 2, pp. 1769–1776. IEEE
Campolongo F, Cariboni J, Saltelli A (2007) An effective screening design for sensitivity analysis of large models. Environ Model Softw 22(10):1509–1518
Chen W, Weise T, Yang Z, Tang K (2010) Large-scale global optimization using cooperative coevolution with variable interaction learning. In: Parallel problem solving from nature, PPSN XI. Springer, Berlin, pp 300–309
Doerr B, Sudholt D, Witt C (2013) When do evolutionary algorithms optimize separable functions in parallel? In: Proceedings of the twelfth workshop on foundations of genetic algorithms XII. ACM, pp 51–64
Ekstrom PA (2005) Eikos: a simulation toolbox for sensitivity analysis in matlab. Uppsala University, Uppsala
García S, Herrera F. The software for conducting multiple comparison involving all possible pairwise comparisons. https://www.lri.fr/~hansen/cmaes_inmatlab.html
García S, Fernández A, Luengo J, Herrera F (2009a) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13(10):959–977
García S, Molina D, Lozano M, Herrera F (2009b) A study on the use of non-parametric tests for analyzing the evolutionary algorithms behaviour: a case study on the cec2005 special session on real parameter optimization. J Heuristics 15(6):617–644
Hansen N (2016) The CMA evolution strategy: a tutorial. arXiv:1604.00772
Li X, Yao X (2012) Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans Evol Comput 16(2):210–224
Li X, Tang K, Omidvar MN, Yang Z, Qin K (2013) Benchmark functions for the cec2013 special session and competition on large-scale global optimization. Gene 7:33
Liu J, Tang K (2013) Scaling up covariance matrix adaptation evolution strategy using cooperative coevolution. In: Intelligent Data Engineering and Automated Learning–IDEAL 2013. Springer, Berlin, pp 350–357
Liu Y, Yao X, Zhao Q, Higuchi T (2001) Scaling up fast evolutionary programming with cooperative coevolution. In: Evolutionary computation, 2001. Proceedings of the 2001 congress on IEEE, vol 2, pp 1101–1108
Luengo J, García S, Herrera F (2009) A study on the use of statistical tests for experimentation with neural networks: analysis of parametric test conditions and non-parametric tests. Exp Syst Appl 36(4):7798–7808
Mahdavi Sedigheh, Shiri Mohammad Ebrahim, Rahnamayan Shahryar (2014). Cooperative co-evolution with a new decomposition method for large-scale optimization. In: Evolutionary computation (CEC), 2014 IEEE congress on IEEE, pp 1285–1292
Mahdavi S, Shiri ME, Rahnamayan S (2015) Metaheuristics in large-scale global continues optimization: a survey. Inform Sci 295:407–428
Mei Y, Omidvar MN, Li X, Yao X (2016) A competitive divide-and-conquer algorithm for unconstrained large-scale black-box optimization. ACM Trans Math Softw (TOMS) 42(2):13
Miller BL, Goldberg DE (1995) Genetic algorithms, tournament selection, and the effects of noise. Complex Syst 9(3):193–212
Molina D, Lozano M, Herrera F (2010) Ma-sw-chains: Memetic algorithm based on local search chains for large scale continuous global optimization. In: Evolutionary Computation (CEC), 2010 IEEE Congress on IEEE, pp 1–8
Morris MD (1991) Factorial sampling plans for preliminary computational experiments. Technometrics 33(2):161–174
Omidvar MN, Li X (2010) A comparative study of CMA-ES on large scale global optimisation. In: Australasian joint conference on artificial intelligence. Springer, Berlin
Omidvar MN, Li X (2011) A comparative study of CMA-ES on large scale global optimisation. In: AI 2010: advances in artificial intelligence. Springer, Berlin, pp 303–312
Omidvar MN, Li X, Yang Z, Yao X (2010a) Cooperative co-evolution for large scale optimization through more frequent random grouping. In: Evolutionary computation (CEC), 2010 IEEE Congress on IEEE, pp 1–8
Omidvar MN, Li X, Yao X (2010b) Cooperative co-evolution with delta grouping for large scale non-separable function optimization. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp 1–8
Omidvar MN, Li X, Yao X (2011) Smart use of computational resources based on contribution for cooperative co-evolutionary algorithms. In: Proceedings of the 13th annual conference on genetic and evolutionary computation, ACM, pp 1115–1122
Omidvar MN, Li X, Mei Y, Yao X (2014a) Cooperative co-evolution with differential grouping for large scale optimization. IEEE Trans Evol Comput 18(3):378–393
Omidvar MN, Mei Y, Li X (2014b) Effective decomposition of large-scale separable continuous functions for cooperative co-evolutionary algorithms. In: 2014 IEEE congress on evolutionary computation (CEC), pp 1305 – 1312. IEEE
Potter MA (1997) The design and analysis of a computational model of cooperative coevolution. PhD thesis, Citeseer
Potter MA, De Jong KA (1994) A cooperative coevolutionary approach to function optimization. In: Parallel Problem Solving from NaturePPSN III. Springer, Berlin, pp 249–257
Rabitz H, Aliş ÖF (1999) General foundations of high-dimensional model representations. J Math Chem 25(2–3):197–233
Rao SS, Rao SS (2009) Engineering optimization: theory and practice. Wiley, New York
Ray T, Yao X (2009) A cooperative coevolutionary algorithm with correlation based adaptive variable partitioning. In: IEEE congress on evolutionary computation, 2009. CEC’09, pp 983–989. IEEE
Saltelli A, Chan K, Scott EM et al (2000) Sensitivity analysis, vol 134. Wiley, New York
Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, New York
Sayed E, Essam D, Sarker R (2012a) Dependency identification technique for large scale optimization problems. In: 2012 IEEE Congress on Evolutionary computation (CEC), pp 1–8. IEEE
Sayed E, Essam D, Sarker R (2012b) Using hybrid dependency identification with a memetic algorithm for large scale optimization problems. In: Simulated evolution and learning. Springer, Berlin, pp 168–177
Shan S, Wang GG (2010) Metamodeling for high dimensional simulation-based design problems. J Mech Des 132(5):051009
Shi Y, Teng H, Li Z (2005) Cooperative co-evolutionary differential evolution for function optimization. In: Proceedings of the first international conference on advances in natural computation. Springer, Berlin, vol Part II, pp 1080–1088
Singh HK, Ray T (2010). Divide and conquer in coevolution: a difficult balancing act. In Agent-based evolutionary search. Springer, Berlin, pp 117–138
Sun L, Yoshida S, Cheng X, Liang Y (2012) A cooperative particle swarm optimizer with statistical variable interdependence learning. Inform Sci 186(1):20–39
Tang K, Li X, Suganthan PN, Yang Z, Weise T (2010) Benchmark functions for the CEC’2010 special session and competition on large-scale global optimization. Technical report, Nature inspired computation and applications laboratory (NICAL), USTC, China. http://www.it-weise.de/documents/files/TLSYW2009BFFTCSSACOLSGO.pdf
Van den Bergh F, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 8(3):225–239
Wang H, Rahnamayan S, Wu Z (2013a) Parallel differential evolution with self-adapting control parameters and generalized opposition-based learning for solving high-dimensional optimization problems. J Parallel Distrib Comput 73(1):62–73
Wang Y, Huang J, Dong WS, Yan JC, Tian CH, Li M, Mo WT (2013b) Two-stage based ensemble optimization framework for large-scale global optimization. Eur J Oper Res 228(2):308–320
Weicker K, Weicker N (1999) On the improvement of coevolutionary optimizers by learning variable interdependencies. In: Evolutionary computation, 1999. CEC 99. Proceedings of the 1999 congress on IEEE, vol 3
Yang Z, Tang K, Yao X (2008a) Large scale evolutionary optimization using cooperative coevolution. Inform Sci 178(15):2985–2999
Yang Z, Tang K, Yao X (2008b) Multilevel cooperative coevolution for large scale optimization. In: Evolutionary computation, 2008. CEC 2008. (IEEE World Congress on computational intelligence). IEEE congress on IEEE, pp 1663–1670
Yang Zhenyu, Tang Ke, Yao Xin (2008c) Self-adaptive differential evolution with neighborhood search. In: Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence). IEEE Congress on IEEE, pp 1110–1116
Zhao SZ, Suganthan PN, Das S (2011) Self-adaptive differential evolution with multi-trajectory search for large-scale optimization. Soft Comput 15(11):2175–2185
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Mahdavi, S., Rahnamayan, S. & Shiri, M.E. Incremental cooperative coevolution for large-scale global optimization. Soft Comput 22, 2045–2064 (2018). https://doi.org/10.1007/s00500-016-2466-6
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DOI: https://doi.org/10.1007/s00500-016-2466-6