Abstract
A multi-objective problem must simultaneously satisfy some conditions that may conflict with each other. Some examples of this problem are the design of machines with low power consumption and high power, or the development of software products in a short time and with high quality. Several algorithms have been proposed to solve this type of problems, such as NSGA-II, MOEA/D, SPEA2, and MSOPS. Each of these algorithms is based on different techniques such as the combination of objectives, Pareto efficiency, and prioritization. The selection of the best algorithm for a problem may become a cumbersome task. By its part, MOGBHS is a multi-objective algorithm based on the Global-Best Harmony Search, non-dominated sorting, and crowding distance that has shown great efficiency. This paper presents a comparative analysis of MOGBHS against other state-of-the-art algorithms. The analysis was performed over 21 multi-objective optimization problems from the IEEE CEC competition, 12 without restrictions and 9 with restrictions. The evaluation was performed using several evaluations of the objective function (2000, 5000, 10000 and 20000) and different metrics: Hypervolume, Epsilon, Generational Distance, Inverse Generational Distance, and Spacing. Finally, the analysis of the results was performed using non-parametric statistical tests (Wilcoxon and Friedman). MOGBHS obtained the best results according to the Inverse Generational Distance for 10000 and 20000 evaluations of the objective functions. Likewise, MOGBHS achieved competitive results for 2000 and 5000 evaluations. On the other hand, SPEA2 algorithm reached the best average results in all metrics.
Keywords
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Luo, J., Liu, Q., Yang, Y., Li, X., Chen, M.R., Cao, W.: An artificial bee colony algorithm for multi-objective optimisation. Appl. Soft Comput. J. 50, 235–251 (2017)
Li, B., Li, J., Tang, K., Yao, X.: Many-objective evolutionary algorithms. ACM Comput. Surv. 48, 1–35 (2015)
Ruano, E., Cobos, C., Torres-Jimenez, J.: Transit network frequencies-setting problem solved using a new multi-objective global-best harmony search algorithm and discrete event simulation. In: Pichardo-Lagunas, O., Miranda-Jiménez, S. (eds.) MICAI 2016. LNCS (LNAI), vol. 10062, pp. 341–352. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62428-0_27
Von Lücken, C., Barán, B., Brizuela, C.: A survey on multi-objective evolutionary algorithms for many-objective problems. Comput. Optim. Appl. 58, 707–756 (2014)
Bechikh, S., Elarbi, M., Ben Said, L.: Many-objective optimization using evolutionary algorithms: a survey. In: Bechikh, S., Datta, R., Gupta, A. (eds.) Recent Advances in Evolutionary Multi-objective Optimization. ALO, vol. 20, pp. 105–137. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-42978-6_4
Zhang, X., Tian, Y., Jin, Y.: Approximate non-dominated sorting for evolutionary many-objective optimization. Inf. Sci. (NY). 369, 14–33 (2016)
Zhang, J., Xing, L.: A survey of multiobjective evolutionary algorithms. In: 2017 IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC), pp. 93–100. IEEE (2017)
Vachhani, V.L., Dabhi, V.K., Prajapati, H.B.: Survey of multi objective evolutionary algorithms. In: 2015 International Conference on Circuits, Power and Computing Technologies, ICCPCT 2015, pp. 1–9. IEEE (2015)
Trivedi, A., Srinivasan, D., Sanyal, K., Ghosh, A.: A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans. Evol. Comput. 21, 1 (2016)
Shi, J.-C., Qian, C., Yu, Y.: Evolutionary multi-objective optimization made faster by sequential decomposition. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 2488–2493. IEEE (2017)
Cao, B., et al.: Distributed parallel particle swarm optimization for multi-objective and many-objective large-scale optimization. IEEE Access 5, 8214–8221 (2017)
Cao, B., Zhao, J., Lv, Z., Liu, X.: A distributed parallel cooperative coevolutionary multiobjective evolutionary algorithm for large-scale optimization. IEEE Trans. Ind. Inform. 13, 2030–2038 (2017)
Menchaca-Mendez, A., Hernandez, C., Coello, C.A.C.: Δp-MOEA: a new multi-objective evolutionary algorithm based on the Δp indicator. In: 2016 IEEE Congress on Evolutionary Computation, CEC 2016, pp. 3753–3760. IEEE (2016)
Li, K., Deb, K., Zhang, Q., Kwong, S.: An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans. Evol. Comput. 19, 694–716 (2015)
Wang, H., Jiao, L., Yao, X.: Two Arch2: an improved two-archive algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 19, 524–541 (2015)
Menchaca-Mendez, A., Coello, C.A.C.: MD-MOEA: a new MOEA based on the maximin fitness function and Euclidean distances between solutions. In: Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, pp. 2148–2155 (2014)
Cremene, M., Suciu, M., Pallez, D., Dumitrescu, D.: Comparative analysis of multi-objective evolutionary algorithms for QoS-aware web service composition. Appl. Soft Comput. 39(C), 124—139 (2016). https://doi.org/10.1016/j.asoc.2015.11.012. ISSN 1568-4946
Deb, K., Pratab, S., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NGSA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2002)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Swiss Federal Institute of Technology (ETH) Zurich (2001). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.4617
He, Z., Yen, G.G.: Diversity improvement in decomposition-based multi-objective evolutionary algorithm for many-objective optimization problems. In: Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics, pp. 2409–2414 (2014)
Mirjalili, S., Lewis, A.: Novel performance metrics for robust multi-objective optimization algorithms. Swarm Evol. Comput. 21, 1–23 (2015)
Rostami, S., Neri, F.: A fast hypervolume driven selection mechanism for many-objective optimisation problems. Swarm Evol. Comput. 34, 50–67 (2017)
Durillo, J.J., Nebro, A.J.: JMetal: a Java framework for multi-objective optimization. Adv. Eng. Softw. 42, 760–771 (2011)
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Ordoñez, C., Ruano, E., Cobos, C., Ordoñez, H., Ordoñez, A. (2018). Comparative Analysis of MOGBHS with Other State-of-the-Art Algorithms for Multi-objective Optimization Problems. In: Castro, F., Miranda-Jiménez, S., González-Mendoza, M. (eds) Advances in Soft Computing. MICAI 2017. Lecture Notes in Computer Science(), vol 10632. Springer, Cham. https://doi.org/10.1007/978-3-030-02837-4_13
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