New approach for uncertain random multi-objective programming problems based on CESD criterion

doi:10.23919/JSEE.2021.000053

Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (3): 619-630.doi: 10.23919/JSEE.2021.000053

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New approach for uncertain random multi-objective programming problems based on C_ESD criterion

Yun SUN^1,*(), Ying WANG¹(), Xiangfei MENG²(), Chaoqi FU¹(), Chengkun LUO³()

¹ Equipment Management and UAV Engineering College, Air Force Engineering University, Xi’an 710051, China
² Air Force Command College, Beijing 100097, China
³ Beijing Institute of System Engineering, Beijing 100101, China

Received:2020-08-04 Online:2021-06-18 Published:2021-07-26
Contact: Yun SUN E-mail:1259006637@qq.com;yingwangkgd@163.com;mengxiangfeikgd@163.com;fuchaoqi2011@163.com;afeulck@163.com
About author:|SUN Yun was born in 1993. He received his B.S. degree in control science and engineering from Air Force Engineering University, Xi’an, China, in 2016, where he is currently pursuing his Ph.D. degree. His research interests include equipment system engineering. E-mail: 1259006637@qq.com||WANG Ying was born in 1967. She received her Ph.D. degree in management science and engineer- ing from Xi’an Jiaotong University in 2003. She is a professor in Air Force Engineering University. Her research interests are uncertainty theory and supply chain management. E-mail: yingwangkgd@163.com||MENG Xiangfei was born in 1989. He received his Ph.D. degree in control science and engineering from Air Force Engineering University, Xi’an, China, in 2018. He is currently a lecturer with Air Force Command College. His current research interests include equipment system engineering. E-mail: mengxiangfeikgd@163.com||FU Chaoqi was born in 1988. He received his Ph.D. degree in control science and engineering from Air Force Engineering University, Xi’an, China, in 2017. He is currently a lecturer with Air Force Engineering University. His current research interests include equipment system engineering and complex network. E-mail: fuchaoqi2011@163.com||LUO Chengkun was born in 1990. He received his Ph.D. degree in management science and engineering from Air Force Engineering University, Xi’an, China, in 2019. He is currently an assistant researcher with Beijing Institute of System Engineering. His current research interest is equipment system engineering. E-mail: afeulck@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (72001213), and the basic research program of Natural Science of Shaanxi Province, China (2021JQ-369)

Abstract

Abstract:

To overcome the defects that the traditional approach for multi-objective programming under uncertain random environment (URMOP) neglects the randomness and uncertainty of the problem and the volatility of the results, a new approach is proposed based on expected value-standard deviation value criterion (C_ESD criterion). Firstly, the effective solution to the URMOP problem is defined; then, by applying sequence relationship between the uncertain random variables, the URMOP problem is transformed into a single-objective programming (SOP) under uncertain random environment (URSOP), which are transformed into a deterministic counterpart based on the C_ESD criterion. Then the validity of the new approach is proved that the optimal solution to the SOP problem is also efficient for the URMOP problem; finally, a numerical example and a case application are presented to show the effectiveness of the new approach.

Key words: chance theory, independent-uncertain random multi-objective programming, expected value-standard derivation value criterion (C_ESD criterion)

Yun SUN, Ying WANG, Xiangfei MENG, Chaoqi FU, Chengkun LUO. New approach for uncertain random multi-objective programming problems based on C_ESD criterion[J]. Journal of Systems Engineering and Electronics, 2021, 32(3): 619-630.

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References 24

1	MAVROTAS G Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied Mathematics & Computation, 2009, 213 (2): 455- 465.
2	SEPAHVAND R, SAFAVI H R, REZAEI F Multi-objective planning for conjunctive use of surface and ground water resources using genetic programming. Water Resources Management, 2019, 33 (6): 2123- 2137. doi: 10.1007/s11269-019-02229-4
3	SILVA S, ALCADA-ALMEIDA L, DIAS L C Multi-objective programming for sizing and locating biogas plants: a model and an application in a region of Portugal. Computers & Operations Research, 2017, 83, 189- 198.
4	XU B, ZHONG P A, WU Y, et al A multi-objective stochastic programming model for hydropower hedging operations under inexact information. Water Resources Management, 2017, 31 (14): 1- 19.
5	HASSANNAYEBI E, ZEGORDI S H, AMIN-NASERI M R, et al Train timetabling at rapid rail transit lines: a robust multi-objective stochastic programming approach. Operational Research, 2017, 17, 435- 477. doi: 10.1007/s12351-016-0232-2
6	TABAR V S, JIRDEHI M A, HEMMATI R Energy management in microgrid based on the multi objective stochastic programming incorporating portable renewable energy resource as demand response option. Energy, 2017, 118, 827- 839. doi: 10.1016/j.energy.2016.10.113
7	LIU B D. Uncertainty theory. 2nd ed. Berlin: Springer-Verlag, 2007.
8	KAHNEMAN D, TVERSKY A Prospect theory: an analysis of decisions under risk. Econometrica, 1979, 47 (2): 263- 291. doi: 10.2307/1914185
9	TVERSKY A, KAHNEMAN D Rational choice and the framing of decisions. Journal of Business, 1986, 59 (4): 251- 278.
10	LIU B D Why is there a need for uncertainty theory?. Jour-nal of Uncertain Systems, 2012, 6 (1): 3- 10.
11	ZADEH L A Fuzzy sets. Information & Control, 1965, 8 (3): 338- 353.
12	ARASTEH A Supply chain management under uncertainty with the combination of fuzzy multi-objective planning and real options approaches. Soft Computing, 2020, 24 (7): 5177- 5198. doi: 10.1007/s00500-019-04271-1
13	KUMAR D, RAHMAN Z, CHAN F T S A fuzzy AHP and fuzzy multi-objective linear programming model for order allocation in a sustainable supply chain: a case study. International Journal of Computer Integrated Manufacturing, 2017, 30 (6): 535- 551. doi: 10.1080/0951192X.2016.1145813
14	TSAO Y C, THANH V V, LU J C, et al Designing sustainable supply chain networks under uncertain environments: fuzzy multi-objective programming. Journal of Cleaner Production, 2017, 174, 1550- 1565.
15	LIU B D. Uncertainty theory: a branch of mathematics for modeling human uncertainty. Berlin: Springer-Verlag, 2010.
16	LIU B D. Theory and practice of uncertain programming. Berlin: Springer-Verlag, 2009.
17	LIU B D, CHEN X W Uncertain multi-objective programming and uncertain goal programming. Journal of Uncertainty Analysis and Applications, 2015, 3 (1): 3- 10. doi: 10.1186/s40467-015-0027-7
18	LIU Y H Uncertain random variables: a mixture of uncertainty and randomness. Soft Computing, 2013, 17 (4): 625- 634. doi: 10.1007/s00500-012-0935-0
19	LIU Y H Uncertain random programming with applications. Fuzzy Optimization & Decision Making, 2013, 12 (2): 153- 169.
20	ZHOU J, YANG F, WANG K Multi-objective optimization in uncertain random environments. Fuzzy Optimization and Decision Making, 2014, 13 (4): 397- 413. doi: 10.1007/s10700-014-9183-3
21	ZHENG M F, YI Y, WANG Z T, et al Uncertain random approach to multi-objective programming problem based on chance theory. Journal of Uncertain Systems, 2014, 8 (4): 301- 308.
22	QI Y, WANG Y, LIANG Y, et al A novel ideal point method for uncertain random multi-objective programming problem under PE criterion. IEEE Access, 2019, 7, 12982- 12992. doi: 10.1109/ACCESS.2019.2892651
23	JIANG X Y, LIN Z Y, HE T H, et al Optimal path finding with beetle antennae search algorithm by using ant colony optimization initialization and different searching strategies. IEEE Access, 2020, 8, 15459- 15471. doi: 10.1109/ACCESS.2020.2965579
24	JIA Z R, LU F X, WANG H Y Multi-stage attack weapon target allocation method based on defense area analysis. Journal of Systems Engineering and Electronics, 2020, 31 (3): 539- 550. doi: 10.23919/JSEE.2020.000033

Control parameter	Value
Beetle size	50
Maximum cycle number	1 000
[ ${v_{\max }}$ , ${v_{\min }}$ ]	[0.9,0.4]
Constant	[0, 1]

$[{\lambda _1},{\lambda _2},{\lambda _3}]$	Traditional approach		Proposed approach
$[{\lambda _1},{\lambda _2},{\lambda _3}]$	Objective	Solution	Objective	Solution
[0.8,0.1,0.1]	[2.805 4	[0.429 5	[2.683 9	[0.450 1
	6.587 1	2.878 5	6.786 3	2.978 5
	?2.127 6]	3.451 3]	?2.983 1]	3.551 3]
[0.1,0.8,0.1]	[3.997 3	[0.409 7	[3.782 4	[0.389 5
	6.365 4	2.121 3	6.145 8	2.125 8
	?2.247 8]	3.567 1]	?2.895 6]	3.256 9]
[0.3,0.4,0.3]	[3.697 1	[0.420 5	[3.012 4	[0.412 5
	7.092 3	2.356 8	6.458 7	2.235 8
	?2.651 8]	3.167 3]	?3.081 5]	3.895 4]
[0.1,0.1,0.8]	[3.652 3	[0.372 9	[3.789 5	[0.356 9
	7.895 4	2.453 1	7.095 4	2.012 5
	?5.298 3]	3.347 1]	?5.598 3]	3.189 3]

Objective function	Traditional approach	Proposed approach
${f_1}(x,{\eta _1},{\tau _1})$	2.895 1	2.758 3
${f_2}(x,{\eta _2},{\tau _2})$	6.472 2	6.315 6
${f_{\rm{3}}}(x,{\eta _{\rm{3}}},{\tau _{\rm{3}}})$	?3.128 4	?2.943 3
Optimal solution	(0.375 3,2.328 5,3.114 3)	(0.367 4,2.538 1,3.315 4)

Target	TC_ESD-Weapon	C_ESD-Weapon	C_E-Weapon
1	1,1	5	1,2
2	2,3	5	3
3	5	4	4
4	5	4	3
5	4	1,2	4
6	3	3	5
f₁	0.861 7	0.894 6	0.880 2
f₂	5.191 2	4.790 9	4.776 7

Target	TC_ESD-Weapon	C_ESD-Weapon	C_E-Weapon
1	5	4	4
2	3	4	4
3	5	3	5
4	1,1	5	3
5	2	3	1,2
6	3	1,2	1,2
f₁	0.853 1	0.887 2	0.889 1
f₂	4.663 2	4.718 6	4.719 8

New approach for uncertain random multi-objective programming problems based on C_ESD criterion

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