DIP-MOEA: a double-grid interactive preference based multi-objective evolutionary algorithm for formalizing preferences of decision makers

Luda ZHAO; Bin WANG; Xiaoping JIANG; Yicheng LU; Yihua HU

doi:10.1631/FITEE.2100508

Your Location：

Home >

Browse articles >

DIP-MOEA: a double-grid interactive preference based multi-objective evolutionary algorithm for formalizing preferences of decision makers

Regular Papers | Updated：2023-01-11

- DIP-MOEA: a double-grid interactive preference based multi-objective evolutionary algorithm for formalizing preferences of decision makers
  Enhanced Publication
- DIP-MOEA：一种形式化表达决策者偏好的双重网格交互偏好多目标进化算法
- Frontiers of Information Technology & Electronic Engineering Vol. 23, Issue 11, Pages: 1714-1732(2022)
- Affiliations：
  
  1.College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China
  2.Third Interdisciplinary Center, National University of Defense Technology, Hefei 230037, China
  3.Unit 78092 of People's Liberation Army of China, Chengdu 610000
- Author bio：
  
  † E-mail: zhaoluda@nudt.edu.cn;
  ‡Corresponding authors
- Funds：
- DOI：10.1631/FITEE.2100508
  CLC： O224
- Published：0 November 2022，
  
  Published Online：06 September 2022，
  
  Received：26 October 2021，
  
  Accepted：2022-04-14
- Accepted：
Scan QR Code
LUDA ZHAO, BIN WANG, XIAOPING JIANG, et al. DIP-MOEA: a double-grid interactive preference based multi-objective evolutionary algorithm for formalizing preferences of decision makers. [J]. Frontiers of information technology & electronic engineering, 2022, 23(11): 1714-1732.
DOI：

LUDA ZHAO, BIN WANG, XIAOPING JIANG, et al. DIP-MOEA: a double-grid interactive preference based multi-objective evolutionary algorithm for formalizing preferences of decision makers. [J]. Frontiers of information technology & electronic engineering, 2022, 23(11): 1714-1732. DOI： 10.1631/FITEE.2100508.

摘要

几乎所有现有的基于偏好的多目标进化算法（MOEA）给出的最终解集都与决策者偏好信息的表示存在一定距离。因此，提出一种多目标优化算法，称为双重网格交互式基于偏好的多目标进化算法（DIP-MOEA），该算法明确考虑了决策者偏好。首先根据实际多目标优化问题（MOPs）的优化目标和决策者偏好映射隶属度函数，生成决策偏好度网格和偏好误差网格。其次，提出偏好度支配和偏好误差支配两种种群支配方式，并利用该方案更新两个网格中的种群。最后综合两个网格中的种群并结合决策者偏好交互信息可进行偏好多目标优化交互。为验证DIP-MOEA性能，我们在基本DTLZ系列函数和多目标背包问题上对DIP-MOEA进行测试，并将其与几种流行的基于偏好的多目标进化算法进行比较。实验结果表明，DIP-MOEA能较好表达决策者偏好信息，提供满足决策者偏好的解集，快速求解测试问题结果，并在最终解集的Pareto前沿分布性具有较好表现。

Abstract

The final solution set given by almost all existing preference-based multi-objective evolutionary algorithms (MOEAs) lies a certain distance away from the decision makers’ preference information region. Therefore

we propose a multi-objective optimization algorithm

referred to as the double-grid interactive preference based MOEA (DIP-MOEA)

which explicitly takes the preferences of decision makers (DMs) into account. First

according to the optimization objective of the practical multi-objective optimization problems and the preferences of DMs

the membership functions are mapped to generate a decision preference grid and a preference error grid. Then

we put forward two dominant modes of population

preference degree dominance and preference error dominance

and use this advantageous scheme to update the population in these two grids. Finally

the populations in these two grids are combined with the DMs’ preference interaction information

and the preference multi-objective optimization interaction is performed. To verify the performance of DIP-MOEA

we test it on two kinds of problems

i.e.

the basic DTLZ series functions and the multi-objective knapsack problems

and compare it with several different popular preference-based MOEAs. Experimental results show that DIP-MOEA expresses the preference information of DMs well and provides a solution set that meets the preferences of DMs

quickly provides the test results

and has better performance in the distribution of the Pareto front solution set.

关键词

多目标进化算法（MOEA）决策者偏好形式化种群更新策略偏好交互

Keywords

Multi-objective evolutionary algorithm (MOEA)Formalizing preference of decision makersPopulation renewal strategyPreference interaction

references

Akram M, Kahraman C, Zahid K, 2021. Group decision-making based on complex spherical fuzzy VIKOR approach. Knowl-Based Syst, 216:106793. doi: 10.1016/j.knosys.2021.106793http://doi.org/10.1016/j.knosys.2021.106793

Altuzarra A, Moreno-Jiménez JM, Salvador M, 2007. A Bayesian priorization procedure for AHP-group decision making. Eur J Oper Res, 182(1):367-382. doi: 10.1016/j.ejor.2006.07.025http://doi.org/10.1016/j.ejor.2006.07.025

Bazgan C, Hugot H, Vanderpooten D, 2009. Solving efficiently the 0–1 multi-objective knapsack problem. Comput Oper Res, 36(1):260-279. doi: 10.1016/j.cor.2007.09.009http://doi.org/10.1016/j.cor.2007.09.009

Cai XY, Xiao YS, Li MQ, et al., 2021. A grid-based inverted generational distance for multi/many-objective optimization. IEEE Trans Evol Comput, 25(1):21-34. doi: 10.1109/TEVC.2020.2991040http://doi.org/10.1109/TEVC.2020.2991040

Champasak P, Panagant N, Pholdee N, et al., 2020. Self-adaptive many-objective meta-heuristic based on decomposition for many-objective conceptual design of a fixed wing unmanned aerial vehicle. Aerosp Sci Technol, 100:105783. doi: 10.1016/j.ast.2020.105783http://doi.org/10.1016/j.ast.2020.105783

Chen XQ, Lai CS, Ng WWY, et al., 2021. A stochastic sensitivity-based multi-objective optimization method for short-term wind speed interval prediction. Int J Mach Learn Cybern, 12(9):2579-2590. doi: 10.1007/s13042-021-01340-6http://doi.org/10.1007/s13042-021-01340-6

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. doi: 10.1109/TEVC.2016.2519378http://doi.org/10.1109/TEVC.2016.2519378

Chiu WY, Manoharan SH, Huang TY, 2020. Weight induced norm approach to group decision making for multi-objective optimization problems in systems engineering. IEEE Syst J, 14(2):1580-1591. doi: 10.1109/JSYST.2019.2939824http://doi.org/10.1109/JSYST.2019.2939824

Cui ZH, Zhang JJ, Wu D, et al., 2020. Hybrid many-objective particle swarm optimization algorithm for green coal production problem. Inform Sci, 518:256-271. doi: 10.1016/j.ins.2020.01.018http://doi.org/10.1016/j.ins.2020.01.018

Deb K, 2001. Nonlinear goal programming using multi-objective genetic algorithms. J Oper Res Soc, 52(3):291-302. doi: 10.1057/palgrave.jors.2601089http://doi.org/10.1057/palgrave.jors.2601089

Deb K, Pratap A, Agarwal S, et al., 2002a. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput, 6(2):182-197. doi: 10.1109/4235.996017http://doi.org/10.1109/4235.996017

Deb K, Thiele L, Laumanns M, et al., 2002b. Scalable multi-objective optimization test problems. Proc Congress on Evolutionary Computation, p.825-830. doi: 10.1109/CEC.2002.1007032http://doi.org/10.1109/CEC.2002.1007032

Dong MG, Liu B, Jing C, 2020. A many-objective evolutionary algorithm based on decomposition with dynamic resource allocation for irregular optimization. Front Inform Technol Electron Eng, 21(8):1171-1190. doi: 10.1631/FITEE.1900321http://doi.org/10.1631/FITEE.1900321

George T, Amudha T, 2020. Genetic algorithm based multi-objective optimization framework to solve traveling salesman problem. In: Sharma H, Govindan K, Poonia R (Eds.), Advances in Computing and Intelligent Systems: Algorithms for Intelligent Systems. Springer, Singapore. doi:10.1007/978-981-15-0222-4_12http://doi.org/10.1007/978-981-15-0222-4_12

Huang CZ, Yuan HW, Geng YM, 2021. Multi-objective preference optimization method of permanent magnet assisted reluctance motor. Proc 17th Int Conf on Computational Intelligence and Security, p.413-419. doi: 10.1109/CIS54983.2021.00092http://doi.org/10.1109/CIS54983.2021.00092

Ishibuchi H, Matsumoto T, Masuyama N, et al., 2020. Effects of dominance resistant solutions on the performance of evolutionary multi-objective and many-objective algorithms. Proc Genetic and Evolutionary Computation Conf, p.507-515. doi: 10.1145/3377930.3390166http://doi.org/10.1145/3377930.3390166

Jakubovski Filho HL, Ferreira TN, Vergilio SR, 2019. Preference based multi-objective algorithms applied to the variability testing of software product lines. J Syst Softw, 151:194-209. doi: 10.1016/j.jss.2019.02.028http://doi.org/10.1016/j.jss.2019.02.028

Jiang SW, Zhang J, Ong YS, et al., 2015. A simple and fast hypervolume indicator-based multiobjective evolutionary algorithm. IEEE Trans Cybern, 45(10):2202-2213. doi: 10.1109/TCYB.2014.2367526http://doi.org/10.1109/TCYB.2014.2367526

Lai G, Liao MH, Li K, 2021. Empirical studies on the role of the decision maker in interactive evolutionary multi-objective optimization. Proc IEEE Congress on Evolutionary Computation, p.185-192. doi: 10.1109/CEC45853.2021.9504980http://doi.org/10.1109/CEC45853.2021.9504980

Li H, Deng JD, Zhang QF, et al., 2019. Adaptive Epsilon dominance in decomposition-based multiobjective evolutionary algorithm. Swarm Evol Comput, 45:52-67. doi: 10.1016/j.swevo.2018.12.007http://doi.org/10.1016/j.swevo.2018.12.007

Li HR, He FZ, Yan XH, 2019. IBEA-SVM: an indicator-based evolutionary algorithm based on pre-selection with classification guided by SVM. Appl Math A J Chin Univ, 34(1):1-26. doi: 10.1007/s11766-019-3706-1http://doi.org/10.1007/s11766-019-3706-1

Li LM, Wang YL, Trautmann H, et al., 2018. Multiobjective evolutionary algorithms based on target region preferences. Swarm Evol Comput, 40:196-215. doi: 10.1016/j.swevo.2018.02.006http://doi.org/10.1016/j.swevo.2018.02.006

Lin BR, Chen HZ, Liu YC, et al., 2021. A preference-based multi-objective building performance optimization method for early design stage. Build Simul, 14(3):477-494. doi: 10.1007/s12273-020-0673-7http://doi.org/10.1007/s12273-020-0673-7

Liu QQ, Jin YC, Heiderich M, et al., 2020. An adaptive reference vector-guided evolutionary algorithm using growing neural gas for many-objective optimization of irregular problems. IEEE Trans Cybern, 52(5):2698-2711. doi: 10.1109/TCYB.2020.3020630http://doi.org/10.1109/TCYB.2020.3020630

Liu RC, Song XL, Fang LF, et al., 2017. An r-dominance-based preference multi-objective optimization for many-objective optimization. Soft Comput, 21(17):5003-5024. doi: 10.1007/s00500-016-2098-xhttp://doi.org/10.1007/s00500-016-2098-x

López-Jaimes A, Coello CAC, 2014. Including preferences into a multiobjective evolutionary algorithm to deal with many-objective engineering optimization problems. Inform Sci, 277:1-20. doi: 10.1016/j.ins.2014.04.023http://doi.org/10.1016/j.ins.2014.04.023

Louis SJ, McDonnell J, 2004. Learning with case-injected genetic algorithms. IEEE Trans Evol Comput, 8(4):316-328. doi: 10.1109/TEVC.2004.823466http://doi.org/10.1109/TEVC.2004.823466

Luo WJ, Shi LM, Lin X, et al., 2019. The <math id="M937"><mover accent="true"><mi>g</mi><mo>^</mo></mover></math>-dominance relation for preference-based evolutionary multi-objective optimization. Proc IEEE Congress on Evolutionary Computation, p.2418-2425. doi: 10.1109/CEC.2019.8790321http://doi.org/10.1109/CEC.2019.8790321

Marler RT, Arora JS, 2010. The weighted sum method for multi-objective optimization: new insights. Struct Multidisc Optim, 41(6):853-862. doi: 10.1007/s00158-009-0460-7http://doi.org/10.1007/s00158-009-0460-7

Menchaca-Méndez A, Montero E, Antonio LM, et al., 2019. A co-evolutionary scheme for multi-objective evolutionary algorithms based on <math id="M938"><mi>ϵ</mi></math>-dominance. IEEE Access, 7:18267-18283. doi: 10.1109/ACCESS.2019.2896962http://doi.org/10.1109/ACCESS.2019.2896962

Miguel F, Frutos M, Tohmé F, et al., 2019. A decision support tool for urban freight transport planning based on a multi-objective evolutionary algorithm. IEEE Access, 7:156707-156721. doi: 10.1109/ACCESS.2019.2949948http://doi.org/10.1109/ACCESS.2019.2949948

Mohammadi A, Omidvar MN, Li XD, 2013. A new performance metric for user-preference based multi-objective evolutionary algorithms. Proc IEEE Congress on Evolutionary Computation, p.2825-2832. doi: 10.1109/CEC.2013.6557912http://doi.org/10.1109/CEC.2013.6557912

Paknejad P, Khorsand R, Ramezanpour M, 2021. Chaotic improved PICEA-g-based multi-objective optimization for workflow scheduling in cloud environment. Fut Gener Comput Syst, 117:12-28. doi: 10.1016/j.future.2020.11.002http://doi.org/10.1016/j.future.2020.11.002

Pirouz B, Khorram E, 2016. A computational approach based on the <math id="M939"><mi>ϵ</mi></math>-constraint method in multi-objective optimization problems. Adv Appl Stat, 49(6):453-483. doi: 10.17654/AS049060453http://doi.org/10.17654/AS049060453

Premkumar M, Jangir P, Kumar BS, et al., 2021. A new arithmetic optimization algorithm for solving real-world multiobjective CEC-2021 constrained optimization problems: diversity analysis and validations. IEEE Access, 9:84263-84295. doi: 10.1109/ACCESS.2021.3085529http://doi.org/10.1109/ACCESS.2021.3085529

Sudeng S, Wattanapongsakorn N, 2013. Adaptive geometric angle-based algorithm with independent objective biasing for pruning Pareto-optimal solutions. Proc Science and Information Conf, p.514-523.

Sudeng S, Wattanapongsakorn N, 2015. Post Pareto-optimal pruning algorithm for multiple objective optimization using specific extended angle dominance. Eng Appl Artif Intell, 38:221-236. doi: 10.1016/j.engappai.2014.10.020http://doi.org/10.1016/j.engappai.2014.10.020

Sun YN, Yen GG, Yi Z, 2019. IGD indicator-based evolutionary algorithm for many-objective optimization problems. IEEE Trans Evol Comput, 23(2):173-187. doi: 10.1109/TEVC.2018.2791283http://doi.org/10.1109/TEVC.2018.2791283

Wahid A, Gao XY, Andreae P, 2015. Multi-objective clustering ensemble for high-dimensional data based on strength Pareto evolutionary algorithm (SPEA-II). Proc IEEE Int Conf on Data Science and Advanced Analytics, p.1-9. doi: 10.1109/DSAA.2015.7344795http://doi.org/10.1109/DSAA.2015.7344795

Wang F, Li YX, Zhang H, et al., 2019. An adaptive weight vector guided evolutionary algorithm for preference-based multi-objective optimization. Swarm Evol Comput, 49:220-233. doi: 10.1016/j.swevo.2019.06.009http://doi.org/10.1016/j.swevo.2019.06.009

Wang R, Purshouse RC, Fleming PJ, 2013. Preference-inspired co-evolutionary algorithm using adaptively generated goal vectors. Proc IEEE Congress on Evolutionary Computation, p.916-923. doi: 10.1109/CEC.2013.6557665http://doi.org/10.1109/CEC.2013.6557665

Wang R, Purshouse RC, Giagkiozis I, et al., 2015a. The iPICEA-g: a new hybrid evolutionary multi-criteria decision making approach using the brushing technique. Eur J Oper Res, 243(2):442-453. doi: 10.1016/j.ejor.2014.10.056http://doi.org/10.1016/j.ejor.2014.10.056

Wang R, Purshouse RC, Fleming PJ, 2015b. Preference-inspired co-evolutionary algorithms using weight vectors. Eur J Oper Res, 243(2):423-441. doi: 10.1016/j.ejor.2014.05.019http://doi.org/10.1016/j.ejor.2014.05.019

Yu G, Zheng J, Shen R, et al, 2016. Decomposing the user-preference in multiobjective optimization. Soft Comput, 20(10):4005-4021. doi: 10.1007/s00500-015-1736-zhttp://doi.org/10.1007/s00500-015-1736-z

Zhang QF, Li H, 2007. MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput, 11(6):712-731. doi: 10.1109/TEVC.2007.892759http://doi.org/10.1109/TEVC.2007.892759

Zhang ZX, Chen WN, Jin H, et al., 2021. A preference biobjective evolutionary algorithm for the payment scheduling negotiation problem. IEEE Trans Cybern, 51(12):6105-6118. doi: 10.1109/TCYB.2020.2966492http://doi.org/10.1109/TCYB.2020.2966492

Zhao LD, Wang B, Shen CY, 2021. A multi-objective scheduling method for operational coordination time using improved triangular fuzzy number representation. PLoS ONE, 16(6):e0252293. doi: 10.1371/journal.pone.0252293http://doi.org/10.1371/journal.pone.0252293

Zheng JH, Xie ZZ, 2014. A study on how to use angle information to include decision maker's preferences. Acta Electron Sin, 42(11):2239-2246(in Chinese). doi: 10.3969/j.issn.0372-2112.2014.11.017http://doi.org/10.3969/j.issn.0372-2112.2014.11.017

Zheng JH, Lai N, Guo GQ, 2014. <math id="M940"><mi>ϵ</mi></math>-Pareto dominance strategy based on angle preference in MOEA. PR AI, 27(6):569-576(in Chinese). doi: 10.3969/j.issn.1003-6059.2014.06.013http://doi.org/10.3969/j.issn.1003-6059.2014.06.013

Zitzler E, Künzli S, 2004. Indicator-based selection in multiobjective search. Proc 8th Int Conf on Parallel Problem Solving from Nature, p.832-842. doi: 10.1007/978-3-540-30217-9_84http://doi.org/10.1007/978-3-540-30217-9_84

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

Multi-objective differential evolution with diversity enhancement

Related Author

Bo-yang QU

Ponnuthurai-Nagaratnam SUGANTHAN

Related Institution

School of Electrical and Electronic Engineering, Nanyang Technological University

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰