Comparison of a novel dominance-based differential evolution method with the state-of-the-art methods for solving multi-objective real-valued optimization problems
Differential Evolution algorithm (DE) is a well-known nature-inspired method in evolutionary computations scope. This paper adds some new features to DE algorithm and proposes a novel method focusing on ranking technique. The proposed method is named as Dominance-Based Differential Evolution, called DBDE from this point on, which is the improved version of the standard DE algorithm. The suggested DBDE applies some changes on the selection operator of the Differential Evolution (DE) algorithm and modifies the crossover and initialization phases to improve the performance of DE. The dominance ranks are used in the selection phase of DBDE to be capable of selecting higher quality solutions. A dominance-rank for solution X is the number of solutions dominating X. Moreover, some vectors called target vectors are used through the selection process. Effectiveness and performance of the proposed DBDE method is experimentally evaluated using six well-known benchmarks, provided by CEC2009, plus two additional test problems namely Kursawe and Fonseca & Fleming. The evaluation process emphasizes on specific bi-objective real-valued optimization problems reported in literature.
Likewise, the Inverted Generational Distance (IGD) metric is calculated for the obtained results to measure the performance of algorithms. To follow up the evaluation rules obeyed by all state-of-the-art methods, the fitness evaluation function is called 300.000 times and 30 independent runs of DBDE is carried out. Analysis of the obtained results indicates that the performance of the proposed algorithm (DBDE) in terms of convergence and robustness outperforms the majority of state-of-the-art methods reported in the literature
Marler, R. T., Arora, J. S. (2004). Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, 26 (6), 369–395. doi: https://doi.org/10.1007/s00158-003-0368-6
Coello, C. A. C., Lamont, G. B., van Veldhuizen, D. A. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems. Springer, 800. doi: https://doi.org/10.1007/978-0-387-36797-2
Li, Y., Wang, S., Yang, B. (2020). An improved differential evolution algorithm with dual mutation strategies collaboration. Expert Systems with Applications, 153, 113451. doi: https://doi.org/10.1016/j.eswa.2020.113451
Mezura-Montes, E., Reyes-Sierra, M., Coello, C. A. C. (2008). Multi-objective Optimization Using Differential Evolution: A Survey of the State-of-the-Art. Studies in Computational Intelligence, 173–196. doi: https://doi.org/10.1007/978-3-540-68830-3_7
Salomon, M., Perrin, G.-R., Heitz, F., Armspach, J.-P. (2005). Parallel Differential Evolution: Application to 3-D Medical Image Registration. Differential Evolution, 353–411. doi: https://doi.org/10.1007/3-540-31306-0_12
Ma, J.-P., Zheng, Z.-B., Tong, Q.-X., Zheng, L.-F. (2003). An application of genetic algorithms on band selection for hyperspectral image classification. Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693). doi: https://doi.org/10.1109/icmlc.2003.1260030
Zhang, Q., Zhou, A., Zhao, S., Suganthan, P. N., Liu, W. (2009). Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition. 2009 IEEE Congress on Evolutionary Computation (CEC 2009). Available at: https://www.researchgate.net/profile/Ponnuthurai-Suganthan/publication/265432807_Multiobjective_optimization_Test_Instances_for_the_CEC_2009_Special_Session_and_Competition/links/54b7d9940cf2c27adc473433/Multiobjective-optimization-Test-Instances-for-the-CEC-2009-Special-Session-and-Competition.pdf
jMetal Web site. Available at: http://jmetal.sourceforge.net/index.html
Savsani, V., Tawhid, M. A. (2017). Non-dominated sorting moth flame optimization (NS-MFO) for multi-objective problems. Engineering Applications of Artificial Intelligence, 63, 20–32. doi: https://doi.org/10.1016/j.engappai.2017.04.018
Zhang, Q., Li, H. (2007). MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Transactions on Evolutionary Computation, 11 (6), 712–731. doi: https://doi.org/10.1109/tevc.2007.892759
Yu, D., Hong, J., Zhang, J., Niu, Q. (2018). Multi-Objective Individualized-Instruction Teaching-Learning-Based Optimization Algorithm. Applied Soft Computing, 62, 288–314. doi: https://doi.org/10.1016/j.asoc.2017.08.056
Chen, C.-M., Chen, Y., Zhang, Q. (2009). Enhancing MOEA/D with guided mutation and priority update for multi-objective optimization. 2009 IEEE Congress on Evolutionary Computation. doi: https://doi.org/10.1109/cec.2009.4982950
Zong, P. (2011). MTS Algorithm Based on Vague Set. 2011 International Conference on Intelligence Science and Information Engineering. doi: https://doi.org/10.1109/isie.2011.123
Liu, M., Zou, X., Chen, Y., Wu, Z. (2009). Performance assessment of DMOEA-DD with CEC 2009 MOEA competition test instances. 2009 IEEE Congress on Evolutionary Computation. doi: https://doi.org/10.1109/cec.2009.4983309
Khan Mashwani, W., Salhi, A., Yeniay, O., Hussian, H., Jan, M. A. (2017). Hybrid non-dominated sorting genetic algorithm with adaptive operators selection. Applied Soft Computing, 56, 1–18. doi: https://doi.org/10.1016/j.asoc.2017.01.056
Sindhya, K., Sinha, A., Deb, K., Miettinen, K. (2009). Local search based evolutionary multi-objective optimization algorithm for constrained and unconstrained problems. 2009 IEEE Congress on Evolutionary Computation. doi: https://doi.org/10.1109/cec.2009.4983310
Huang, V. L., Qin, A. K., Suganthan, P. N., Tasgetiren, M. F. (2007). Multi-objective optimization based on self-adaptive differential evolution algorithm. 2007 IEEE Congress on Evolutionary Computation. doi: https://doi.org/10.1109/cec.2007.4424939
Lin, Q., Liu, S., Wong, K.-C., Gong, M., Coello Coello, C. A., Chen, J., Zhang, J. (2019). A Clustering-Based Evolutionary Algorithm for Many-Objective Optimization Problems. IEEE Transactions on Evolutionary Computation, 23 (3), 391–405. doi: https://doi.org/10.1109/tevc.2018.2866927
Vrugt, J. A., Robinson, B. A. (2007). Improved evolutionary optimization from genetically adaptive multimethod search. Proceedings of the National Academy of Sciences, 104 (3), 708–711. doi: https://doi.org/10.1073/pnas.0610471104
Zeng, S., Yao, S., Kang, L., Liu, Y. (2005). An Efficient Multi-objective Evolutionary Algorithm: OMOEA-II. Evolutionary Multi-Criterion Optimization, 108–119. doi: https://doi.org/10.1007/978-3-540-31880-4_8
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6 (2), 182–197. doi: https://doi.org/10.1109/4235.996017
Sedarous, S., El-Gokhy, S. M., Sallam, E. (2018). Multi-swarm multi-objective optimization based on a hybrid strategy. Alexandria Engineering Journal, 57 (3), 1619–1629. doi: https://doi.org/10.1016/j.aej.2017.06.017
Wu, D., Liu, Y., Zhou, K., Li, K., Li, J. (2019). A multi-objective particle swarm optimization algorithm based on human social behavior for environmental economics dispatch problems. Environmental Engineering and Management Journal, 18 (7), 1599–1607. doi: https://doi.org/10.30638/eemj.2019.150
Fonseca, C. M., Fleming, P. J. (1995). An Overview of Evolutionary Algorithms in Multiobjective Optimization. Evolutionary Computation, 3 (1), 1–16. doi: https://doi.org/10.1162/evco.19184.108.40.206
Coello, C. A. C., Pulido, G. T., Lechuga, M. S. (2004). Handling multiple objectives with particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8 (3), 256–279. doi: https://doi.org/10.1109/tevc.2004.826067
Coello Coello, C. A., Pulido, G. T. (2005). Multiobjective structural optimization using a microgenetic algorithm. Structural and Multidisciplinary Optimization, 30 (5), 388–403. doi: https://doi.org/10.1007/s00158-005-0527-z
Lim, W. J., Jambek, A. B., Neoh, S. C. (2015). Kursawe and ZDT functions optimization using hybrid micro genetic algorithm (HMGA). Soft Computing, 19 (12), 3571–3580. doi: https://doi.org/10.1007/s00500-015-1767-5
Knowles, J., Corne, D. (1999). The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation. Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406). doi: https://doi.org/10.1109/cec.1999.781913
Kursawe, F. (1991). A variant of evolution strategies for vector optimization. Lecture Notes in Computer Science, 193–197. doi: https://doi.org/10.1007/bfb0029752
Sierra, M. R., Coello Coello, C. A. (2005). Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and ∈-Dominance. Evolutionary Multi-Criterion Optimization, 505–519. doi: https://doi.org/10.1007/978-3-540-31880-4_35
Durillo, J. J., Nebro, A. J. (2011). jMetal: A Java framework for multi-objective optimization. Advances in Engineering Software, 42 (10), 760–771. doi: https://doi.org/10.1016/j.advengsoft.2011.05.014
Lwin, K. T., Qu, R., MacCarthy, B. L. (2017). Mean-VaR portfolio optimization: A nonparametric approach. European Journal of Operational Research, 260 (2), 751–766. doi: https://doi.org/10.1016/j.ejor.2017.01.005
Copyright (c) 2021 Mustafa Tuncay, Ali Haydar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.