Abstract
The classical uncertain random multi-objective programming is based on strictly monotonic functions, which limits the application of general monotonic functions. In order to overcome the problem, considering the general monotonic functions, this paper proposes a general uncertain random multi-objective programming, focusing on the multi-objective programming with correlation. Firstly, the solution of expected value and standard deviation value of uncertain random variables is extended to general monotonic functions. Secondly, considering the influence of correlation on the objective functions, the order relationship of expected values among comonotonic functions considering general monotonic functions is deduced. On this basis, the order relationship of expected values and standard deviation values of uncertain random multi-objective function with correlation is obtained, and the order relationship of uncertain random multi-objective function on the basis of the expected value-standard deviation value criterion (CESD criterion) is derived. Then, for the two decision-making situations where the importance of the objective functions is known and the ideal points of the objective functions are known, two methods are proposed, respectively, which are proved that the methods can retain the uncertainty and randomness of the original problem. Finally, a numerical example is given to prove the effectiveness of the methods, which shows that the results obtained on the basis of the CESD criterion can consider both the long-term stability and short-term volatility of decision-making.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data used to support the finding are cited within the article.
References
Afshari H, Tosarkani BM, Jaber MY, Searcy C (2020) The effect of environmental and social value objectives on optimal design in industrial energy symbiosis: A multi-objective approach. Resour Conserv Recycl 158:104825. https://doi.org/10.1016/j.resconrec.2020.104825
Ding SB, Zeng XJ (2018) Uncertain random assignment problem. Appl Math Model 56:96–104. https://doi.org/10.1016/j.apm.2017.11.026
Ding SB, Zeng XJ, Zhang HM (2019) Uncertain random simulation algorithm with application to bottleneck assignment problem. Soft Comput 23(21):10977–10982. https://doi.org/10.1007/s00500-018-3652-5
Ding SB (2020) Uncertain random quadratic bottleneck assignment problem. J Ambient Intell Humaniz Comput 11(8):3259–3264. https://doi.org/10.1007/s12652-019-01510-z
Jenkins PR, Lunday BJ, Robbins MJ (2020) Robust, multi-objective optimization for the military medical evacuation location-allocation problem. Omega-Int. J. Manage. Sci. 97:102088. https://doi.org/10.1016/j.omega.2019.07.004
Karimi H, Jadid S (2020) Optimal energy management for multi-microgrid considering demand response programs: a stochastic multi-objective framework. Energy 195(15):116992.1-1169921.3. https://doi.org/10.1016/j.energy.2020.116992
Ke H, Su TY, Ni YD (2015) Uncertain random multilevel programming with application to production control problem. Soft Comput 19(6):1739–1746. https://doi.org/10.1007/s00500-014-1361-2
Li B, Teo KL (2021) Portfolio optimization in real financial markets with both uncertainty and randomness. Appl Math Model 100:125–137. https://doi.org/10.1016/j.apm.2021.08.006
Liu B (2015) Uncertainty theory, 4th edn. Springer, Berlin
Liu YH (2013a) Uncertain random programming with applications. Fuzzy Optim Decis Mak 12:153–169. https://doi.org/10.1007/s10700-012-9149-2
Liu YH (2013b) Uncertain random variables: a mixture of uncertainty and randomness. Soft Comput 17(4):625–634. https://doi.org/10.1007/s00500-012-0935-0
Liu YY, Liu J, Wang K, Zhang H (2016) A theoretical extension on the operational law for monotone functions of uncertain variables. Soft Comput 20(11):4363–4376. https://doi.org/10.1007/s00500-015-1992-y
Majumder S, Kar MB, Kar S, Pal T (2020) Uncertain programming models for multi-objective shortest path problem with uncertain parameters. Soft Comput 24(12):8975–8996. https://doi.org/10.1007/s00500-019-04423-3
Majumder S, Kar S, Pal T (2019) Uncertain multi-objective Chinese postman problem. Soft Comput 23(22):11557–11572. https://doi.org/10.1007/s00500-018-03697-3
Mehlawat MK, Gupta P, Khan AZ (2021) Portfolio optimization using higher moments in an uncertain random environment. Inf Sci 567:348–374. https://doi.org/10.1016/j.ins.2021.03.019
Molavi A, Shi J, Wu YW, Lim GJ (2020) Enabling smart ports through the integration of microgrids: A two-stage stochastic programming approach. Appl Energy 258:114022. https://doi.org/10.1016/j.apenergy.2019.114022
Pisacane O, Severini M, Fagiani M, Squartini S (2019) Collaborative energy management in a micro-grid by multi-objective mathematical programming. Energy Build. 203:109432. https://doi.org/10.1016/j.enbuild.2019.109432
Qi Y, Wang Y, Liang Y, Sun Y (2019) A novel ideal point method for uncertain random multi-objective programming problem under PE criterion. IEEE Access 7:12982–12992. https://doi.org/10.1109/ACCESS.2019.2892651
Qin ZF (2018) Uncertain random goal programming. Fuzzy Optim Decis Mak 17(4):375–386. https://doi.org/10.1007/s10700-017-9277-9
Saffari M, Kia M, Vahidinasab V, Mehran K (2020) Integrated active/reactive power scheduling of interdependent microgrid and EV fleets based on stochastic multi-objective normalised normal constraint. IET Gener Transm Distrib 14(11):2055–2064. https://doi.org/10.1049/iet-gtd.2019.1406
Su HY, Hong HH (2020) A stochastic multi-objective approach to pilot bus selection for secondary voltage regulation. IEEE Trans Power Syst 35(4):3262–3265. https://doi.org/10.1109/TPWRS.2020.2981004
Varas M, Basso F, Maturana S, Osorio D, Pezoa R (2020) A multi-objective approach for supporting wine grape harvest operations. Comput Ind Eng 145:106497. https://doi.org/10.1016/j.cie.2020.106497
Wang J, Guo JS, Chen JC, Tian S, Gu TY (2019) Uncertain Team Orienteering Problem With Time Windows Based on Uncertainty Theory. IEEE Access 7:63403–63414. https://doi.org/10.1109/ACCESS.2019.2917089
Wang TT, Yang L, Liu Q (2020) Beetle Swarm optimization algorithm: theory and application. FILOMAT 34(15):5121–5137. https://doi.org/10.2298/FIL2015121W
Wang ZT, Zheng MF, Guo JS, Huang HQ (2017) Uncertain UAV ISR mission planning problem with multiple correlated objectives. J Intell Fuzzy Syst 32(1):321–335. https://doi.org/10.3233/JIFS-151781
Yang M, Gong XM (2021) Optimal decisions and Pareto improvement for green supply chain considering reciprocity and cost-sharing contract. Environ Sci Pollut Res 28(23):29859–29874. https://doi.org/10.1007/s11356-021-12752-w
Yang M, Zhang T, Wang CX (2021) The optimal e-commerce sales mode selection and information sharing strategy under demand uncertainty. Comput Ind Eng 162:107718. https://doi.org/10.1016/j.cie.2021.107718
Yang M, Zhang T, Zhang YH (2022) Optimal pricing and green decisions in a dual-channel supply chain with cap-and-trade regulation. Environ Sci Pollut Res. https://doi.org/10.1007/s11356-021-18097-8
Yang XH (2013) On comonotonic functions of uncertain variables. Fuzzy Optim Decis Mak 12(1):89–98. https://doi.org/10.1007/s10700-012-9143-8
Zhang F, Guo SS, Liu X, Wang YZ, Engel BA, Guo P (2020) Towards sustainable water management in an arid agricultural region: a multi-level multi-objective stochastic approach. Agric Syst 182:102848. https://doi.org/10.1016/j.agsy.2020.102848
Zheng Mingfa YY, Zutong W, Long Y (2014) Uncertain random approach to multi-objective programming problem based on chance theory. J Uncertain Syst 8:301–308
Zhou J, Yang F, Wang K (2014) Multi-objective optimization in uncertain random environments. Fuzzy Optim Decis Mak 13(4):397–413. https://doi.org/10.1007/s10700-014-9183-3
Acknowledgements
This work was supported in part by Grants from the National Natural Science Foundation of China (No. 71601183).
Funding
No funding is provided for the preparation of manuscript.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest to this work.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sun, Y., Wang, Y. & Meng, X. Uncertain random multi-objective programming problem given general monotonic function and its solution under CESD criterion. Soft Comput 26, 5297–5313 (2022). https://doi.org/10.1007/s00500-022-06898-z
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-022-06898-z