Abstract
The multi-objective optimization problem has been encountered in numerous fields such as high-speed train head shape design, overlapping community detection, power dispatch, and unmanned aerial vehicle formation. To address such issues, current approaches focus mainly on problems with regular Pareto front rather than solving the irregular Pareto front. Considering this situation, we propose a many-objective evolutionary algorithm based on decomposition with dynamic resource allocation (MaOEA/D-DRA) for irregular optimization. The proposed algorithm can dynamically allocate computing resources to different search areas according to different shapes of the problem’s Pareto front. An evolutionary population and an external archive are used in the search process, and information extracted from the external archive is used to guide the evolutionary population to different search regions. The evolutionary population evolves with the Tchebycheff approach to decompose a problem into several subproblems, and all the subproblems are optimized in a collaborative manner. The external archive is updated with the method of shift-based density estimation. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms using a variety of test problems with irregular Pareto front. Experimental results show that the proposed algorithm out-performs these five algorithms with respect to convergence speed and diversity of population members. By comparison with the weighted-sum approach and penalty-based boundary intersection approach, there is an improvement in performance after integration of the Tchebycheff approach into the proposed algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asafuddoula M, Ray T, Sarker R, 2015. A decomposition-based evolutionary algorithm for many objective optimization. IEEE Trans Evol Comput, 19(3):445–460. https://doi.org/10.1109/TEVC.2014.2339823
Cai XY, Li YX, Fan Z, et al., 2015. An external archive guided multiobjective evolutionary algorithm based on decomposition for combinatorial optimization. IEEE Trans Evol Comput, 19(4):508–523. https://doi.org/10.1109/TEVC.2014.2350995
Cai XY, Yang ZX, Fan Z, et al., 2017. Decomposition-based-sorting and angle-based-selection for evolutionary multi-objective and many-objective optimization. IEEE Trans Cybern, 47(9):2824–2837. https://doi.org/10.1109/TCYB.2016.2586191
Cai XY, Mei ZW, Fan Z, et al., 2018. A constrained decomposition approach with grids for evolutionary multiobjective optimization. IEEE Trans Evol Comput, 22(4):564–577. https://doi.org/10.1109/TEVC.2017.2744674
Chand S, Wagner M, 2015. Evolutionary many-objective optimization: a quick-start guide. Surv Oper Res Manag Sci, 20(2):35–42. https://doi.org/10.10167/j.sorms.2015.08.001
Cheng R, Jin YC, Olhofer M, et al., 2016. A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput, 20(5):773–791. https://doi.org/10.1109/TEVC.2016.2519378
Cheng R, Li MQ, Tian Y, et al., 2018. Benchmark Functions for the CEC’2018 Competition on Many-Objective Optimization. University of Birmingham, United Kingdom.
Coello CAC, 2006. Evolutionary multi-objective optimization: a historical view of the field. IEEE Comput Intell Mag, 1(1):28–36. https://doi.org/10.1109/MCI.2006.1597059
Coello CAC, Lechuga MS, 2002. MOPSO: a proposal for multiple objective particle swarm optimization. Proc Congress on Evolutionary Computation, p.1051–1056. https://doi.org/10.1109/CEC.2002.1004388
Corne DW, Jerram NR, Knowles JD, et al., 2001. PESA-II: region-based selection in evolutionary multiobjective optimization. Proc 3rd Annual Conf on Genetic and Evolutionary Computation, p.283–290.
Das I, Dennis JE, 1998. Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim, 8(3): 631–657. https://doi.org/10.1137/S1052623496307510
Deb K, Goyal M, 1996. A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inform, 26(4):30–45.
Deb K, Jain H, 2014. An evolutionary many-objective optimization algorithm using reference-point-based non-dominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput, 18(4):577–601. https://doi.org/10.1109/TEVC.2013.2281535
Deb K, Pratap A, Agarwal S, et al., 2002. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput, 6(2):182–197. https://doi.org/10.1109/4235.996017
Deb K, Thiele L, Laumanns M, et al., 2005. Scalable test problems for evolutionary multiobjective optimization. In: Abraham A, Jain L, Goldberg R (Eds.), Evolutionary Multiobjective Optimization. Springer, London, p.105–145. https://doi.org/10.1007/1-84628-137-7_6
Elarbi M, Bechikh S, Gupta A, et al., 2018. A new decomposition-based NSGA-II for many-objective optimization. IEEE Trans Syst Man Cybern Syst, 48(7):1191–1210. https://doi.org/10.1109/TSMC.2017.2654301
He C, Tian Y, Jin YC, et al., 2017. A radial space division based evolutionary algorithm for many-objective optimization. Appl Soft Comput, 61:603–621. https://doi.org/10.1016/j.asoc.2017.08.024
He ZN, Yen GG, 2016. Many-objective evolutionary algorithm: objective space reduction and diversity improvement. IEEE Trans Evol Comput, 20(1):145–160. https://doi.org/10.1109/tevc.2015.2433266
Huband S, Hingston P, Barone L, et al., 2006. A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput, 10(5):477–506. https://doi.org/10.1109/tevc.2005.861417
Jain H, Deb K, 2014. An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput, 18(4):602–622. https://doi.org/10.1109/TEVC.2013.2281534
Kukkonen S, Lampinen J, 2005. GDE3: the third evolution step of generalized differential evolution. IEEE Congress on Evolutionary Computation, p.443–450. https://doi.org/10.1109/CEC.2005.1554717
Li BD, Li JL, Tang K, et al., 2015. Many-objective evolutionary algorithms: a survey. ACM Comput Surv, 48(1):13. https://doi.org/10.1145/2792984
Li H, Zhang QF, 2009. Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput, 13(2):284–302. https://doi.org/10.1109/TEVC.2008.925798
Li K, Deb K, Zhang QF, et al., 2015. An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput, 19(5):694–716. https://doi.org/10.1109/TEVC.2014.2373386
Li MQ, Yang SX, Liu XH, 2014. Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput, 18(3):348–365. https://doi.org/10.1109/tevc.2013.2262178
Li MQ, Yang SX, Liu XH, 2015. Bi-goal evolution for many-objective optimization problems. Artif Intell, 228:45–65. https://doi.org/10.1016/j.artint.2015.06.007
Liu YP, Gong DW, Sun XY, et al., 2017. Many-objective evolutionary optimization based on reference points. Appl Soft Comput, 50:344–355. https://doi.org/10.1016/j.asoc.2016.11.009
Purshouse RC, Fleming PJ, 2007. On the evolutionary optimization of many conflicting objectives. IEEE Trans Evol Comput, 11(6):770–784. https://doi.org/10.1109/TEVC.2007.910138
Qi YT, Ma XL, Liu F, et al., 2014. MOEA/D with adaptive weight adjustment. Evol Comput, 22(2):231–264. https://doi.org/10.1162/EVCO_a_00109
Ruan WY, Duan HB, 2020. Multi-UAV obstacle avoidance control via multi-objective social learning pigeon-inspired optimization. Front Inform Technol Electron Eng, 21(5):740–748. https://doi.org/10.1631/FITEE.2000066
Santiago A, Huacuja HJF, Dorronsoro B, et al., 2014. A survey of decomposition methods for multi-objective optimization. In: Castillo O, Melin P, Pedrycz W (Eds.), Recent Advances on Hybrid Approaches for Designing Intelligent Systems. Springer, Cham, p.453–465. https://doi.org/10.1007/978-3-319-05170-3_31
Seada H, Deb K, 2016. A unified evolutionary optimization procedure for single, multiple, and many objectives. IEEE Trans Evol Comput, 20(3):358–369. https://doi.org/10.1109/TEVC.2015.2459718
Seada H, Abouhawwash M, Deb K, 2019. Multiphase balance of diversity and convergence in multiobjective optimization. IEEE Trans Evol Comput, 23(3):503–513. https://doi.org/10.1109/TEVC.2018.2871362
Tian Y, Cheng R, Zhang XY, et al., 2017. PlatEMO: a MATLAB platform for evolutionary multi-objective optimization [Educational Forum]. IEEE Comput Intell Mag, 12(4):73–87. https://doi.org/10.1109/MCI.2017.2742868
Tian Y, Cheng R, Zhang XY, et al., 2018. An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility. IEEE Trans Evol Comput, 22(4):609–622. https://doi.org/10.1109/TEVC.2017.2749619
Trivedi A, Srinivasan D, Sanyal K, et al., 2017. A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans Evol Comput, 21(3):440–462. https://doi.org/10.1109/TEVC.2016.2608507
Wang GP, Jiang HW, 2007. Fuzzy-dominance and its application in evolutionary many objective optimization. Int Conf on Computational Intelligence and Security Workshops, p.195–198. https://doi.org/10.1109/CISW.2007.4425478
Wang TC, Ting CK, 2018. Fitness inheritance assisted MOEA/D-CMAES for complex multi-objective optimization problems. IEEE Congress on Evolutionary Computation, p.1–8. https://doi.org/10.1109/CEC.2018.8477898
Wen XY, Chen WN, Lin Y, et al., 2017. A maximal clique based multiobjective evolutionary algorithm for overlapping community detection. IEEE Trans Evol Comput, 21(3):363–377. https://doi.org/10.1109/TEVC.2016.2605501
Yang SX, Li MQ, Liu XH, et al., 2013. A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput, 17(5):721–736. https://doi.org/10.1109/TEVC.2012.2227145
Zeng YJ, Sun YG, 2014. Comparison of multiobjective particle swarm optimization and evolutionary algorithms for optimal reactive power dispatch problem. IEEE Congress on Evolutionary Computation, p.258–265. https://doi.org/10.1109/CEC.2014.6900260
Zhang HP, Hui Q, 2019. Many objective cooperative bat searching algorithm. Appl Soft Comput, 77:412–437. https://doi.org/10.1016/j.asoc.2019.01.033
Zhang L, Zhang JY, Li T, et al., 2017. Multi-objective aerodynamic optimization design of high-speed train head shape. J Zhejiang Univ-Sci A (Appl Phys & Eng), 18(11): 841–854. https://doi.org/10.1631/jzus.A1600764
Zhang QF, Li H, 2007. MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput, 11(6):712–731. https://doi.org/10.1109/TEVC.2007.892759
Zhang QF, Liu WD, Tsang E, et al., 2010. Expensive multi-objective optimization by MOEA/D with Gaussian process model. IEEE Trans Evol Comput, 14(3):456–474. https://doi.org/10.1109/TEVC.2009.2033671
Zhang XY, Tian Y, Jin YC, 2015. A knee point-driven evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput, 19(6):761–776. https://doi.org/10.1109/TEVC.2014.2378512
Zhou AM, Jin YC, Zhang QF, et al., 2006. Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. IEEE Int Conf on Evolutionary Computation, p.892–899. https://doi.org/10.1109/CEC.2006.1688406
Zhu QL, Zhang QF, Lin QZ, et al., 2019. MOEA/D with two types of weight vectors for handling constraints. IEEE Congress on Evolutionary Computation, p.1359–1365. https://doi.org/10.1109/CEC.2019.8790336
Zitzler E, Künzli S, 2004. Indicator-based selection in multi-objective search. Proc 8th Int Conf on Parallel Problem Solving from Nature, p.832–842. https://doi.org/10.1007/978-3-540-30217-9_84
Zitzler E, Laumanns M, Thiele L, 2001. SPEA2: improving the strength Pareto evolutionary algorithm. TIK-Report, Vol. 103. Eidgenössische Technische Hochschule Zürich (ETH), Institut für Technische Informatik und Kommunikationsnetze (TIK). https://doi.org/10.3929/ethz-a-004284029
Zou XF, Chen Y, Liu MZ, et al., 2008. A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans Syst Man Cybern, 38(5):1402–1412. https://doi.org/10.1109/TSMCB.2008.926329
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 61563012, 61802085, and 61203109), the Guangxi Natural Science Foundation of China (Nos. 2014GXNSFAA118371, 2015GXNSFBA139260, and 2020GXNSFAA159038), the Guangxi Key Laboratory of Embedded Technology and Intelligent System Foundation (No. 2018A-04), and the Guangxi Key Laboratory of Trusted Software Foundation (Nos. kx202011 and kx201926)
Contributors
Ming-gang DONG guided the research. Bao LIU designed the research and drafted the manuscript. Chao JING helped organize the manuscript. Ming-gang DONG and Chao JING revised and finalized the paper.
Compliance with ethics guidelines
Ming-gang DONG, Bao LIU, and Chao JING declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Dong, Mg., Liu, B. & Jing, C. A many-objective evolutionary algorithm based on decomposition with dynamic resource allocation for irregular optimization. Front Inform Technol Electron Eng 21, 1171–1190 (2020). https://doi.org/10.1631/FITEE.1900321
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.1900321
Key words
- Many-objective optimization problems
- Irregular Pareto front
- External archive
- Dynamic resource allocation
- Shift-based density estimation
- Tchebycheff approach